tag:blogger.com,1999:blog-35965504356829439262024-03-18T15:18:47.245-07:00Hop's BlogHop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.comBlogger79125tag:blogger.com,1999:blog-3596550435682943926.post-86042577086543729232023-06-15T15:58:00.017-07:002023-07-02T07:48:19.510-07:00Orbital Tethers as Momentum Capacitors<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#Capacitors">Orbital tethers as momentum capacitors</a></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#Musk">Carmack to Musk: What about rotovators?</a></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#Doom">Carmack's game set on Phobos</a></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#ZRVTO">Zero Relative Velocity Transfer Orbit (ZRVTO) between Phobos and Deimos tethers</a></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#Savings">ZRVTO mass savings</a></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#Equations">ZRVTO equations</a></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#Sats">End of life sats to use as a momentum bank anchors</a></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#Propellant">Propellant mass as cost driver</a></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#Re-Entry">Re-entry propellent imported by tethers</a></div>
<div id="Capacitor"></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#Heteroclinic">The Heteroclinic Zone</a></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#EDL">Phobos help with Mars EDL</a></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#Well">Park trans-planetary vehicles at the edge of gravity wells</a></div>
<div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1icYmLc0EzDzK6THDc-4ENhEx7FUKN5U6o7HGXWxLGeF4pcSvILO1JZ_HM-S7pCwbWRW83CmlZ0jVOyp51QPDPZoGiDEfrH2nM4HENTkixlLigNMxzAvcl1RCeqNi5Hicsr7dn50Zf_LynGmEx5sdd87QDoKFY7hKpFEmYJjjiL7-zJEjdOM50ONYog/s2340/MightyCapacitor.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1080" data-original-width="2340" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1icYmLc0EzDzK6THDc-4ENhEx7FUKN5U6o7HGXWxLGeF4pcSvILO1JZ_HM-S7pCwbWRW83CmlZ0jVOyp51QPDPZoGiDEfrH2nM4HENTkixlLigNMxzAvcl1RCeqNi5Hicsr7dn50Zf_LynGmEx5sdd87QDoKFY7hKpFEmYJjjiL7-zJEjdOM50ONYog/w640-h296/MightyCapacitor.jpg" width="640" /></a></div>
<p>Some years ago I was knocked off my chair when I was soldering a flash for our camera. The flash was powered by two AA batteries. How could such a dinky power source pack such a wallop?</p><p>It was because of the flash's capacitors. A capacitor will build up a charge over time and then release the accumulated charge suddenly. In this case the flash would deliver a very bright and brief flash of light when the camera shutter was open.</p>
<p><b><span style="font-size: large;">The orbital tether as a capacitor for momentum.</span></b></p><p>An ion engine can have an exhaust velocity of ~30 kilometers per second. That is nearly eight times that of the best chemical exhaust, around 4 kilometers per second. That means a much smaller exponent in the rocket equation. When we're taking exponents, scaling by 1/8 can make a huge difference in delta v delivered per kilogram of propellent.</p><p>The problem is the ion engine's dinky thrust. A chemical rocket can slam you back in your seat with 4 or 5 g's. But an ion engine's delicate push is barely perceptible, like the push of a feather. It takes a long time to build up delta V which makes it difficult to enjoy an Oberth benefit. It can also mean a trip lasting months for a trip that would take hours via a chemical rock</p><p>But a tether with an ion engine can take months or weeks between catches or throws to build up momentum. So while it takes a long to build up momentum, it can release or impart it suddenly with a Catch or a throw.</p><p>So a tether can impart a brief and powerful change in momentum even with the ion rocket's barely perceptible thrust. It is like a capacitor but for momentum instead of electricity.</p>
<p><b><span style="font-size: large;">More tether stuff</span></b></p><p>It's been a long time since I did a post on tethers. So I'm going to toss in some other random bits that have accumulated in my head over the years.</p>
<div id="Musk"></div>
<p><b><span style="font-size: large;">Musk and Carmack on orbital tethers.</span></b></p>
<p>Back in 2016, shortly after SpaceX had landed a booster on an earth platform, <a href="https://twitter.com/ID_AA_Carmack/status/757551370702434306?lang=en" target="_blank">John Carmack tweeted</a>:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLhZ_xv1WccGgrGLE_0ZOk0rGzHrhfB1VCe9Wp3sysSQMZ3lG81MtqQExNYqDeY_WjDrPn6Mi75gDGP_CGpDxFb4JvtyVjMePtRFJk3lLIn77HxbVaaRNHFRA670tmPOuknwGtB0GlOEJJyTAsK580xHVQ1HU-dtHzdsrg89lbpeOPyBvfaO0We9T4XA/s1178/Screenshot%202023-05-13%20at%209.33.20%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="432" data-original-width="1178" height="234" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLhZ_xv1WccGgrGLE_0ZOk0rGzHrhfB1VCe9Wp3sysSQMZ3lG81MtqQExNYqDeY_WjDrPn6Mi75gDGP_CGpDxFb4JvtyVjMePtRFJk3lLIn77HxbVaaRNHFRA670tmPOuknwGtB0GlOEJJyTAsK580xHVQ1HU-dtHzdsrg89lbpeOPyBvfaO0We9T4XA/w640-h234/Screenshot%202023-05-13%20at%209.33.20%20AM.png" width="640" /></a></div><br /><p><a href="https://twitter.com/elonmusk/status/757600711714701312" target="_blank">Elon replied</a>:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgskwF3as5QXgv_hrdYF86UnHqZ8gpDmbka-Rq1uOgaADtvgB4nRp_-9B29amo_po4yp_y5VsEsXhtvDYzNqBx7G33o2pOsMeyzOfSJqpWz4qZjBVXmLTaijYLKudRcI86XvvS5N6GFV6nt2AjCNrkVWKtH4cJdHQ2CH6kkyXaKMCJ3T5npjQvzvklJmA/s1182/Screenshot%202023-05-13%20at%2010.40.08%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="424" data-original-width="1182" height="230" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgskwF3as5QXgv_hrdYF86UnHqZ8gpDmbka-Rq1uOgaADtvgB4nRp_-9B29amo_po4yp_y5VsEsXhtvDYzNqBx7G33o2pOsMeyzOfSJqpWz4qZjBVXmLTaijYLKudRcI86XvvS5N6GFV6nt2AjCNrkVWKtH4cJdHQ2CH6kkyXaKMCJ3T5npjQvzvklJmA/w640-h230/Screenshot%202023-05-13%20at%2010.40.08%20AM.png" width="640" /></a></div><br /><p>I was delighted to see this exchange. I've been hanging around spaceflight forums since the 90s and Carmack has long been a big name in new space. Carmack and Armadillo Aerospace were <a href="https://en.wikipedia.org/wiki/X_Prize_Foundation#2006–2009_Northrop_Grumman_Lunar_Lander_XCHALLENGE" target="_blank">X-Prize winners in 2006</a>. I don't think I need to review what Musk has been doing.</p>
<div id="Doom"></div>
<p><b><span style="font-size: large;">Carmack, Fear and Dread</span></b></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2RHcQPt5vQkAwONKPJ19W5q3UC5q5g1gl504rrpqDcKblrFvNZPQpZnpNwExPa8qzCUqxePPzMUzRhIgvZ7Pvp4aMA8qPS17rTT3nPjZk0uWUWz_jacltk0eYuroRimkV25IcKRsyPxwwkj2t5cimRPnKck0PIogQkEOKNJV9JfyGjjFwG-1K6mZjrw/s3246/Screenshot%202023-06-15%20at%2010.19.08%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2228" data-original-width="3246" height="440" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2RHcQPt5vQkAwONKPJ19W5q3UC5q5g1gl504rrpqDcKblrFvNZPQpZnpNwExPa8qzCUqxePPzMUzRhIgvZ7Pvp4aMA8qPS17rTT3nPjZk0uWUWz_jacltk0eYuroRimkV25IcKRsyPxwwkj2t5cimRPnKck0PIogQkEOKNJV9JfyGjjFwG-1K6mZjrw/w640-h440/Screenshot%202023-06-15%20at%2010.19.08%20AM.png" width="640" /></a></div><br /><p>Carmack and <a href="https://en.wikipedia.org/wiki/Id_Software" target="_blank">ID software</a> made a very successful computer game set on the Martian moon Phobos. The names of the Martian moons (Phobos and Deimos) means Fear and Dread. Which is very appropriate for the computer game <a href="https://en.wikipedia.org/wiki/Doom_(1993_video_game)" target="_blank">Doom</a>.</p><p>I love the idea of using the Martian moons as settings for science fiction stories. I believe they will be great assets in humanity's effort to settle the solar system. I've done a number of blog posts on Phobos and Deimos:</p><p><a href="https://hopsblog-hop.blogspot.com/2015/06/phobos-panama-canal-of-inner-solar.html" target="_blank">Phobos, Panama Canal of the Inner Solar System.</a></p><p><a href="http://hopsblog-hop.blogspot.com/2016/01/upper-phobos-tether.html" target="_blank">Upper Phobos Tether</a></p><p><a href="https://hopsblog-hop.blogspot.com/2015/12/lower-phobos-tether.html">Lower Phobos Tether</a></p><p><a href="http://hopsblog-hop.blogspot.com/2016/01/deimos-tether.html" target="_blank">Deimos Tether.</a></p><p>But if I'm trying to sell Phobos and Deimos maybe I shouldn't be mentioning Doom. Oh well.</p>
<div id="ZRVTO"></div>
<p><b><span style="font-size: large;">ZRVTO between Phobos and Deimos</span></b></p><p>Thinking about elevators anchored on Phobos and Deimos it occurred to me there would be a Zero Relative Velocity Transfer Orbit (ZRVTO) between the moons' tethers.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0yoUXo2cL6Ia9s0fdZmHlNpZE3xZJUzGMKfbgixklnEfXk1PFib0vemqkWkunj7ApD178auT7AKyKh1HQB1A46O44_R_9Vg09gbbCNmqBmMxN9--EfSvsytp-aVIAFt4wkXdbg2jeg30waskQTZHFR8mvMRBrbr8IO0_GyP4Z-wiMGE9wJzFgNPulOQ/s1703/PhobosToDeimos.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1703" data-original-width="1385" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0yoUXo2cL6Ia9s0fdZmHlNpZE3xZJUzGMKfbgixklnEfXk1PFib0vemqkWkunj7ApD178auT7AKyKh1HQB1A46O44_R_9Vg09gbbCNmqBmMxN9--EfSvsytp-aVIAFt4wkXdbg2jeg30waskQTZHFR8mvMRBrbr8IO0_GyP4Z-wiMGE9wJzFgNPulOQ/w520-h640/PhobosToDeimos.jpg" width="520" /></a></div><br /><p>The transfer orbit's velocity at periapsis matches the speed of Phobos' tether top. Velocity at apoapsis matches the foot of the Deimos tether. Thus passengers and cargo could be exchanged between the moons using very little propellent.</p><p>I hope this idea will eventually be used.</p>
<div id="Savings"></div>
<p><b><span style="font-size: large;">ZRVTOs in other settings</span></b></p><p>There can be ZRVTOs in other settings. The tether anchor masses need to be tide locked in circular, coplanar orbits. Which describes a lot of the moons of Jupiter, Saturn, Uranus and Neptune. I look at this in <a href="https://hopsblog-hop.blogspot.com/2013/01/mini-solar-systems.html" target="_blank">Mini Solar Systems</a>.</p><p>In <a href="https://hopsblog-hop.blogspot.com/2016/08/tran-cislunar-railroad.html" target="_blank">Trans Cislunar Railroad</a> I look at ZRVTOs between possible tethers in earth orbit:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaHc8NuNortWx_okfm3P2FTYkz5rmmwcY0wy15LAUs-NxHBFxINleUv_FLbwMaevRp6JvWAf7GjbhonAnlUQ1K4dVoAxGJkyNCa7jpIPGqvVNjd4tENub04FQuo6WPy2bmXgtnyuygdRaPIvPyItgc7Algo7zai-43VHoBGTK8o5qKGwwudfvOCY3CcQ/s1150/Screen%20Shot%202015-05-27%20at%205.23.23%20PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1150" data-original-width="1057" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaHc8NuNortWx_okfm3P2FTYkz5rmmwcY0wy15LAUs-NxHBFxINleUv_FLbwMaevRp6JvWAf7GjbhonAnlUQ1K4dVoAxGJkyNCa7jpIPGqvVNjd4tENub04FQuo6WPy2bmXgtnyuygdRaPIvPyItgc7Algo7zai-43VHoBGTK8o5qKGwwudfvOCY3CcQ/w588-h640/Screen%20Shot%202015-05-27%20at%205.23.23%20PM.png" width="588" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div>In some ways tether mass is like propellent mass in the rocket equation — tether mass goes up exponentially with increasing delta V.<div><br /></div><div>But tossing payloads between tethers breaks the the delta V budget into chunks. And thus greatly reduces the needed tether mass.</div><div><br /></div><div><b><span style="font-size: large;">How much mass is saved with with ZRVTOs?</span></b></div><div><br /></div><div>The above system tosses payloads up to the moon. For kicks I decided to see what would happen if I made a single LEO tether long enough to throw payloads to the moon.</div><div><br /></div><div>I placed an anchor mass 1000 kilometers above earth's surface and tweaked tether length until the apoapsis of a flung payload was a lunar distance (384,400 km).</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHB8RuYTsvvGI6ybuPIYM8erdR7gdvpKZ-F2ABoNtDylISXh0m0aFqMJWWuUCMK_DcqzKUcQCGvlEpLCJ3GtG-Q3fiisTWwpFTr9QXMTLzOaK_gX6TF7xgH30WuVZp2BpNT-A9_8lM8MtNvwAWOIjYLnE-Lkq6usbDb_o9EHpQZ313qdJOL60BKMiNNA/s1292/Screenshot%202023-06-15%20at%2012.09.13%20PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1004" data-original-width="1292" height="498" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHB8RuYTsvvGI6ybuPIYM8erdR7gdvpKZ-F2ABoNtDylISXh0m0aFqMJWWuUCMK_DcqzKUcQCGvlEpLCJ3GtG-Q3fiisTWwpFTr9QXMTLzOaK_gX6TF7xgH30WuVZp2BpNT-A9_8lM8MtNvwAWOIjYLnE-Lkq6usbDb_o9EHpQZ313qdJOL60BKMiNNA/w640-h498/Screenshot%202023-06-15%20at%2012.09.13%20PM.png" width="640" /></a></div><br /><div>Taper ratio about 35. The tether would need to be about 106 times as massive of the payload it throws given a safety factor of three. It would need to about 1,842 kilometers long.</div><div><br /></div><div>Let's compare that to my system of tethers in the <a href="http://hopsblog-hop.blogspot.com/2016/08/tran-cislunar-railroad.html" target="_blank">Tran Cislunar Railroad</a>:</div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjddRlow4sTp0ILpJ5pXsNkxrQYy1hq6-TEoEvpTuTEtu2H6mQ4W3EcDFqC4uiUQI4ShrgGtnyG_GUkJ2Zt-Ir2pgmVP6LF5Vg5pXXJdGJ9C80LSdRVC1PQbi5CmBYRPHxgyQy8EKsR1aPaNNx-_dPnCQXNh6JeYLUPf_baEZ9XRwlTuOP4HUuLXS86kA/s1054/Screenshot%202023-06-15%20at%2012.28.52%20PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="1054" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjddRlow4sTp0ILpJ5pXsNkxrQYy1hq6-TEoEvpTuTEtu2H6mQ4W3EcDFqC4uiUQI4ShrgGtnyG_GUkJ2Zt-Ir2pgmVP6LF5Vg5pXXJdGJ9C80LSdRVC1PQbi5CmBYRPHxgyQy8EKsR1aPaNNx-_dPnCQXNh6JeYLUPf_baEZ9XRwlTuOP4HUuLXS86kA/w640-h364/Screenshot%202023-06-15%20at%2012.28.52%20PM.png" width="640" /></a></div><br />So my system of tethers is actually about 5,000 kilometers longer than LEO tether capable of slinging payloads to the moon. That's a little disappointing. But tether to payload mass is less than 4.</div><div><br /></div><div><i><b><span style="color: red;">So there is more than a 25 fold savings in tether mass</span>.</b></i> That is gratifying.</div><div><br /></div>
<div id="Sats"></div>
<div><b><span style="font-size: large;">"Would only matter if it was extremely big"</span></b></div><div><br /></div><div>Recall Musk's reply to Carmack was "Would only matter if it was extremely big".</div><div><br /></div><div>The tether anchor would need to be a lot more massive than the payloads it handles. Or else the act of catching or throwing a payload would destroy the tether's orbit.</div><div><br /></div><div>That's not an issue for tethers anchored on planetary moons. But it seems like a show stopper for tethers in earth orbits. Or maybe not....</div><div><br /></div><div><b>Big Balls of Dead Sats</b></div><div><br /></div><div>There is a lot of dead sats that could be harvested for a momentum bank. As of 2015 it was <a href="https://space.stackexchange.com/questions/9185/how-many-dead-sats-near-geo/9705#9705" target="_blank">estimated that there were 670 tonnes of dead sats in the graveyard orbit just above geosynchronous orbit.</a> </div><div><br /></div><div>Gathering these into a single anchor mass would vastly reduce their surface area and those lessen the likelihood of impacts generating orbital debris.</div><div><br /></div><div>Many of them still have solar panels that can provide electricity. There are high gain antenna dishes. Some of the harvested momentum mass might even be useful.</div><div><br /></div><div><b>What about LEO?</b></div><div><br /></div><div>In 2016 I was wondering how we could provide a massive anchor for a LEO tether. But since then Elon Musk and SpaceX have been launching StarLink, a huge constellation of communication satellites.</div><div><br /></div><div>I expect at the present time the plan is send an aging StarLink satellite down to the upper atmosphere and let it become a shooting star. But couldn't satellites in similar orbits be gathered together to form a momentum bank? If so, Musk has already made huge deposits into an LEO momentum bank.</div><div><br /></div><div>And the StarLink satellites have a lot of solar panels as well as ion engines that could be salvaged.</div><div><br /></div>
<div id="Equations"></div>
<div><b><span style="font-size: large;">Some ZRVTO equations</span></b></div><div><br /></div><div>Some equations to figure lengths of tethers that accomodate Zero Relative Velocity Transfer Orbits. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0EYMD9aiCDGvQKWASeUPnw4ewtJFxK5E-BZuPyP6xnC7p4afNV-i7vsn4lZa6AYkD2V_TNxN2z5r3wg1zFFnRGiL3VaOXwI2e-0WZEO0EXsrbsi_3qZOfv7WlD1sRetaJSZvr2nAyWou9fE3fA81h-2-IcuYr945A-5adzPVlT4j1JUm9FqgcNxMqFw/s948/Screenshot%202023-06-17%20at%2011.59.32%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="948" data-original-width="872" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0EYMD9aiCDGvQKWASeUPnw4ewtJFxK5E-BZuPyP6xnC7p4afNV-i7vsn4lZa6AYkD2V_TNxN2z5r3wg1zFFnRGiL3VaOXwI2e-0WZEO0EXsrbsi_3qZOfv7WlD1sRetaJSZvr2nAyWou9fE3fA81h-2-IcuYr945A-5adzPVlT4j1JUm9FqgcNxMqFw/w588-h640/Screenshot%202023-06-17%20at%2011.59.32%20AM.png" width="588" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>Lower tether length would be L1((1+e)^(1/3) - 1).<div>Upper tether length would be L2(1 - (1-e)^(1/3))</div><div><br /></div><div><b><span style="font-size: large;">Momentum Exchange</span></b></div><div><br /></div><div>At the outset of this post I mentioned tethers could impart momentum gradually built up by ion engines whose exhaust velocity is a lot higher than chemical rockets.</div><div><br /></div><div>If there is downward traffic as well as upward that could greatly reduce the argon or xenon propellant used by the ion engines.</div><div><b>Momentum boosting maneuvers</b></div><div>Catching payloads from above or dropping them into lower orbits</div><div><b>Momentum depleted maneuvers</b></div><div>Catching payload from below or tossing them into higher orbits</div><div><br /></div><div>These could be balanced to achieve most of delta v needed, in my opinion.</div><div><br /></div>
<div id="Propellant"></div>
<div><b><span style="font-size: large;">Propellent Mass as cost driver?</span></b></div><div><br /></div><div>Reducing propellant mass should be a top priority. In even the best circumstances Gross Lift Off Weight (GLOW) from earth's surface will be dominated by propellant.</div><div><br /></div><div>Charlie Stross was indignant when<a href="http://hopsblog-hop.blogspot.com/2018/06/space-meow-boys_30.html" target="_blank"> I was ridiculing space naysayers</a>. He said he wouldn't dignify my criticisms with a public response. But then proceeded to make several thoughtful public responses. <a href="https://james-davis-nicoll.dreamwidth.org/12153580.html?thread=115898092#cmt115898092" target="_blank">Link</a>. I quote:</div><div><br /></div><div></div><blockquote><div>"My cost estimate was for near-future transport to LEO.</div><div><br /></div><div>"Contemporary civil airlines' operating costs are on the order of triple the cost of fuel. (Equal shares: fuel, airframe depreciation and maintenance, and crew/ground support costs.)</div><div><br /></div><div>"If you want to do it for less than triple the fuel cost, you need to beat the standards of a viciously competitive industry that's been trying to pare costs for around a century.</div><div><br /></div><div>"SpaceX currently cite the cost of fuel for a Falcon 9 as ~$200,000. So my BOTE would get us to $600,000 for a ~20 ton payload. I gather they're currently quoting about $60M, so there' someroom for improvement."</div></blockquote><div></div><div>That's from a comment Charlie made in 2018. And I would agree that spaceflight dominated by propellent cost is optimistic. You would also need very durable, reusable rockets that don't require a great deal of maintenance.</div><div><br /></div>
<div id="Re-Entry"></div>
<div><b><span style="font-size: large;">What could we import from above?</span></b></div><div><br /></div><div>For a momentum exchange tether to work you need two way traffic. So what mass from above could provide up momentum?</div><div><br /></div><div>Lunar propellent might be the first import from above. In 2010 India's lunar orbiter Chandrayaan 1 found evidence of massive ice deposits on the lunar poles <a href="https://timesofindia.indiatimes.com/india/chandrayaan-finds-ice-on-moon/articleshow/5635005.cms" target="_blank">Link</a>. The late lunar geologist Paul Spudis would argue an off earth source of propellent could confer a commercial and military advantage to the power that controls it <a href="https://phys.org/news/2011-10-paul-spudis-sustainable-lunar-base.html">Link</a>. Former NASA administrator Jim Bridenstine also made the same argument <a href="http://hopsblog-hop.blogspot.com/2019/04/bridenstines-why-moon-matters.html" target="_blank">Link</a>. </div><div><br /></div><div>Jon Goff <a href="https://selenianboondocks.com/2013/12/the-slings-and-arrows-of-outrageous-lunar-transportation-schemes-part-1-gear-ratios/" target="_blank">voiced some objections</a> to lunar propellent. Given the delta V between the lunar surface and and earth orbits, only a small fraction of lunar propellent would arrive to supply propellent depots in earth orbits. If propellent were delivered by conventional rockets. </div><div><br /></div><div>However more would arrive if lunar propellent were delivered via momentum exchange tethers. And they would provide up momentum for the momentum exchange tethers and reduce the need for propellent mass. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCKla5AApsCvpypoWZjIoMh9dFlVSJM-YkvyoAQWdUcbbag-E97yJseTWRlc-LbvgB0OFus5Uoo6BvFnFs-XVU7sv7lOGfPRxtkMtl7l02qaTonYe-Sr7qjJ-Mnxfi64RhkiC-ifewvsmB-UCxxO9Xf8cx-NVw45RV8eWkkTdQO2TJ_dbTAAJgglECsECl/s482/starship-tiles.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="409" data-original-width="482" height="544" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCKla5AApsCvpypoWZjIoMh9dFlVSJM-YkvyoAQWdUcbbag-E97yJseTWRlc-LbvgB0OFus5Uoo6BvFnFs-XVU7sv7lOGfPRxtkMtl7l02qaTonYe-Sr7qjJ-Mnxfi64RhkiC-ifewvsmB-UCxxO9Xf8cx-NVw45RV8eWkkTdQO2TJ_dbTAAJgglECsECl/w640-h544/starship-tiles.jpg" width="640" /></a></div><br /><div style="text-align: center;">A photo of Starship thermal tiles from</div><div style="text-align: center;"><a href="https://zapatatalksnasa.com/2022/06/09/about-starships-and-the-not-what-you-think-reusability-we-need/" target="_blank">About Starships, and the (not what you think) reusability we need</a>.</div><div><br /></div><div>The Starship upper stages will likely re-enter at a much higher velocity than the booster stages. 35 kilo pascals is typical max Q for ascent. But for for descent 90 kilo pascals is common. Will Starship be able to economically refurbish after re-entry? Unlike the Space Shuttle Starship has a stainless steel hull. It looks like the thermal tiles are mechanically attached rather than glued on.</div><div><br /></div><div>SpaceX likely has improved on thermal protection since the Space Shuttle Days. But I still expect re-uses after an 8 km/re-entry to be difficult.</div><div><br /></div><div>If the upper stage could refuel in Low Earth Orbit (LEO), the upper stage could re-enter with an even lower velocity than the booster stage. Re-use would be far less difficult. Re-usability may even become so advanced that cost of transportation would be triple the fuel costs, as Charlie Stross imagines in his best case scenario.</div><div><br /></div>
<div><b><span style="font-size: large;"><div ID="Heteroclinic">The Heteroclinic Zone</div></span></b></div><div><br /></div><div>There are a family of loosely bound lunar orbits where a little delta V and use of earth's tidal influence can make a big change to the orbit. It's possible to move from Earth Moon Lagrange 2 (EML2) to Earth Moon Lagrange 1 (EML1) with only a tiny burn. These low delta V routes between lunar orbits are called heteroclinic paths. They talk about these paths in chapter 3 of <a href="http://www.cds.caltech.edu/~marsden/volume/missiondesign/KoLoMaRo_DMissionBook_2011-04-25.pdf" target="_blank">Dynamical Systems, the Three-Body Problem and Space Mission Design</a> by Koon, Lo, Marsden and Ross.</div><div><br /></div><div>EML1 is around .3 km/s from the top tether I mentioned in <a href="https://hopsblog-hop.blogspot.com/2023/06/orbital-tethers-as-momentum-capacitors.html#ZRVTO" target="_blank">ZRVTOs in Other Settings</a> earlier in this post.</div><div><br /></div><div>From EML it's easy to reach EML2</div><div><br /></div><div>EML2 is only .9 km/s from Trans Mars Insertion using <a href="https://hopsblog-hop.blogspot.com/2015/05/eml2.html#Farquhar" target="_blank">the Farquhar route</a>.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtq2NO_cLyj4gzchudBbR6VMz4J8kFWgyn0ZK8Yco3ow3o2dLrAcFgTgsvjjNiJsQudbTdt89b6NbOwpgi2Gn3PJ4olHH2SmNdoyL-IVltpFkTvdsvtltKLz_6qy7mgheRYFJmzpp5cUOTyyUpGV25ejTJsDvKLJByzK_YgWLPDkU2VjkSGKfVEI7ie39y/s2521/DeltaVEarthMoonMarsAsteroid.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2521" data-original-width="1247" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtq2NO_cLyj4gzchudBbR6VMz4J8kFWgyn0ZK8Yco3ow3o2dLrAcFgTgsvjjNiJsQudbTdt89b6NbOwpgi2Gn3PJ4olHH2SmNdoyL-IVltpFkTvdsvtltKLz_6qy7mgheRYFJmzpp5cUOTyyUpGV25ejTJsDvKLJByzK_YgWLPDkU2VjkSGKfVEI7ie39y/w316-h640/DeltaVEarthMoonMarsAsteroid.jpg" width="316" /></a></div><br /><div>I am a little obsessed with EML2. I have <a href="http://hopsblog-hop.blogspot.com/2015/05/eml2.html" target="_blank">a post devoted to this Lagrange point</a>.</div><div><br /></div><div><b>NHROs</b></div><div><br /></div><div>Included in The Heteroclinic Zone are Nearly Rectilinear Halo Orbits NHRO. I like these orbits for a number of reasons.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8fmR0OFIyzlV2xaIUSwbO6COeIs2rn4VQPNpc_rvBdmOksFIM97-2n7jB5lCvztMIlI132Cods0js2RkELNO9O_u_PrShoPwqUiYI8TPgz3aqoJDOUJbk1v6hTccSn65ErgjMJHvfOFxpQQEyrwCv7YeqVyefBMBLvuQR3GKuRY1ZeA6clkySqMSqOobh/s1384/Screenshot%202023-07-02%20at%206.44.50%20AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1258" data-original-width="1384" height="582" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8fmR0OFIyzlV2xaIUSwbO6COeIs2rn4VQPNpc_rvBdmOksFIM97-2n7jB5lCvztMIlI132Cods0js2RkELNO9O_u_PrShoPwqUiYI8TPgz3aqoJDOUJbk1v6hTccSn65ErgjMJHvfOFxpQQEyrwCv7YeqVyefBMBLvuQR3GKuRY1ZeA6clkySqMSqOobh/w640-h582/Screenshot%202023-07-02%20at%206.44.50%20AM.png" width="640" /></a></div><br /><div>The perilune of these orbits are near the lunar poles. The lunar poles and cold traps are where I daydream of lunar propellent mines. So orbital insertion from the propellent mines to <i>The Heteroclinic Zone</i> is quite doable. </div><div><br /></div><div>I like to imagine advanced propellent mines with a rail guns that launch propellent into NHROs. </div><div><br /></div><div>A distant apolune is at the other end of an NRHO. It travels slowly in this region giving it lots of hang time over the lunar poles. It can give long periods line of sight periods to the lunar cold traps. In some ways this is like an earthly <a href="https://en.wikipedia.org/wiki/Molniya_orbit" target="_blank">Molniya orbit</a>. This would be useful in the early stages of a propellent mine when construction is being done by remotely controlled robots.</div><div><br /></div>
<div><b><span style="font-size: large;"><div id="EDL">Phobos lending a hand with Mars EDL</div></span></b></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaamLOvShpHvUqSeJLq6qtn0PJDMEMIDK189ba1FalYy60kIkP88NimVs6KyDbeTIv7mDrZslmKgmznLwgl-ZNxpU8_fHD_E6GViTAPwyFuF98rj41M04_W6QSNuC-XoAYFXTJ4kUt8PYMQ_smiIPrTVAWJCfIh5L5QG1jaokfZjm5aBjXks1jQeA4iO-C/s1807/TetherPhobos.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1643" data-original-width="1807" height="582" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaamLOvShpHvUqSeJLq6qtn0PJDMEMIDK189ba1FalYy60kIkP88NimVs6KyDbeTIv7mDrZslmKgmznLwgl-ZNxpU8_fHD_E6GViTAPwyFuF98rj41M04_W6QSNuC-XoAYFXTJ4kUt8PYMQ_smiIPrTVAWJCfIh5L5QG1jaokfZjm5aBjXks1jQeA4iO-C/w640-h582/TetherPhobos.jpg" width="640" /></a></div><br /><div>A 1340 kilometer tether from Phobos could drop payloads into periaerion skimming Mars atmosphere. The payload would enter Mars atmosphere at about 3.6 km/s. Entry from an Earth to Mars Hohmann would be about 5.5 km/s. (3.6/5.5)^2 = ~.43. So less than half the kinetic energy to be shed.</div><div><br /></div><div>And it may be doable to mine oxygen from Phobos minerals so propellent could also lend a hand in shedding velocity.</div><div><br /></div><div>A 5680 km/s tether from Phobos would allow entry to Mars atmosphere about about .6 km/s However a Phobos tether going deep in Mars' gravity well is more difficult. Given Zylon and a safety factor of 3, taper ratio would be 84 and tether to payload mass ratio would be 640. See my <a href="http://hopsblog-hop.blogspot.com/2015/12/lower-phobos-tether.html" target="_blank">lower Phobos Tether post</a>.</div><div><br /></div>
<div><b><span style="font-size: large;"><div id="Well">Park Trans Planetary Vehicles at the edge of gravity wells</div></span></b>.</div><div><br /></div><div>Vehicles that can keep humans alive for months must be massive. Vehicles for shorter trips can be much smaller.</div><div><br /></div><div>What is the point of launching a trans Mars vehicle from earth's surface and landing it on Mars' surface? It would be like using a huge Mac truck to deliver a pizza from a restaurant to a customer's front porch.</div><div><br /></div><div>Far better, in my opinion, to park trans planetary vehicles at EML2 or Phobos. Then there is no need for a thermal protection system to endure re-entry. And there is no need for the ship to be 90% propellent to climb up steepest slopes of planetary gravity wells.</div><div><br /></div><div><br /></div><div><br /></div><div><br /></div>Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com3tag:blogger.com,1999:blog-3596550435682943926.post-43260098268387556222021-05-29T12:09:00.002-07:002023-06-12T11:25:29.147-07:00The wrong question. Who invented calculus, Newton or Leibniz?<p>Science historian <a href="https://thonyc.wordpress.com" target="_blank">Thony Christie</a> (also known as <a href="https://twitter.com/rmathematicus" target="_blank">@rmathematicus</a>) had a number of essays on the Scientopia website. Scientopia bit the dust and I thought the essays were lost. But <a href="https://twitter.com/BryanKeIIy" target="_blank">Bryan Kelly</a> showed me they still exist on the Wayback Machine.</p><p>This essay by Christie is one I often refer to. I copied and pasted it from the Wayback machine with Thony Christie's permission.</p><p>Edit June 12, 2023: Scientopia is back in business! <a href="https://guestblog.scientopia.org/2011/03/05/ich-bin-ein-gastblogger-ii-the-wrong-question/" target="_blank">Here</a> is the original essay. </p><header class="entry-header" style="box-sizing: inherit; caret-color: rgb(34, 34, 34); color: #222222; font-family: "Open Sans"; font-size: 14px; letter-spacing: 0.1px;"><h2 class="entry-title" itemprop="headline" style="box-sizing: inherit; color: #111111; font-family: Roboto; font-size: 41px; font-weight: 400; letter-spacing: 0.1px; line-height: 1.2; margin: 10px 0px;">Ich bin ein Gastblogger II: The wrong question.</h2></header><div class="entry-meta" style="box-sizing: inherit; caret-color: rgb(34, 34, 34); color: #222222; font-family: "Open Sans"; font-size: 14px; letter-spacing: 0.1px; margin: 20px 0px;"><span class="meta-cat" style="box-sizing: inherit;"><span class="fa fa-folder-o" style="-webkit-font-smoothing: antialiased; box-sizing: inherit; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; line-height: 1; text-rendering: auto;"></span> <a href="https://web.archive.org/web/20190522053433/https://guestblog.scientopia.org/category/uncategorized/" rel="category tag" style="box-sizing: inherit; color: #c3251d; text-decoration-skip: objects; text-decoration: none;">Uncategorized</a></span> <span class="meta-author" itemprop="name" style="box-sizing: inherit; display: inline-block; font-weight: 700; padding: 2px 4px;"><span class="fa fa-user-o" style="-webkit-font-smoothing: antialiased; box-sizing: inherit; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-weight: normal; line-height: 1; text-rendering: auto;"></span> <a href="https://web.archive.org/web/20190522053433/https://guestblog.scientopia.org/author/thony/" rel="author" style="box-sizing: inherit; color: #c3251d; text-decoration-skip: objects; text-decoration: none;" title="Posts by thony">thony</a></span> <span class="meta-date" itemprop="datePublished" pubdate="" style="box-sizing: inherit; display: inline-block; padding: 2px 4px;"><span class="fa fa-clock-o" style="-webkit-font-smoothing: antialiased; box-sizing: inherit; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; line-height: 1; text-rendering: auto;"></span> March 5, 2011</span></div><div class="entry-content" itemprop="text" style="box-sizing: inherit; caret-color: rgb(34, 34, 34); color: #222222; font-family: Verdana, Geneva, sans-serif; font-size: 15px; letter-spacing: 0.1px; line-height: 1.5; margin-bottom: 20px; margin-top: 9px;"><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">I’m an alien</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">I’m a legal alien</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">I’m an Englishman in Nürnberg<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">1</span></p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">Being an English historian of mathematics resident in Germany I have been often asked, over the years, by people who know a little about the history of mathematics, “Who invented the calculus, Newton or Leibniz?” This is probably the most famous argument about priority of discovery and possible plagiarism in the history of science and still able to provoke nationalist sensibilities 300 years after the fact. Now as I mentioned in my first post this was the first theme in the history of mathematics that caught my attention and over the years I have devoted a considerable amount of time and effort to investigating the subject. There are two possible answers to the question. The short semi-correct answer is, both of them. The much longer and much more correct answer is nobody, calculus wasn’t invented by a single person but evolved piece by piece over more than two thousand years. What follows is not a history of calculus but a very bare and incomplete skeleton naming some of the important stations between the first appearance of concepts considered central to the calculus and the work of Newton and Leibniz.</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">The fundamental idea behind the infinitesimal integral calculus is first recorded in the so-called method of exhaustion of the Greek mathematician Eudoxus of Cnidus who flourished at the beginning of the fourth century BCE and is used for a handful of proofs by Euclid in his Elements. Refined by possibly the greatest of all Greek mathematicians, Archimedes, it became a powerful tool for the determination of areas and volumes as well as centres of gravity and most famously for his, for the time, highly accurate determination of the value of P, the relation between the circumference and diameter of a circle. The Greeks were also nominally aware of the problem of determining tangents to given curves, the fundamental concept of the differential calculus, but it did not play a significant role in their mathematical considerations. No further progress was made in antiquity before the general decline in learning beginning in the 2<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">nd</span> century CE and it was first in the High Middle Ages that integration returned to European mathematics.</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">However earlier than that there were interesting developments in Kerala in West India. At its core calculus is about summing infinite converging series, diverging series can’t be summed, and in the 17<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century several important series representing important geometrical constants such as P and trigonometrical functions such as sine and cosine were analysed and discussed by European mathematicians and named after their supposed discoverers such as Gregory, Leibniz and Newton. The series had however already been discovered and analysed by the so-called Madhava or Kerala school of mathematics founded by Madhava who flourished in the second half of the 14<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century. The same mathematicians also made extensive use of the method of Archimedes to determine areas and volumes. Attempts have been made to prove the hypothesis that the further development of the calculus in the 17<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century was stimulated by Jesuit missionaries bringing knowledge of the work of the Kerala School to Europe, however despite extensive research no evidence of transition has been found up to now. In the Early Middle Ages Islamic mathematicians were also aware of and used Archimedean methods.</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">In the 14<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century the Oxford Calculatores proved the mean speed theorem, which is usually attributed to Galileo, and in the next century Oresme proved it graphically (drawing graphs two hundred years before Fermat and Descartes!) and integrating the area under the graph. In the 16<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century the works of Archimedes experienced a renaissance in Europe and many of the leading mathematicians devoted themselves to determining centres of gravity using his methods. The 17<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century sees an acceleration in the application of what would become the calculus. Kepler used integration to prove his second law of planetary motion, the areas law, basically summing segment of the ellipse and letting them become smaller and smaller until infinitesimal. However as he had no concept of limits even he was aware of the fact that he was claiming to be able to add areas after they had ceased to exist! This piece of highly dubious mathematics contributed to the fact that the second law was still rejected long after the first and third laws had been accepted. In fact the second law was only finally accepted in 1672 when Nicolas Mercator provided a new more reliable proof. Kepler also used a form of integral calculus in his small pamphlet on determining the volume of wine barrels, a work that is often mentioned in a mocking tone but is actually an important milestone in the history of the calculus. The developments now come thick and fast with Galileo, Cavalieri (a pupil of Galileo’s), Grégoire de Saint-Vincent (a Jesuit mathematician who first gave the method of exhaustion its name), the Frenchmen Roberval, Fermat, Pascal and Descartes, the Dutchman van Schooten and in Britain John Wallis, Isaac Barrow and James Gregory all making significant contributions. It was also in the 17<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century with the development of the science of mechanics that the differential calculus came to the fore with the problem of finding tangents to curves in order to determine rates of change. Many people in the list above made major contributions to the solution to this problem. Fermat is sometimes referred to as the “father of calculus” because he was the first mathematician to use what we now call the h-method (a method that I have to explain regularly to my private maths pupils) to determine first derivatives of functions. However like Kepler he has no real concept of a limit and just lets his ‘h’ (in his case its actually an ‘e’) disappear at the appropriate moment without explanation!</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">I hope I have said enough to make it clear that there was an awful lot of calculus around before Newton and Leibniz even considered the subject, so what did they do? It is often claimed that their major contribution was the discovery of the fundamental theorem of the calculus, i.e. that integration and differentiation are inverse operations but even this is not true. The theorem first appears in an implied form in the work of James Gregory and more explicitly in that of Isaac Barrow both of which are explicitly cited by both Leibniz and Newton in their own work. Newton and Leibniz collected up the strands scattered throughout the work of the mathematicians listed above and collating, sorting and standardising create a coherent body of work that we now call infinitesimal calculus but even their effort where actually only a milestone along the route. Finding sums of numerous infinite series and determining integrals and derivatives of many functions proved a very difficult process and many 18<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century mathematicians won their spurs by solving a particularly difficult problem in the now developing analysis, most notably Leonard Euler. However one central and absolutely fundamental problem still remained, neither Leibniz nor Newton had a limit concept and their rather cavalier attitude to elimination of infinitesimals led to Bishop George Berkeley’s famous and very justified retort about ghosts of departed quantities. This problem was not really solved until the German mathematician Karl Weierstraß came along in the 19<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century.</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">I have entitled my post “The wrong question” because I personally thing that in any area of science the question as to who discovered/invented a particular discipline, method, theory etc is almost always displaced. We shouldn’t be asking who invented the calculus Leibniz or Newton but rather what did Leibniz and Newton contribute to the on going evolution of that branch of mathematics that we now call the calculus? All branches of science (and I consider mathematics to be a science, see my last guest post here next week), all theories all discoveries have long evolutionary histories and individuals only make contributions to those histories they don’t write the whole history alone.</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">Let’s take a very brief look at another example where people tend to express themselves as if one individual had produced a major scientific theory complete in one go, like Athena springing fully armed from the head of Zeus, the theory of relativity. If one were to take the popular accounts literally then Einstein dreamt up the whole affair whilst travelling to his work at the Patent Office in Bern on the tram. However the theory of relativity also has a long history. The principle of the relativity of motion to a frame of reference can be found in the works of Galileo, to whom it is oft falsely attributed, but it can also be found in Copernicus’ De revolutionibus and two thousand years earlier in the works of Euclid. The central discussion as to whether time and space are absolute or relative can be found in the Leibniz Clarke correspondence at the beginning of the 18<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century with Samuel Clarke basically fronting for Newton. Einstein own work was largely prompted by the incompatibility of the theories of Newton and James Clerk Maxwell, a problem much discussed and analysed in the 19<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century. Einstein famous discussion of synchronicity of clocks is foreshadowed by a similar discussion in the 19<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century by the operators of railway networks. Moving from special to general relativity we have the contributions of Minkowski, Hilbert and others.</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">To close I have made much use of the concept of evolution in this post and anybody who regularly reads John Wilkins at <a href="https://web.archive.org/web/20190522053433/http://evolvingthoughts.net/" style="box-sizing: inherit; color: #c3251d; text-decoration-skip: objects; text-decoration: none;">Evolving Thoughts </a>will know that the biological theory of evolution has a long history before Darwin published that book 150 plus years ago and readers of <a href="https://web.archive.org/web/20190522053433/http://sandwalk.blogspot.com/" style="box-sizing: inherit; color: #c3251d; text-decoration-skip: objects; text-decoration: none;">Larry Moran</a> or the fearsome <a href="https://web.archive.org/web/20190522053433/http://scienceblogs.com/pharyngula/?utm_source=bloglist&utm_medium=dropdown" style="box-sizing: inherit; color: #c3251d; text-decoration-skip: objects; text-decoration: none;">P Z Myers</a> will know that modern evolutionary theorists object to being called Darwinians because the theory of evolution has evolved since Charles’ day. To recap, it is wrong to ask who invented or discovered a scientific discipline or theory, one should instead ask what did a given individual contribute to the theory or discipline in question?</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">For those who wish to know more about such things as the method of exhaustion or the fundamental theory of calculus then the articles at Wikipedia are mostly OK. On the individual mathematicians and their contributions to the history of calculus a visit to <a href="https://web.archive.org/web/20190522053433/http://www-history.mcs.st-and.ac.uk/" style="box-sizing: inherit; color: #c3251d; text-decoration-skip: objects; text-decoration: none;">MacTutor </a>is recommended.</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">For those who prefer books, you can read about the details of the priority dispute between Leibniz and Newton in definitive form in Rupert Hall’s “Philosophers at War” or in more popular form in Jason Bardi’s “The Calculus Wars”. A very general popular account of the history of infinite in mathematics is Ian Stewart’s “Taming the Infinite” a much more challenging book on the history of the infinite in mathematics is David Foster Wallace’s “Everything or More”.</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">On the history of calculus the standard works are, in ascending order of technical difficulty, Carl B. Boyer’s “The History of the Calculus”, Margaret E. Baron’s “The Origins of the Infinitesimal Calculus” and C. H. Edwards Jr.’s “The Historical Development of the Calculus”.</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">There is a chapter on the Kerala School in George Gheverghese Joseph’s “The Crest of the Peacock”. Joseph has also written a complete book on the subject his “Passage to Infinity”. For a corrective to some of Joseph’s more exaggerated claims I recommend reading the relevant parts of Kim Plofker’s “Mathematics of India”.</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">“The Leibniz-Clarke Correspondence” has been edited and annotated by H.G. Alexander and anybody interested in the connections between 19<span style="box-sizing: inherit; font-size: 11.25px; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">th</span> century train time tables and Einsteins Theory of Relativity should read Peter Galison’s excellent “Einstein’s Clocks and Poincare’s Maps”</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">If you actually read and digest all of the above then you can start writing your own blog posts on the history of calculus.</p><p style="box-sizing: inherit; margin: 0px 0px 10px; padding: 0px;">1) With apologies to Sting!</p></div>Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com3tag:blogger.com,1999:blog-3596550435682943926.post-15155087519256800922019-08-25T13:37:00.000-07:002020-04-13T12:42:19.748-07:00Wish list for space video games.<div class="separator" style="clear: both;">
<b><span style="font-size: large;">Kerbal Space Program</span></b></div>
<br />
The Kerbal Space Program has demonstrated video games can be a very effective teaching tool.<br />
<br />
It used to be very frustrating trying to talk about orbital mechanics. Use a word like "perigee" and eyes would glaze over as the audience tunes out.<br />
<br />
But now there are many KSP players who are comfortable with terms like The Oberth Benefit, Bi Elliptic Transfers and other what use to be arcane, esoteric notions.<br />
<br />
I'm hoping for more scientifically accurate games to make their way into pop culture.<br />
<br />
<b><span style="font-size: large;">Wish Number 1: Shotgun N-body simulations</span></b><br />
<br />
Readers of this blog may know I'm a little obsessed with <a href="http://hopsblog-hop.blogspot.com/2015/05/eml2.html">EML2</a> (Earth Moon Lagrange 2).<br />
<br />
Many of my delta V numbers from EML2 assume dropping from EML2 using the Farquhar route and then insertion to a transfer orbit when moving ~11 km/s at perigee.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiV78Fl6EopSO_6YGtBko9pIisySVYVTRM4FTLPxcxBqCtewFGmE_qtJckv3BH9Qqgv-FMuOb5IOThxa6HQQxYJxM_haR-HXyGsCdW5XB6oaZ5zxc73rq0peQ4anW1IAnIpXatf7Cb9DGas/s1600/LEO-lunar-L2+transfer.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="665" data-original-width="1000" height="424" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiV78Fl6EopSO_6YGtBko9pIisySVYVTRM4FTLPxcxBqCtewFGmE_qtJckv3BH9Qqgv-FMuOb5IOThxa6HQQxYJxM_haR-HXyGsCdW5XB6oaZ5zxc73rq0peQ4anW1IAnIpXatf7Cb9DGas/s640/LEO-lunar-L2+transfer.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
The Farquhar Route</div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
However Farquhar's well done graphic is a simplification. A ship departing from from the EML2 region would not depart from a point. Rather it would drop from a halo or lissajous orbit about EML2. There are a multitude of possible orbits in this region.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Dropping from different parts of a halo orbit will result in different longitudes and latitudes for a perigee. And if you're doing a perigee burn for injection to a Mars transfer orbit, you want to be at a specific location and heading a specific direction when making your burn. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Years ago Tom Powell helped me build a <a href="http://clowder.net/hop/railroad/OrbSim.html">shotgun Java n-body sim</a> from Bob Jenkins' code. blast many pellets in the general direction of your target. See which pellets pass closest and then narrow the shotgun blast.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwyMwZbCnQOfVWMGxyITxJyoimvwtUktgezt4EEAgYhLOnLnW_3h32snFF-N2Sv-UQ6HWBmIkGuAKXmxIJfvZQDRAbiH-j8hs023Y-HrOPxSFiSXrvYvG7d8ZUaeAAnVTcuBNAbYvN4a8l/s1600/HopShotGun.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1294" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwyMwZbCnQOfVWMGxyITxJyoimvwtUktgezt4EEAgYhLOnLnW_3h32snFF-N2Sv-UQ6HWBmIkGuAKXmxIJfvZQDRAbiH-j8hs023Y-HrOPxSFiSXrvYvG7d8ZUaeAAnVTcuBNAbYvN4a8l/s640/HopShotGun.jpg" width="516" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Above is an attempt to show the shotgun concept. A fellow going by the handle "Impaler" was annoying me in a space forum. First I blast the varmint with broad scattering of buckshot. Then I more thoroughly pepper his backside by narrowing the blast between pellets 5 and 7.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
By successively narrowing buck shot from earth to EML2 I found this route 3.1 km/s route from LEO to EML2:</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijfo9kYJ89Qwe1Qk3PugToZXtxySXzYoBmx_4nKmAmwTaG31gFkMiPtWVLeU_3x5XPD2kiwkV3HcqK-Iw1gHFYufx9eeYOgp_17F37tj8-I-x7CWbOqQAAOfRCCWoVhdpTIJA0XNWWI4V2/s1600/LEOtoEML2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="484" data-original-width="900" height="344" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijfo9kYJ89Qwe1Qk3PugToZXtxySXzYoBmx_4nKmAmwTaG31gFkMiPtWVLeU_3x5XPD2kiwkV3HcqK-Iw1gHFYufx9eeYOgp_17F37tj8-I-x7CWbOqQAAOfRCCWoVhdpTIJA0XNWWI4V2/s640/LEOtoEML2.png" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7QR7lJEWyb9YKb-ByVYLm12BtKtQadiJE8O2nyptY2-CNcpH24RX57y1rWdSEwXH2-dYtzSH4MbEe_CwEEo7g440mhYTDf5B8ndva-sWBEP7_FvF38-BjRksqc1B5sTvYjO_BgDr1uCBx/s1600/LEOtoEML2ZoomOut.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="360" data-original-width="259" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7QR7lJEWyb9YKb-ByVYLm12BtKtQadiJE8O2nyptY2-CNcpH24RX57y1rWdSEwXH2-dYtzSH4MbEe_CwEEo7g440mhYTDf5B8ndva-sWBEP7_FvF38-BjRksqc1B5sTvYjO_BgDr1uCBx/s400/LEOtoEML2ZoomOut.png" width="287" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
The sim included earth, moon and sun. A lunar swing by boosts apogee on the way out. And then sun's tidal influence serves to raise perigee to EML2 altitude.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
There are some serious limitations to my shot gun sim. There are only a few very limited scenarios that Tom Powell and I set up, very specific times and places. I would like to be able to have the user get location and velocity of a body at any time. I under stand there's software called SPICE that does this but I don't know how to use it.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Also JAVA seems obsolete. It's very difficult for me to use my own pages any more.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
And my sims cans only specify the initial burns. Once you have a transfer path to a location it'd be nice to be able to do burns to park at that location.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
I would use such a tool to learn how to move between different loosely bound lunar orbits.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Perhaps dropping from one EML2 halo orbit during a launch window wouldn't put the perigee in the right place for an injection burn. How much delta V would it take to move to a more favorable halo orbit?</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Supposedly there are <a href="https://en.wikipedia.org/wiki/Heteroclinic_orbit">heteroclinic paths</a> between halo orbits EML1 and EML2. A shotgun sim might help a player find these paths.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Halo orbits about EML1 and EML2 are part of a family of orbits that also include Near Rectilinear Halo Orbits (NHROs). If a lunar gateway is placed in an NHRO, it'd be fun and useful to explore different lunar orbits you could enter from an NHRO.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Wish Number 2: Tunneling on small bodies</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
For planets and large moons we are limited to exploiting only the thin outer shell of a body. Heat and pressure prohibit us from tunneling deeply.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
But the entire <i>volume</i> is accessible for a small body.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
If we could exploit the entire volume of Ceres, the dwarf planet could make Trantor look like Dogpatch.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
I am hoping some planetary scientists and geologists could build tools to guesstimate how deeply we could tunnel given a body's surface temperature, radius and mass.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Wish Number 3: Tensile towers on small bodies</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Also known as space elevators.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
I'd be so happy to see a world building game use something like <a href="http://hopsblog-hop.blogspot.com/2015/12/how-wolfes-tether-spreadsheet-works.html">Wolfe's spreadsheet</a> to examine effort and materials needed for various elevators. The user could input tensile strength, planet's angular velocity and body mass to examine various scenarios.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
For example given Ceres' high angular velocity and shallow gravity well, Ceres synchronous orbit is only 706 kilometers above Ceres' surface. Materials needed for a Ceres or Vesta elevator are only a tiny fraction of what a <a href="http://hopsblog-hop.blogspot.com/2012/09/beanstalks-elevators-clarke-towers.html">Clarke Tower</a> from earth or Mars would need.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Besides elevators from synchronous orbits it would also be good to enable users to build from planet-moon L1 and L2 points. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The <a href="http://hopsblog-hop.blogspot.com/2016/01/upper-phobos-tether.html">Mars Phobos</a> and <a href="http://hopsblog-hop.blogspot.com/2016/01/deimos-tether.html">Mars Deimos</a> are the moon elevators I like most. But elevators from L2 or L2 are usable in any family of tide locked moons.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh52DYvkRWnlScXGGR-3ww5p_Xv1bZKHAz8MpMT9OqL07GydblQgVnttv22zqxCvC6WcDI465Xoee2kFyFlynP_idsi4WGoh-W1MuosmTxvjzkY6D9sYQV_6ETOav-6juPROcK2lRfqQOl/s1600/SaturnMoonTethers.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1250" data-original-width="1132" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh52DYvkRWnlScXGGR-3ww5p_Xv1bZKHAz8MpMT9OqL07GydblQgVnttv22zqxCvC6WcDI465Xoee2kFyFlynP_idsi4WGoh-W1MuosmTxvjzkY6D9sYQV_6ETOav-6juPROcK2lRfqQOl/s640/SaturnMoonTethers.jpg" width="578" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
Various tethers enabling <a href="http://hopsblog-hop.blogspot.com/2016/01/deimos-tether.html#ZRVTO">ZRVTO</a>s between Saturn's moons.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
A gas giant's family of moons with tethers could be a rich setting for dramatic stories.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Hohmann trip times and launch windows between moons are on the order of days and weeks so it'd be possible to have a fast paced story without resorting to implausible engineering.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Dramatic situations might include missing a tether catch and being trapped in an orbit that won't rendezvous with a tether catcher until the passengers have died from using up air, food or water. Or terrorists could sever a tether. There are many possibilities.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Wish Number 4: Compressive towers on small bodies.</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Given lower gravity it's possible to build taller structures even given constraints imposed by a material's compressive strength. Likewise, sky scrapers are less plausible if a body has greater surface gravity.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
I'd like the user to be able to specify a material's compressive strength and body gravity to get maximum plausible height for structures.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
This would be especially useful for elevators between mutually tidally locked bodies like Pluto and Charon. Compressive towers built from the surfaces of Pluto and Charon could extend a fair distance towards Pluto-Charon-L1 and the also the Pluto Charon barycenter. This would considerably reduce the stress on the elevator and thus reducing the mass of the materials needed.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Wish Number 5: Thermal management.</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
This section dded on 9-8-19 on the suggestion of Winchell Chung and other thoughtful readers. There's three thermal management subjects I'd love to see a game address.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Limits to population growth</b></div>
<div class="separator" style="clear: both; text-align: left;">
<b><br /></b></div>
<div class="separator" style="clear: both; text-align: left;">
Earlier I mentioned a fully exploited Ceres volume could be a megapolis that makes Trantor look like Dogpatch. In the comments below Jim Baerg noted big populations generate heat. How would a growing population dump heat?</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
A good world building sim would take thermal management into account as a barrier to population growth.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Stealth</b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Infra red signature could make military craft visible. <a href="http://www.projectrho.com/public_html/rocket/spacewardetect.php">A topic Chung talks about in his Atomic Rockets page</a>.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Rocket propulsion.</b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Nuclear power electricity generation for ion propelled rockets would generate considerable waste heat. Dumping waste heat requires big radiators which make for a <a href="http://hopsblog-hop.blogspot.com/2015/05/the-need-for-better-alpha.html">poorer power source alpha</a>. There are other heat sources that need radiators to dump waste heat. These should be counted when calculating mass requirements for a space ship.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Any other ideas?</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Well made multi user games could be a way to educate as well as stimulate interest in space exploration. If a reader has any other suggestions please comment. I screen comments for spam but I eventually post what I believe are worthwhile comments. It's unlikely an actual video game developer will ever read these but there's no harm in day dreaming.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com27tag:blogger.com,1999:blog-3596550435682943926.post-8526490006520527042019-04-06T15:47:00.001-07:002020-04-13T12:42:44.321-07:00Bridenstine's Why The Moon Matters<div class="separator" style="clear: both;">
Back in December 29, 2016 Bridenstine made a blog post "Why The Moon Matters". Bridenstine was representative of Oklahoma at the time.</div>
<br />
Sadly the post was taken down when Bridenstine left his post as representative and became NASA administrator. But I recently found the post using the<a href="https://web.archive.org/web/20170903084343/https://bridenstine.house.gov/news/documentsingle.aspx?DocumentID=772"> Wayback Machine</a>.<br />
<br />
Bridenstine's reasons were pretty the same arguments made by lunar scientist Paul Spudis (RIP).<br />
<br />
I post it here for historical reference. Copying and pasting:<br />
<br />
<h2 style="color: #3499d5; font-family: "Droid Serif", serif; font-size: 27px; font-stretch: normal; font-weight: normal; line-height: 27px; margin: 0px 0px 1.2em; max-height: 100000px;">
<span id="ctl00_PageLink" style="max-height: 100000px;">Jim's Blog</span></h2>
<div class="buffer" style="caret-color: rgb(100, 106, 112); color: #646a70; font-family: Arial, Helvetica, sans-serif; font-size: 12px; max-height: 100000px;">
<table cellpadding="0" cellspacing="0" style="border-collapse: collapse; border-spacing: 0px; max-height: 100000px; width: 649px;"><tbody style="max-height: 100000px;">
<tr style="max-height: 100000px;"><td id="ctl00_ContentCell" style="max-height: 100000px;"><div class="news-item-page" id="ctl00_ctl15_ControlBody" style="max-height: 100000px;">
<div id="fb-root" style="max-height: 100000px;">
</div>
<h3 class="middleheadline" style="color: #333333; font-family: "Droid Serif", serif; font-size: 26px; font-stretch: normal; font-weight: normal; line-height: 28px; margin: 0px 0px 21px; max-height: 100000px;">
Why the Moon Matters</h3>
<h4 class="middleheadline" style="color: #555555; font-size: 15px; font-style: italic; line-height: 1.2em; margin: 5px 0px 0px; max-height: 100000px;">
<i style="max-height: 100000px;">by Rep. Jim Bridenstine</i></h4>
<div class="topnewsbar" style="background-color: #ebebeb; border-bottom-color: rgb(204, 204, 204); border-bottom-style: solid; border-bottom-width: 2px; border-top-color: rgb(204, 204, 204); border-top-style: solid; border-top-width: 2px; clear: right; color: #555555; margin: 7px 0px 10px; max-height: 100000px; padding: 3px 10px;">
<div class="topshare" style="float: right; margin: -1px 2px 1px 5px; max-height: 100000px;">
<a class="webicon" href="https://www.blogger.com/null" style="color: #888888; cursor: pointer; font-family: Icons; font-size: 18px; margin-right: 3px; max-height: 100000px; vertical-align: top;">f</a> <a class="webicon" href="https://www.blogger.com/null" style="color: #888888; cursor: pointer; font-family: Icons; font-size: 18px; margin-right: 3px; max-height: 100000px; vertical-align: top;">t</a> <a class="webicon" href="https://www.blogger.com/null" style="color: #888888; cursor: pointer; font-family: Icons; font-size: 18px; margin-right: 3px; max-height: 100000px; vertical-align: top;">#</a> <a class="addthis_button_email webicon" href="https://web.archive.org/web/20170903084343/http://www.addthis.com/bookmark.php" style="color: #888888; cursor: pointer; font-family: Icons; font-size: 18px; margin-right: 3px; max-height: 100000px; text-decoration: none; vertical-align: top;">e</a></div>
<div class="topnewstext" style="float: left; line-height: 18px; max-height: 100000px; min-height: 1px;">
<b style="max-height: 100000px;">Washington, December 29, 2016</b> <span class="news-comments" style="max-height: 100000px;">| <a href="https://web.archive.org/web/20170903084343/https://bridenstine.house.gov/news/documentsingle.aspx?DocumentID=772#Comments" style="color: #555555; max-height: 100000px; text-decoration: none;"><fb:comments-count class=" fb_comments_count_zero" fb-xfbml-state="rendered" href="bridenstine.house.gov/news/documentsingle.aspx?DocumentID=772" style="max-height: 100000px;"><span class="fb_comments_count" style="max-height: 100000px;">0</span></fb:comments-count> comments</a></span></div>
</div>
<div class="middlecopy" style="max-height: 100000px;">
<div class="bodycopy" style="margin: 15px 0px; max-height: 100000px; text-align: justify;">
On July 20, 1969, the free world won the space race when an American flag was planted on the Moon. Twelve Americans walked on the Moon during the Apollo program, resulting in a treasure trove of knowledge not only about the Moon, but about the universe. Even better, by demonstrating the United States’ political, economic, and technological prowess, it played a part winning the Cold War. In 1983, Ronald Reagan introduced the Strategic Defense Initiative to defend the free world from nuclear ballistic missiles. While many called it destabilizing, and even suggested it was impossible to achieve, the Soviet Union took it very seriously, made every effort to eliminate it, and spent whatever it took to compete. They eventually went bankrupt. SDI, while not fully implemented, was a geopolitical success built on the technical credibility provided by Apollo. As Ronald Reagan predicted, “We win. They lose.”<br />
<br style="max-height: 100000px;" />
Through SDI, the Brilliant Pebbles program was born as a space based system to track and destroy ICBMs. Years later, in 1994, a Brilliant Pebbles satellite was repurposed to orbit and map the Moon. That mission, called Clementine, tested military sensors and made history when it provided evidence of lunar water ice. Later experiments by NASA and other space agencies indicated billions of tons of water ice at each lunar pole.<br />
<br style="max-height: 100000px;" />
This single discovery should have immediately transformed America’s space program. Water ice not only represents a critical in situ resource for life support, but it can be cracked into its components, hydrogen and oxygen, to create the same chemical propellant that powers rockets.<br />
<br style="max-height: 100000px;" />
All of this is available on a world that has no atmosphere and a gravity well that is 1/6th that of Earth. In other words, standard aerodynamic limitations do not apply, permitting the placement of the propellant into orbit either around the Moon or around the Earth.<br />
<br style="max-height: 100000px;" />
From the discovery of water ice on the Moon until this day, the American objective should have been a permanent outpost of rovers and machines, with occasional manned missions for science and maintenance, in order to utilize the materials and energy of the Moon to drive down the costs and increase the capabilities of American operations in cis-lunar and interplanetary space.<br />
<br style="max-height: 100000px;" />
Water ice on the Moon could be used to refuel satellites in orbit or perform on-orbit maintenance. Government and commercial satellite operators could save hundreds of millions of dollars by servicing their satellites with resources from the Moon rather than disposing of, and replacing, their expensive investments. Eventually, the customers of Direct TV, Dish Network, internet broadband from space, satellite radio, weather data, and others could see their bills reduced and their service capacities greatly increased.<br />
<br style="max-height: 100000px;" />
While most satellites are not currently powered by liquid oxygen and liquid hydrogen, next generation satellite architectures could utilize lunar propellant if low-cost in-orbit servicing were available. Commercial operators will follow if the United States leads with its own constellations. Such leadership would require a whole-of-government approach with the interagency support of the newly reconstituted National Space Council. The objective is a self-sustaining, cis-lunar economy, whereby government and commercial operators save money and maximize the utilization of space through the use of lunar resources.<br />
<br style="max-height: 100000px;" />
This is also the first step for manned missions deeper into our solar system. A permanent human presence on other celestial bodies requires in situ resource utilization. The Moon, with its three-day emergency journey back to Earth, represents the best place to learn, train, and develop the necessary technologies and techniques for in situ resource utilization and an eventual long term human presence on Mars. Fortunately, the Space Launch System and Orion will start testing in 2018. This system, with a commercial lander, could quickly place machines and robots on the Moon to begin the cis-lunar economy. With the right presidential guidance, humans could return in short order as well; this time, to stay.<br />
<br style="max-height: 100000px;" />
There are other economic benefits to a permanent presence on the Moon. Utilization of lunar oxides for in situ additive manufacturing (3-D printing) could sustain and develop lunar operations. If economical, we should pioneer the extraction of highly valuable platinum group metals and the ability to transport them back to Earth. The development of practical solar power satellites that beam energy directly to all areas of the Earth is made possible through the use of the resources of the Moon. Research on this concept is already being done in Japan, as well as at the Naval Research Lab here in the United States. The United States government should lead the way in retiring risk for these endeavors with the intent to empower commercial companies to sustain the cis-lunar economy. This could fundamentally alter the economic balance of power on Earth.<br />
<br style="max-height: 100000px;" />
As the cis-lunar economy develops, competition for locations and resources on the Moon is inevitable. The Chinese currently have landers and rovers on the Moon. The United States does not. Very soon, the Chinese will be the first of humanity to explore the far side of the Moon and place robots at the poles. As my friend Congressman Bill Posey says, “They are not going there to collect rocks.” China has its own manned space station. The United States’ commitment to the International Space Station ends in 2024. China has a domestic capability to launch its Taikonauts into orbit. The United States relies on Russia. American adversaries are testing antisatellite weapons and proliferating satellite jamming, spoofing, and dazzling technologies. It is time for the United States to re-posture and assert true space leadership.<br />
<br style="max-height: 100000px;" />
It must be stated that constitutionally, the U.S. government is required to provide for the common defense. This includes defending American military AND commercial assets in orbit, many of which have the dual role of providing commercial and military capabilities. The same applies for assets on and around the Moon. The U.S. government must establish a legal framework and be prepared to defend private and corporate rights and obligations, all keeping within the 1967 Outer Space Treaty. The United States must have cis-lunar situational awareness, a cis-lunar presence, and eventually must be able to defend freedom of action in space. Cis-lunar development will proceed with American values and the rule of law if the United States leads.<br />
<br style="max-height: 100000px;" />
Space utilization has transformed the human condition, including how we communicate, navigate, produce food and energy, conduct banking, predict weather and perform disaster relief. While many of these gains are a result of private investment and commercial markets, they are only possible because the United States government took the lead and retired risk for these capabilities. Today, we are experiencing a space renaissance. The first launch of the Space Launch System is less than two years away. In 2021, we will use the Orion capsule to send astronauts beyond low Earth orbit for the first time since the 1970s. Commercial launch vehicles are maturing and commercial deep space habitats are currently in development. A renewed focus on utilizing the Moon can help further these advances and achievements. The choices we make now can forever make America the preeminent spacefaring nation.</div>
<div class="bodycopy" style="margin: 15px 0px; max-height: 100000px; text-align: justify;">
<br /></div>
</div>
</div>
</td></tr>
</tbody></table>
</div>
<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com8tag:blogger.com,1999:blog-3596550435682943926.post-3448002645441096942019-03-13T10:48:00.000-07:002020-05-04T13:10:06.880-07:00Orbital Mechanics Coloring Book 2nd edition<div style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BlZSc9Kk862jiNsHHjx_5B51GZXbe6ygiPw9gVdu9UYMHFgiosfhWClqzp8p_OfUtpQ7uF-kdSSmSeWa7AeOA3l_tU_p-Av9wlOfey83WwWuQqFC9KzZWP242zIWsmyBk6MPg0OVvtKq/s1600/ConicSectionsCover-01.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1039" data-original-width="1600" height="414" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BlZSc9Kk862jiNsHHjx_5B51GZXbe6ygiPw9gVdu9UYMHFgiosfhWClqzp8p_OfUtpQ7uF-kdSSmSeWa7AeOA3l_tU_p-Av9wlOfey83WwWuQqFC9KzZWP242zIWsmyBk6MPg0OVvtKq/s640/ConicSectionsCover-01.jpg" width="640" /></a></div>
<br />
<br />
<span style="font-size: large; text-align: center;"><a href="https://ajo-copper-news.com/collections/frontpage/products/conic-sections-and-celestial-mechanics-coloring-book" style="text-align: center;">Now Available at our online store</a></span><br />
<br />
Hopefully it will soon be available on Amazon as a Kindle book.<br />
<br />
I am not happy with this coloring book. Pages should be opaque enough that images on the other side don't show through. I had failed to specify heavier weight paper when printing this book.<br />
<br />
So I am cutting the price of this book from $5.00 to $2.00. I will print a version with better quality paper when I can afford to.<br />
<br />
<b><span style="font-size: large;">New in the second edition</span></b><br />
<br />
Given 24 more pages I can add a lot of extra stuff. I've kept most of the original 40 pages and added:<br />
<br />
<b>Page 18</b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHSgUcvjMPTiZQVcvP2lAF9tepjc6RZPZ5GaatBAZbMDG_HqoYBwpAwz0d3kaZLLwNLkuDwq1mkTRTREopRi7CQ5MoD827wntpi-GHIC61bl3qxyPQqxCUwIPTm1JfyPBBdZ9FcWVT318k/s1600/Screen+Shot+2019-03-13+at+9.12.34+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1187" data-original-width="887" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHSgUcvjMPTiZQVcvP2lAF9tepjc6RZPZ5GaatBAZbMDG_HqoYBwpAwz0d3kaZLLwNLkuDwq1mkTRTREopRi7CQ5MoD827wntpi-GHIC61bl3qxyPQqxCUwIPTm1JfyPBBdZ9FcWVT318k/s640/Screen+Shot+2019-03-13+at+9.12.34+AM.png" width="478" /></a></div>
<br />
In the section on Kepler's 2nd Law I've added a visualization that helps show <b>r</b> X <b>v</b> is twice the area swept out over a given time period. That specific angular momentum is twice the area of the ellipse per orbital period.<br />
<br />
<b>Page 22</b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLmg5wFRzlNCzZgnyC8Ia6zwIiWM4bb3d3LlRXtnDy5owKTl6uXYK8mmFfjHcu-pYPHRw-5NA4tGsgk-Gkl2fJ5Dzuz0fwP8gCLdeOMDwtwuIE0nHLpZvdh9h1fQHL214l_S0JrAFU9xow/s1600/Screen+Shot+2019-03-13+at+9.17.14+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1187" data-original-width="881" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLmg5wFRzlNCzZgnyC8Ia6zwIiWM4bb3d3LlRXtnDy5owKTl6uXYK8mmFfjHcu-pYPHRw-5NA4tGsgk-Gkl2fJ5Dzuz0fwP8gCLdeOMDwtwuIE0nHLpZvdh9h1fQHL214l_S0JrAFU9xow/s640/Screen+Shot+2019-03-13+at+9.17.14+AM.png" width="474" /></a></div>
<br />
Page 22 attempts to portray my visualization that helps me remember centrifugal acceleration is <span style="background-color: white;">ω<sup>2</sup>r.</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;"><b>Pages 28 and 29</b></span><br />
<span style="background-color: white;"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhH_mG6dR5ZqJdlwrDF3wScmU7oo4NSkCt6ob5yg54VHVw_ezTDzYFKKe2pGGNvayPn4svw9JrkFHXlSYfiXO2Y8YAo7eTvsJ0hB82EqIzV8r0yXUslFhMVYenKKJeyC08tY8czXyPfJOZH/s1600/Screen+Shot+2019-03-13+at+9.21.40+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1014" data-original-width="1600" height="404" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhH_mG6dR5ZqJdlwrDF3wScmU7oo4NSkCt6ob5yg54VHVw_ezTDzYFKKe2pGGNvayPn4svw9JrkFHXlSYfiXO2Y8YAo7eTvsJ0hB82EqIzV8r0yXUslFhMVYenKKJeyC08tY8czXyPfJOZH/s640/Screen+Shot+2019-03-13+at+9.21.40+AM.png" width="640" /></a></div>
<span style="background-color: white;"><br /></span>
Attempts to explain radians and to show circular motion is <span style="background-color: white;">ωr where </span><span style="background-color: white;">ω is angular velocity in radians.</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;"><b>Pages 30 to 35</b></span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Are devoted to orbital vertical tethers. I am going to try to start calling these Sarmount tethers as I have recently learned Eagle Sarmount proposed these in the 1990s.</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Perhaps science fiction device but I like them any way. The geometry and math associated with these is pleasing, in my opinion. Here are two pages from this section:</span><br />
<span style="background-color: white;"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBhKg0Ohf1gXu0TNpUYAH8ehEJ1Ozzv0O0fXFq6J_3BUAhyvup3a8qAJr7G_v3NJ5j0c67IKrOGLTQkoMjvgl70YRgSPBwketKRZfnvhonRa1bDG3xWyet1Pb2wjF1X0c3D84znqVTy5UW/s1600/Screen+Shot+2019-03-13+at+9.32.27+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="928" data-original-width="685" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBhKg0Ohf1gXu0TNpUYAH8ehEJ1Ozzv0O0fXFq6J_3BUAhyvup3a8qAJr7G_v3NJ5j0c67IKrOGLTQkoMjvgl70YRgSPBwketKRZfnvhonRa1bDG3xWyet1Pb2wjF1X0c3D84znqVTy5UW/s640/Screen+Shot+2019-03-13+at+9.32.27+AM.png" width="472" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjboj05_d-_GZbFomuzyoWjPIY3trXDIEFjBy51OBrCgaG29DYV1jKt9SAr4TtXyVp3_AcilzTGngeGw9gen4XGkXQL8o4qQCV7E6W86t9GXsSJrR3TFK73CXztczhhi_2rekMR7mOQTcl2/s1600/Screen+Shot+2019-03-13+at+9.39.23+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1018" data-original-width="1600" height="406" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjboj05_d-_GZbFomuzyoWjPIY3trXDIEFjBy51OBrCgaG29DYV1jKt9SAr4TtXyVp3_AcilzTGngeGw9gen4XGkXQL8o4qQCV7E6W86t9GXsSJrR3TFK73CXztczhhi_2rekMR7mOQTcl2/s640/Screen+Shot+2019-03-13+at+9.39.23+AM.png" width="640" /></a></div>
<span style="background-color: white;"><br /></span>
<span style="background-color: white;"><b>Pages 49 - 51</b></span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Are about the Oberth Benefit and EML2</span><br />
<span style="background-color: white;"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghFg6JpnTALphwuuSzNtMAUxWYmQnzFIaByE3OPEmA7HYIf8I2okokqHqFzWPIWjVyL9AIzFoeSUQW6it1rY1okl0H9IhYMGCESWB7rMPrFZpK7eagdBoUGhyCdcWjkCL-rdHyUC7IipUp/s1600/Screen+Shot+2019-03-13+at+9.42.46+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1101" data-original-width="818" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghFg6JpnTALphwuuSzNtMAUxWYmQnzFIaByE3OPEmA7HYIf8I2okokqHqFzWPIWjVyL9AIzFoeSUQW6it1rY1okl0H9IhYMGCESWB7rMPrFZpK7eagdBoUGhyCdcWjkCL-rdHyUC7IipUp/s640/Screen+Shot+2019-03-13+at+9.42.46+AM.png" width="474" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqIe1rhLQJtmSMMGhYT6PPl3b0Dc0BehxAsj5FMtNrxOrT6FGmyRTI20duX2YFsMNm5GyoWvtQyfiIqJay2DfRVa2YM8DGkNmq5Ax7KYUnzyx5sDR9tdAvPEFu2NsMdjP3WhyphenhyphenIyxhbnR7N/s1600/Screen+Shot+2019-03-13+at+9.43.49+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1024" data-original-width="1600" height="408" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqIe1rhLQJtmSMMGhYT6PPl3b0Dc0BehxAsj5FMtNrxOrT6FGmyRTI20duX2YFsMNm5GyoWvtQyfiIqJay2DfRVa2YM8DGkNmq5Ax7KYUnzyx5sDR9tdAvPEFu2NsMdjP3WhyphenhyphenIyxhbnR7N/s640/Screen+Shot+2019-03-13+at+9.43.49+AM.png" width="640" /></a></div>
<span style="background-color: white;"><br /></span><span style="background-color: white;"><b>Pages 51 - 52</b></span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Are about the rocket equation and mass fractions.</span><br />
<span style="background-color: white;"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGlq1JiOTgM2wPvWQ0l6FHx8oMX_3l8rlkyZrYgyTReCAFS7WUT9oHvxOIwrEZbqWsAM5KaaQkZhrHY26FSwNxVakgVZKG1ouFU5bG1pfI5kvUTIBmh0Uf1uZe-pXQiWILXj4BMwZ_G1ME/s1600/Screen+Shot+2019-03-13+at+9.49.55+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1021" data-original-width="1600" height="408" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGlq1JiOTgM2wPvWQ0l6FHx8oMX_3l8rlkyZrYgyTReCAFS7WUT9oHvxOIwrEZbqWsAM5KaaQkZhrHY26FSwNxVakgVZKG1ouFU5bG1pfI5kvUTIBmh0Uf1uZe-pXQiWILXj4BMwZ_G1ME/s640/Screen+Shot+2019-03-13+at+9.49.55+AM.png" width="640" /></a></div>
<span style="background-color: white;"><br /></span>
<br />
<span style="background-color: white;"><b>Pages 53 to 63</b></span><br />
<span style="background-color: white;"></span><br />
<span style="background-color: white;">Looks at thrust vs exhaust velocity, dynamic pressure and the need to make a rapid ascent from a planetary surface to avoid gravity loss.</span><br />
<span style="background-color: white;"><b><br /></b></span>
<span style="background-color: white;"><b>Page 64</b></span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Resources that have helped me. Books, websites, forums. Atomic Rockets, NasaSpaceflightForums, Space Stack Exchange, Tough SF and others. I am adding to this list as more occur to me.</span><br />
<br />
<b>Inside back cover</b><br />
<br />
My favorite equations. The Vis Viva Equation will be at the top. I've been thinking of making a reference sheet to pin to the wall next to my computer. This would serve.<br />
<br />
<a href="http://www.cunews.info/ConicColoringBook200223.pdf">Here is the coloring book as of March 2020</a> (6.4 MB pdf, not too big). Reviews would be appreciated. Steven Pietroban invested a fair amount of time looking over the first edition and found many small errors and a few substantial errors. Given my tendency to make misteaks, I'm sure there are errors hiding in my more recent effort. A heads up would be much appreciated if you see something wrong.<br />
<br />
My email is hopd at cunews dot info.<br />
<br />
<br />
<br />
<br />
<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com3tag:blogger.com,1999:blog-3596550435682943926.post-49868899036289905222018-06-30T20:15:00.001-07:002020-04-13T12:43:11.873-07:00Asteroid Day<div class="separator" style="clear: both;">
On June 30 in 1908 the Tunguska object took out a good chunk of forest in Siberia.</div>
<br />
In February of 2016 the United Nations approved a resolution stating<br />
<br />
<blockquote class="tr_bq">
<span style="background-color: white; color: #222222; font-family: sans-serif; font-size: 14px;">30 June International Asteroid Day to observe each year at the international level the anniversary of the Tunguska impact over Siberia, Russian Federation, on 30 June 1908 and to raise public awareness about the asteroid impact hazard</span></blockquote>
<br />
A good time to talk about a project on my wish list. An orbital telescope devoted to finding asteroids.<br />
<br />
A wide field infrared scope much like WISE. But unlike WISE positioned at SEL1 or SEL2 so the earth isn't a major heat source.<br />
<br />
A scope that can make simultaneous observations in visual wavelengths as well as infrared. This would tell us the asteroid's albedo from which we'd get a good estimate of size.<br />
<br />
A scope that points towards the inner solar system. For various reasons asteroids within the earth's orbit are very hard to see from earth's surface. An orbital scope pointing towards the inner solar system would give us an inventory of a body of objects we presently know almost nothing about.<br />
<br />
I was surprised and pleased to learn such a telescope had already been proposed. <a href="https://en.wikipedia.org/wiki/Near-Earth_Object_Camera">NEOCam</a>. Principal Investigator Amy Mainzer.<br />
<br />
We're presently getting a pretty good inventory of Chixculub size rocks. But Tunguska sized rocks are much harder to see. And there's a bunch more rocks this size. NEOCam would help us get a better handle on potential city killers.<br />
<br />
Another potential NEOCam benefit: It could inventory potential asteroids for mining companies like Planetary Resources or Deep Space Industries.<br />
<br />
NASA administrator Jim Bridenstine is enthusiastic about developing space as a source of resources and enabling economic growth. He's show interest in lunar poles as low hanging fruit.<br />
<br />
Near Earth Asteroids are also a low hanging fruit. If Bridenstine's goal is to expand our economic activity into deep space, NEOCam is a great investment.<br />
<br />
A few days ago Marshall Eubanks commented:<br />
<br />
<blockquote class="tr_bq">
<span style="background-color: #eff1f3; color: #1d2129; font-family: , , "blinkmacsystemfont" , ".sfnstext-regular" , sans-serif; font-size: 13px;">NEOCam is not in good shape. Over a year ago it was given one additional year of fairly minimal support. About all that was said about it in this month's SBAG meeting was that it "Continues in extended Phase A" - i.e., on life support.</span></blockquote>
<br />
I hope this changes. We need a telescope devoted to asteroid discovery.<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com4tag:blogger.com,1999:blog-3596550435682943926.post-62914819081912389442018-06-30T09:46:00.000-07:002020-04-13T12:43:57.064-07:00Space Meow Boys<div class="separator" style="clear: both;">
<br /></div>
<span style="font-size: large;"><b>Sections of this long post:</b></span><br />
<br />
1) <b><a href="http://hopsblog-hop.blogspot.com/2018/06/space-meow-boys_30.html#SpaceCadets">Space Cadets</a></b><br />
2) <b><a href="http://hopsblog-hop.blogspot.com/2018/06/space-meow-boys_30.html#MeowBoys">Space Meow Boys</a></b><br />
3) <b><a href="http://hopsblog-hop.blogspot.com/2018/06/space-meow-boys_30.html#Murphy">Tom Murphy</a></b><br />
4) <b><a href="http://hopsblog-hop.blogspot.com/2018/06/space-meow-boys_30.html#Nicoll">James Nicoll</a></b><br />
5) <b><a href="http://hopsblog-hop.blogspot.com/2018/06/space-meow-boys_30.html#Stross">Charlie Stross</a></b><br />
6) <b><a href="http://hopsblog-hop.blogspot.com/2018/06/space-meow-boys_30.html#Frontier">Opening A New Frontier Is Doable</a></b><br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="SpaceCadets">
<b><span style="font-size: large;">Space Cadets</span></b></div>
<br />
<br />
We are confined to a small, fragile planet. Being limited to a finite body of resources mean <a href="http://hopsblog-hop.blogspot.com/2016/02/limits-to-growth-logistic-vs-exponential.html">logistic growth</a>. And we're rapidly approaching the ceiling to our logistic growth.<br />
<br />
Opening a vast new frontier would allow growth for centuries or even thousands of years. Breaking free of Cradle Earth would be the most dramatic turning point in human history. If it’s possible then this goal is well worth pursuing.<br />
<br />
But can we open the solar system to settlement and economic use? This is an open question in my opinion.<br />
<br />
Some say space settlement is impractical. Be content with our limits, we’re told. Trying to push past our boundaries is a waste of time and we shouldn’t even try.<br />
<br />
Civil, rational arguments are worth listening to. But some discussions are long on vitriol and short on math and physics.<br />
<br />
<b>Tarring With A Wide Brush</b><br />
<br />
One dirty technique is tarring with a wide brush -- First find weak members in a group. Then hold up these members up as representative of the entire group. Give them a label.<br />
<br />
Physics professor Tom Murphy does this. He holds up his clueless students as examples of space enthusiasts and tars us all with the label <b><i>space cadets</i></b>. Judging by <a href="https://dothemath.ucsd.edu/2011/10/why-not-space/">the stories he tells</a>, his students are some of the stupidest people on the planet. I suspect he teaches Astronomy 101 for Liberal Arts Majors.<br />
<br />
Science fiction writer Charles Stross and book reviewer James Nicoll also like to use the label <b><i>space cadet</i></b>. They point to folks from Usenet who are long on wishful thinking and short on math skills. Their flavor of space cadet tends to be white and Libertarian.<br />
<br />
<b>Wrestling With A Pig</b><br />
<br />
Friends tell me “Don’t wrestle with a pig. You both get dirty and the pig likes it.” What they don’t realize is that I too am a pig. I love to wrestle in the mud!<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5mQeCm3BWnm4fcjB3AxBnkehVa7gHYv7jDbwy7b_-4b3JHWNRcuhH-fh94koD2KwvJIf87IBBy7eiNsK-qdMdi1nkia4YtrNozMCS8bEwChKzAOXYybMRJ91P9fTgw62JFKMBoMvzkIXm/s1600/Hop+the+Hog.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="774" data-original-width="1115" height="222" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5mQeCm3BWnm4fcjB3AxBnkehVa7gHYv7jDbwy7b_-4b3JHWNRcuhH-fh94koD2KwvJIf87IBBy7eiNsK-qdMdi1nkia4YtrNozMCS8bEwChKzAOXYybMRJ91P9fTgw62JFKMBoMvzkIXm/s320/Hop+the+Hog.jpg" width="320" /></a></div>
<br />
<br />
I don't mind their dirty tricks. I'll do the same.<br />
<br />
First I'll find nay sayers clueless in math and science. My label will be <b><i>Space Meow Boys.</i></b><br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="MeowBoys">
<b><span style="font-size: large;">Space Meow Boys</span></b></div>
<br />
<br />
Tom Murphy, James Nicoll and Charlie Stross are my examples of space meow boys.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFcC4mvhfCQw3HtCZ2JvElbMikdFCO10C2yt4Sl2kokR-v8OJOmAOTB4T3tbyy3aHGueU2vMu3N7iHbsYxmVW9Lwru8McLSvAfbMR7R79NltjXIP_m6dnt8Qn3x5q7DE39VFFy3KmrCIq1/s1600/StrossNicoll.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="801" data-original-width="1301" height="394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFcC4mvhfCQw3HtCZ2JvElbMikdFCO10C2yt4Sl2kokR-v8OJOmAOTB4T3tbyy3aHGueU2vMu3N7iHbsYxmVW9Lwru8McLSvAfbMR7R79NltjXIP_m6dnt8Qn3x5q7DE39VFFy3KmrCIq1/s640/StrossNicoll.jpg" width="640" /></a></div>
<br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="Murphy">
<b><span style="font-size: large;">Tom Murphy</span></b></div>
<br />
<br />
Let's look at Murphy’s blog post <a href="https://dothemath.ucsd.edu/2011/10/stranded-resources/">Stranded Resources</a>.<br />
<br />
Murphy correctly puts a big emphasis on delta V and <a href="http://hopsblog-hop.blogspot.com/2012/08/mf-is-mofo-tyranny-of-rocket-equation_21.html">Tsiolkovsky’s rocket equation</a>. But he sucks at calculating delta V. From his blog:<br />
<br />
<blockquote class="tr_bq">
The next plot puts this in perspective, albeit only in simplified, approximate terms. The bottom of the plot represents the Earth’s ground. It takes 7.7 km/s of velocity to get to LEO (actually, it takes the equivalent of about 9.5 km/s because much effort is expended just climbing out, in addition to establishing the orbital speed). At 11.2 km/s, we’re free to take on the solar system. The plot is based on minimum-energy Hohmann transfer orbits.</blockquote>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBeWurjfSohuJalcdWSHvvBpt8LS4AWM5mDyeSnYIk1iKt-U6bFal9t2aGSpS1Ug0b3szTYqjVUJlSjfihK7lfIk9LloYPa6RDStEVkcObSH0hA8ExrzcHJh61vqAjlcmb3ZffBWm6LD3-/s1600/Screen+Shot+2018-06-21+at+9.39.58+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="815" data-original-width="1032" height="504" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBeWurjfSohuJalcdWSHvvBpt8LS4AWM5mDyeSnYIk1iKt-U6bFal9t2aGSpS1Ug0b3szTYqjVUJlSjfihK7lfIk9LloYPa6RDStEVkcObSH0hA8ExrzcHJh61vqAjlcmb3ZffBWm6LD3-/s640/Screen+Shot+2018-06-21+at+9.39.58+AM.png" width="640" /></a></div>
<br />
<br />
<blockquote class="tr_bq">
Each planet is represented by three dots: the top one being outside the planet’s grip in an identical solar orbit, the next one down at low-planet orbit (akin to LEO), and the lowest represents being at rest on the surface. For Saturn and Jupiter, these surface points are off the chart—so taxing is this requirement. And for these two, there’s no “there” there anyway to land on. Crudely speaking, we must have the means to accomplish all vertical traverses in order to make a trip. <b>For instance, landing on Mars from Earth requires about 17 km/s of climb, followed by a controlled 5 km/s of deceleration for the descent. Thus it takes something like 20 km/s of capability to land on Mars</b>, . . .</blockquote>
<br />
I bolded Murphy’s discussion of the Earth to Mars trip. Let’s look at his delta V.<br />
<br />
He takes Earths 11.2 km/s escape velocity and adds in the ~6 km/s difference between Earth’s and Mars’ heliocentric orbits and then adds in Mars 5 km/s escape velocity. Which gives 22 km/s. Then Murphy leaves us with the impression he‘s being generous when he rounds down to 20 km/s<br />
<br />
A first year aerospace student would cringe at Murphy’s bungled math. You don’t simply add Vescape and <a href="http://hopsblog-hop.blogspot.com/2013/03/what-heck-is-vinf.html">Vinfinity</a>.<br />
<br />
To get velocity of the hyperbolic orbit needed for TMI (Trans Mars Injection):<br />
<br />
<div style="text-align: center;">
Vhyperbola = sqrt(Vescape<sup>2</sup> + Vinfinity<sup>2</sup>)</div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh2rqFVe1X7tbXgzOwNZY2YWNszBRAouJFzA1qC1RtKLFfhW6P2QXqR3yjM7Zqzk7zFaHrDxIpYlMtyLBU712UCTIQH_lc5nYp2Q2XmMYnPmLzA8rAk953tysTxYinW3CCq2SF8Yi-XW36/s1600/Screen+Shot+2017-07-28+at+10.39.45+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="434" data-original-width="772" height="223" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh2rqFVe1X7tbXgzOwNZY2YWNszBRAouJFzA1qC1RtKLFfhW6P2QXqR3yjM7Zqzk7zFaHrDxIpYlMtyLBU712UCTIQH_lc5nYp2Q2XmMYnPmLzA8rAk953tysTxYinW3CCq2SF8Yi-XW36/s400/Screen+Shot+2017-07-28+at+10.39.45+AM.png" width="400" /></a></div>
<br />
<br />
A memory device is to think of Vescape and Vinfinity as the legs of a right triangle. Velocity of a hyperbolic orbit would be the hypotenuse.<br />
<br />
Correctly patching conics get us 17 km/s from Earth surface to Mars surface<br />
<br />
<b>What About The Atmosphere?</b><br />
<br />
Murphy points to a penalty imposed by Earth’s atmosphere:<br />
<br />
<blockquote class="tr_bq">
It takes 7.7 km/s of velocity to get to LEO (actually, it takes the equivalent of about 9.5 km/s because much effort is expended just climbing out, in addition to establishing the orbital speed).</blockquote>
<br />
Yes, we suffer a loss of around 2 km/s to climb above the earth's atmosphere. There's some atmospheric friction as well as gravity loss during ascent. We'll give Murphy this 2 km/s. So our delta v budget goes up to 19 km/s.<br />
<br />
But an atmosphere also offers the possibility of aerobraking. Is it possible Murphy hasn't heard of aerobraking? Or is he dishonestly focusing on the delta V penalties of an atmosphere while ignoring the benefits? The charitable judgement here is that Murphy is horribly clueless.<br />
<br />
Aerobraking at the Mars end of an Earth to Mars trip can shave 6 km/s off the delta V budget. This takes our delta V budget down to 13 km/s. This is less than what it takes to park a satellite in geosynchronous orbit, something we routinely do.<br />
<br />
Aerobraking at the Earth end of a Mars to Earth trip can shave 11 km/s off the delta V budget. This leaves a delta V budget of around 6 km/s for the Earth to Mars trip.<br />
<br />
<b>Grab That Asteroid!</b><br />
<br />
Asteroid retrieval is a notion entertained by <a href="http://www.johnslewis.com/">John S. Lewis</a>, Planetary Resources, Deep Space Industries and others. If not retrieval of an entire asteroid, then retrieval of commodities from an asteroid.<br />
<br />
Murphy argues against this using a ridiculous straw man scenario:<br />
<br />
<blockquote class="tr_bq">
The asteroid belt is over 20 km/s away in terms of velocity impulse. If the goal is to use the raw materials for production on Earth or in Earth orbit, we have to supply about 10 km/s of impulse. We would probably try to get lucky and find a nickel-metal asteroid in an unusual orbit requiring substantially less energy to reel it in. So let’s say we can find something requiring only 5 km/s of delta-v. Our imagined prize will be a cube 1 km on a side, having a mass around 1013 kg. This is very small for an asteroid, but we need to moderate our ambitions. From a resource point of view, it’s still a lot. </blockquote>
<blockquote class="tr_bq">
To get this asteroid moving at 5 km/s with conventional rocket fuel (or any “fuel” that involves spitting the mass elements/ions out at high speed) would require a mass of fuel approximately twice that of the asteroid. As an example, using methane and oxygen, (4 kg of O2 for every 1 kg of CH4), we would require two years’ of global natural gas production to be delivered to the asteroid (now multiply this by a large factor for the fuel to actually deliver it from Earth’s potential well). The point is that we would be crazy to elect to push the asteroid our way with conventional rockets.</blockquote>
<br />
Four things wrong this picture.<br />
<br />
1) Murphy hasn't heard of NEAs? There are NEAs (Near Earth Asteroids) much closer to the Earth-Moon system. The <a href="http://kiss.caltech.edu/final_reports/Asteroid_final_report.pdf">Keck Report</a> talks about NEAs that could be parked in a loose lunar orbit for as little as .17 km/s. <a href="https://en.wikipedia.org/wiki/2006_RH120">2006 RH120</a> was temporarily captured to the earth moon system with no delta V.<br />
<br />
2) Murphy wants to use methane/oxygen bipropellant. This has an exhaust velocity of around 4 km/s in a vacuum. The Keck folks propose using xenon and Hall Thrusters. Exhaust velocity for this sort of ion engine can easily be 30 km/s.<br />
<br />
3) A kilometer asteroid is far too large for practical rockets to retrieve. It would also be insanely dangerous. The Tunguska event likely came from an object between 60 and 200 meters in diameter. The Chixculub impact which wiped out the dinosaurs was thought to have been 10 to 15 kilometers. Perhaps a misdirected rock 1 kilometer in diameter wouldn't be an extinction level event. But it'd certainly cost trillions in property damage. The Keck folks talk about safety considerations at the bottom of page 15 of <a href="http://kiss.caltech.edu/final_reports/Asteroid_final_report.pdf">their report</a>. They look at retrieving a 5 meter rock. Should a 5 meter rock fall earthward, it'd burn up harmlessly in the upper atmosphere.<br />
<br />
4) Murphy assumes a metal rich asteroid. He could spend a few minutes Googling and find that water is the first commodity asteroid miners hope to exploit. Propellant not at the bottom of an 11.2 km/s gravity well would be a game changer that would reduce the cost of spaceflight. And cheaper spaceflight is a prerequisite to profitably exploiting asteroidal metals.<br />
<br />
Plugging Murphy's 5 km/s delta V budget and 4 km/s exhaust velocity into the rocket equations tells use that we'd need more than two tonnes of propellant for every tonne of asteroid.<br />
<br />
Plugging in .17 km/s delta V and 30 km/s exhaust velocity gives 6 kilograms of propellant needed to park a one tonne asteroid.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuuysZ8GJhsn3jmMFE2a3hCDweGcWlhtkGs35KNkwOil_8b_oTj03ZYCSk-laEoxkD9p8rSTNr4duzet6YZKO4N2oOEAEFoxnznqd1IG7JU832XNTSpDwj6-SYUCkQralmsV9_wvpMHRCC/s1600/MurphyHandWaving.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="758" data-original-width="1600" height="302" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuuysZ8GJhsn3jmMFE2a3hCDweGcWlhtkGs35KNkwOil_8b_oTj03ZYCSk-laEoxkD9p8rSTNr4duzet6YZKO4N2oOEAEFoxnznqd1IG7JU832XNTSpDwj6-SYUCkQralmsV9_wvpMHRCC/s640/MurphyHandWaving.jpg" width="640" /></a></div>
<br />
<br />
<div style="text-align: center;">
The fellow on the left is Tom Murphy. To the right is a self portrait.</div>
<br />
Sometimes Murphy tries to excuse himself by pointing to his waffle words and furiously waving his hands. He seems to think words like "approximately" or "roughly" salvage his questionable claims.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKv3jUqXlUvCKHfNHRblER65ncRgEJYO8B7aLRkK0Gtx2nSjZw4ozUFO3vzzYpuP-Y5nrfiCmPoEDYhXdHD1mBsJKFwA4_-vYoyLECGNTIeLKHdUuNJQbjl1dIsfTrGnxCyBJWSlvL0lA_/s1600/Tom+Murphy+2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1098" data-original-width="1584" height="442" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKv3jUqXlUvCKHfNHRblER65ncRgEJYO8B7aLRkK0Gtx2nSjZw4ozUFO3vzzYpuP-Y5nrfiCmPoEDYhXdHD1mBsJKFwA4_-vYoyLECGNTIeLKHdUuNJQbjl1dIsfTrGnxCyBJWSlvL0lA_/s640/Tom+Murphy+2.jpg" width="640" /></a></div>
<br />
<div style="text-align: center;">
Only 3 orders of magnitude off.</div>
<br />
<b>Refuel In Space?</b><br />
<br />
The lunar cold traps <a href="https://www.nasa.gov/mission_pages/Mini-RF/multimedia/feature_ice_like_deposits.html">are thought to have rich deposits of water ice as well as other volatile ices</a>. These potential propellant sources are about 2.5 km/s from EML1 and <a href="http://hopsblog-hop.blogspot.com/2015/05/eml2.html">EML2</a>.<br />
<br />
Here's some delta V maps focusing on EML1 and <a href="http://hopsblog-hop.blogspot.com/2015/05/eml2.html">EML2</a>:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA_x-0ZiVjkgIc46iFlSMm1a6ETqUPwmwXiLTLMGO11Aa5mAb-EQWnkDS1u2bN-HaUy49V9XmUtuEFggqde7U6-dYYR11-NQnsa5YTwIRx4FkMj8AYYHdvsQ4GEh7bAy4icCGa1TIK-OYS/s1600/DeltaVEarthMoonMarsAsteroid+Horiz.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1019" data-original-width="1600" height="406" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA_x-0ZiVjkgIc46iFlSMm1a6ETqUPwmwXiLTLMGO11Aa5mAb-EQWnkDS1u2bN-HaUy49V9XmUtuEFggqde7U6-dYYR11-NQnsa5YTwIRx4FkMj8AYYHdvsQ4GEh7bAy4icCGa1TIK-OYS/s640/DeltaVEarthMoonMarsAsteroid+Horiz.jpg" width="640" /></a></div>
<br />
<br />
There are also asteroid folks who hope to mine water from NEAs. See <a href="https://www.youtube.com/watch?v=VLouRKHknOU">this Planetary Resources video</a> or <a href="https://www.youtube.com/watch?v=J0vkqQN44I4">this Deep Space Industries video</a>. Some NEAs are up to 40% water by mass and are only a small delta V nudge from being parked in lunar orbit. A water rich asteroid parked in lunar orbit would be even closer to EML1 and EML2.<br />
<br />
What is Murphy's argument against refueling in space?<br />
<br />
He tells us it'd take a lot of delta V to get propellant from Jupiter or Titan.<br />
<br />
<blockquote class="tr_bq">
Since the large delta-v’s required to get around the solar system require a lot of fuel, and we have to work hard to lift all that fuel from the Earth’s surface, could we just grab hydrocarbons from Jupiter or Titan and be on our way? </blockquote>
<blockquote class="tr_bq">
Let’s say you arrived in Jupiter orbit running on fumes, relying on the gassy giant to restock your coffers. In order to get close enough to Jupiter, you’ll be skimming the cloud-tops at a minimum of 42 km/s. Getting 1 kg of fuel on board will require you to accelerate the fuel to the speed of your spacecraft, at a kinetic energy cost of 885 MJ. The energy content of methane is 13 kcal/g, or 54 MJ/kg. Oops. Not even enough to pay for itself, energetically. Get used to Jupiter. And I have completely ignored the fact that you need marry two O2 molecules to each molecule of methane, meaning you actually get only 11 MJ per kilogram of total fuel. Utterly hopeless.</blockquote>
<br />
No shit, Sherlock. Knock yourself out beating up this straw man.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWZ9lvHaUUOj4nqfI1qT8ZVTqIaY9t3chWshHHEarzU757MV51hNyWx0lmrMBlbRH-QC4wuA2aymsK7LdG8zGVpDqFvDL-162-hy13T3VB9ETst9HNZHski4Hap3MAPU4pd0D4Jas1O569/s1600/Jupiter+Gas+Pump.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1183" data-original-width="1600" height="472" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWZ9lvHaUUOj4nqfI1qT8ZVTqIaY9t3chWshHHEarzU757MV51hNyWx0lmrMBlbRH-QC4wuA2aymsK7LdG8zGVpDqFvDL-162-hy13T3VB9ETst9HNZHski4Hap3MAPU4pd0D4Jas1O569/s640/Jupiter+Gas+Pump.jpg" width="640" /></a></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: center;">
Tom Murphy's argument is perhaps the stupidest straw man ever.</div>
<br />
<b>Momentum Exchange Tethers</b><br />
<br />
In the comments section for Stranded Resources, Monte Davis writes:<br />
<br />
<blockquote class="tr_bq">
At the level of fundamental elegance, you can’t beat tethers: instead of throwing away momentum in exhaust, you just keep re-using it as payloads are slung around — assuming tethers at all sources/destinations and an abundance of payloads. Before that, make-up energy could be supplied by spinning up tethers slowly with a low-thrust solar-electric or nuclear-electric drive.</blockquote>
<br />
Murphy replies to Davis:<br />
<br />
<blockquote class="tr_bq">
I don’t follow the first point about not throwing away momentum in the form of exhaust in a tether system. Without throwing away momentum, you can gain none (and go nowhere). If stranded on a frictionless lake on a sled piled with bricks, the only way off is to hurl bricks away. If the bricks are tethered to you, you may be able to move about as mass is redistributed, but the center of mass will be in the same place always.</blockquote>
<br />
Momentum isn't thrown away. It's exchanged.<br />
<br />
An orbital tether would not sit motionless like a brick on a frozen lake. It would drop after catching a payload from a lower orbit. It would also drop when throwing a payload to a higher orbit.<br />
<br />
However an orbital tether would rise after dropping a payload to a lower orbit. It would also rise when catching a payload from a higher orbit.<br />
<br />
With two way traffic an orbital tether could balance momentum draining maneuvers with momentum boosting maneuvers and thus maintain an orbit without huge amounts of propellant.<br />
<br />
Also as Davis mentions, a tether can use ion engines. Ion engines can easily have 30 km/s exhaust velocities while the best chemical is around 4.4 km/s. This is a much more efficient way to restore momentum. With low thrust engines it would take a long time to build momentum but that would be okay if there were weeks between tether maneuvers.<br />
<br />
Monte Davis is a science writer and editor who's worked for Omni, Discover, Psychology Today and other publications. He's got a chemistry degree from Princeton. In space forums Davis usually plays the devil's advocate against would be space colonizers.<br />
<br />
Murphy could have invested 4 or 5 minutes Googling momentum exchange tethers. But he blows off Monte Davis as if he's one of his clueless students in Astronomy 101 for Liberal Arts Majors.<br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="Nicoll">
<b><span style="font-size: large;">James Nicoll</span></b></div>
<br />
<br />
James Nicoll reviews science fiction. An old Heinlein chestnut is "If you can get your ship into orbit, you're halfway to anywhere." Nicoll attempts to play with this notion at <a href="https://james-davis-nicoll.dreamwidth.org/3598740.html">More Words Deeper Hole</a>.<br />
<br />
<blockquote class="tr_bq">
Apparently the subject line I was going to use is offensive so I will go with "halfway to anywhere" </blockquote>
<blockquote class="tr_bq">
james_nicoll<br />
april 1st, 2012 </blockquote>
<blockquote class="tr_bq">
Suppose it's the future and further suppose that space tourism actually takes off enough that there are excursions to the Moon akin to what we see in Antarctica. Although probably not the 37,000 people a year you see headed to Antarctica because going to the Moon is going to a crapton more expensive. </blockquote>
<blockquote class="tr_bq">
Further, suppose<br />
it occurs to someone whose life centers on ferrying rich bastards back and forth to the Moon that the delta vee to go from Low Earth Orbit (LEO) to Low Lunar Orbit (LLO) is about 8 km/s. It's the same the other way, assuming no aerobraking at the Earth end (No aerobraking at the Earth end means big mass ratios or some kind of fuel depot in LLO). That's considerably more delta vee than it takes to to Mars from the Moon and it further occurs to them it might be fun on the next trip home to leave the tourists on the Moon and take an unsheduled excursion to Mars.</blockquote>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQqbOmZO1uxNAAQmL30v-Xjkb6vGeT1ErVLjXlJiQ2DLZHIM-0FNjrty_-c2qAWIA4jtKDWXcwRHMFZctOY6W03A-ZFaSlvVggqHUpqA5vAFbQTFW2U_TurLO8IGjJa4ef2-kbOf68naSC/s1600/Screen+Shot+2018-06-19+at+5.50.26+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1058" data-original-width="748" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQqbOmZO1uxNAAQmL30v-Xjkb6vGeT1ErVLjXlJiQ2DLZHIM-0FNjrty_-c2qAWIA4jtKDWXcwRHMFZctOY6W03A-ZFaSlvVggqHUpqA5vAFbQTFW2U_TurLO8IGjJa4ef2-kbOf68naSC/s640/Screen+Shot+2018-06-19+at+5.50.26+PM.png" width="452" /></a></div>
<br />
<br />
<blockquote class="tr_bq">
How would you go about adapting a vehicle designed to do the LEO-LLO trip to a LLO-Mars trip? </blockquote>
<blockquote class="tr_bq">
The first big issue is going to be air. Assuming a dozen passengers and three crew, and about a week to the Moon and back, the ship probably doesn't have more than 105 person-days of O2. Fast but still reasonably delta-vee conservative orbit to Mars is about 180 days. </blockquote>
<blockquote class="tr_bq">
I suppose, this being fiction, you could do it the other way: the would-be Marsnaut needs 180 person-days, therefore the LEO-LLO transfer ship carries a couple of dozen passengers and some crew. That will at least get the Marsnaut to Mars alive.</blockquote>
<br />
<b>Delta V</b><br />
<br />
Let's start with James' delta V budget.<br />
<br />
<blockquote class="tr_bq">
it occurs to someone whose life centers on ferrying rich bastards back and forth to the Moon that the delta vee to go from Low Earth Orbit (LEO) to Low Lunar Orbit (LLO) is about 8 km/s.</blockquote>
<br />
According to the Wikipedia delta V chart James snagged, it's 4.1 km/s from LEO to L4/5 and then .7 km/s to lunar orbit.<br />
<br />
4.1 + .7 = 4.8, not 8.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgU5pc-ZO6VZrUlVGXBzbGsuiTbjiO3K58erS5SFiP8f3IXeLZi4GTV3bvAcfb-WnR-kt1R65CkeHdgHtdJmQGeucSYUpAh-t-IR3QzOYcCuv0CYdjGGYY8zDQJ_8B8ZArvYnSAR56F6L_O/s1600/NicollDV.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="862" data-original-width="1284" height="428" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgU5pc-ZO6VZrUlVGXBzbGsuiTbjiO3K58erS5SFiP8f3IXeLZi4GTV3bvAcfb-WnR-kt1R65CkeHdgHtdJmQGeucSYUpAh-t-IR3QzOYcCuv0CYdjGGYY8zDQJ_8B8ZArvYnSAR56F6L_O/s640/NicollDV.jpg" width="640" /></a></div>
<br />
<br />
A direct route from LEO to LLO would be more like 4 km/s.<br />
<br />
For hard SF folks, 8 km/s from LEO to LLO is a glaring error. But it's no biggie for the English Lit types that participate in James' forum. They don't even notice.<br />
<br />
<b>Aerobraking</b><br />
<br />
James stipulates<br />
<br />
<blockquote class="tr_bq">
It's the same the other way, assuming no aerobraking at the Earth end (No aerobraking at the Earth end means big mass ratios or some kind of fuel depot in LLO). That's considerably more delta vee than it takes to to Mars from the Moon and it further occurs to them it might be fun on the next trip home to leave the tourists on the Moon and take an unsheduled excursion to Mars.</blockquote>
<br />
Why on earth would James stipulate no aerobraking? This is a very standard technique. Is this because his premise rests on LLO to Mars taking less delta V than LLO to LEO?<br />
<br />
Maybe he's heard Mars folks say LEO to Mars is less delta V than LEO to the moon. Which is true enough <i><b>if aerobraking is used</b></i>. With no aerobraking we'd need to do any where from .7 km/s for Mars capture to a 6 km/s burn for a soft landing. Or else we'd sail right past Mars back into a heliocentric orbit.<br />
<br />
<b>Hohmann Launch windows</b><br />
<br />
Here's the biggest howler:<br />
<br />
<blockquote class="tr_bq">
and it further occurs to them it might be fun on the next trip home to leave the tourists on the Moon and take an unsheduled excursion to Mars.</blockquote>
<br />
An unscheduled excursion?! Unless James’ ferry guys have a huge delta V budget, the ship's doing a Hohmann transfer. Windows for Earth to Mars Hohmann open once each 2.14 years. Lots of pre-planning is needed to take advantage of these rare windows. A trip to Mars isn't something you do at the drop of a hat.<br />
<br />
As usually happens, James post stimulates a lively conversation. Most of the participants don't notice the howlers. The biggest concern seems to be sufficient air and food for the long trip.<br />
<br />
A problem they seem oblivious to is radiation. An 8 month trip would expose the passengers to a lot more GCRs and solar flares than the 4 day LLO to LEO trip. Much more radiation protection would be needed. A few meters of water are often suggested to protect the passengers from GCRs. A few meters of water around the ship exterior would be a lot more massive than the air, food and drinking water James and his friends were obsessing over.<br />
<br />
At one time I regarded James was one of the more numerate participants in science fiction forums. But he’s been spending too much time with SJWs and English Lit folks. Not that I dislike social justice or English literature. But if James wants to talk hard SF, he needs to revisit some of his math and physics textbooks.<br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="Stross">
<b><span style="font-size: large;">Charlie Stross</span></b></div>
<br />
<br />
Charlie Stross was one of the participants in the Nicoll post I just fisked. In that forum he goes by the handle <i>autopope</i>. Nicoll’s lack of math and science savvy was not noticed by Stross or most of those commenting.<br />
<br />
Stross was <a href="http://www.antipope.org/charlie/blog-static/2011/10/id-hate-to-have-his-email-inbo.html">also crowing</a> that physics professor Tom Murphy shared his opinions, as if that validates his views.<br />
<br />
But we shouldn’t condemn Stross because of the company he keeps. Instead, let’s look at his <a href="http://www.antipope.org/charlie/blog-static/2007/06/the_high_frontier_redux.html">High Frontier Redux</a>.<br />
<br />
It starts out noting the outer solar system and Alpha Centauri are far away and settling these regions isn’t practical. This is like saying the Americas were out of reach for the early humans in Africa. But the Americas became accessible after humans spread across Asia and reached the Bering Strait.<br />
<br />
To show the Kuiper Belt is forever beyond reach, Stross needs to demonstrate intermediate destinations aren’t within reach.<br />
<br />
Later he does argue against colonizing neighboring bodies. But starting off with the most difficult, furthest destinations is wasting the reader’s time.<br />
<br />
Let’s look at Stross’ argument against developing the moon:<br />
<br />
<blockquote class="tr_bq">
What about our own solar system? </blockquote>
<blockquote class="tr_bq">
After contemplating the vastness of interstellar space, our own solar system looks almost comfortingly accessible at first. Exploring our own solar system is a no-brainer: we can do it, we are doing it, and interplanetary exploration is probably going to be seen as one of the great scientific undertakings of the late 20th and early 21st century, when the history books get written. </blockquote>
<blockquote class="tr_bq">
But when we start examining the prospects for interplanetary colonization things turn gloomy again. </blockquote>
<blockquote class="tr_bq">
Bluntly, we're not going to get there by rocket ship. </blockquote>
<blockquote class="tr_bq">
Optimistic projects suggest that it should be possible, with the low cost rockets currently under development, to maintain a Lunar presence for a transportation cost of roughly $15,000 per kilogram. Some extreme projections suggest that if the cost can be cut to roughly triple the cost of fuel and oxidizer (meaning, the spacecraft concerned will be both largely reusable and very cheap) then we might even get as low as $165/kilogram to the lunar surface. At that price, sending a 100Kg astronaut to Moon Base One looks as if it ought to cost not much more than a first-class return air fare from the UK to New Zealand ... except that such a price estimate is hogwash. We primates have certain failure modes, and one of them that must not be underestimated is our tendency to irreversibly malfunction when exposed to climactic extremes of temperature, pressure, and partial pressure of oxygen. While the amount of oxygen, water, and food a human consumes per day doesn't sound all that serious — it probably totals roughly ten kilograms, if you economize and recycle the washing-up water — the amount of parasitic weight you need to keep the monkey from blowing out is measured in tons. A Russian Orlan-M space suit (which, some would say, is better than anything NASA has come up with over the years — take heed of the pre-breathe time requirements!) weighs 112 kilograms, which pretty much puts a floor on our infrastructure requirements. An actual habitat would need to mass a whole lot more. Even at $165/kilogram, that's going to add up to a very hefty excess baggage charge on that notional first class air fare to New Zealand — and I think the $165/kg figure is in any case highly unrealistic; even the authors of the article I cited thought $2000/kg was a bit more reasonable. </blockquote>
<blockquote class="tr_bq">
Whichever way you cut it, sending a single tourist to the moon is going to cost not less than $50,000 — and a more realistic figure, for a mature reusable, cheap, rocket-based lunar transport cycle is more like $1M. And that's before you factor in the price of bringing them back ... </blockquote>
<blockquote class="tr_bq">
The moon is about 1.3 light seconds away. If we want to go panning the (metaphorical) rivers for gold, we'd do better to send teleoperator-controlled robots; it's close enough that we can control them directly, and far enough away that the cost of transporting food and creature comforts for human explorers is astronomical. There probably are niches for human workers on a moon base, but only until our robot technologies are somewhat more mature than they are today; Mission Control would be a lot happier with a pair of hands and a high-def camera that doesn't talk back and doesn't need to go to the toilet or take naps.</blockquote>
<br />
<b>In Situ Resources</b><br />
<br />
Stross is right that human habitats in space would be massive. But he imagines every kilogram of a lunar habitat would be brought up from earth’s surface. Evidently Stross has never heard of <b><i>in situ resources</i></b>. At the lunar poles there are thought to be volatile ices — water ice as well as carbon dioxide ice and nitrogen compounds. Water and air to breathe could be extracted from local resources. Habs could be covered with regolith for radiation protection.<br />
<br />
Stross acknowledges that robots could establish infrastructure on the lunar surface. And in fact this is what <a href="http://www.spudislunarresources.com/Bibliography/p/118.pdf">Spudis and Lavoie advocate</a>.<br />
<br />
<b>In Situ Resources and Delta V</b><br />
<br />
Besides building habs and infrastructure to extract life support consumables, robots could also build propellant mines. Stross didn’t bat an eye when Nicoll stated LEO to LLO is 8 km/s. It is likely this science fiction writer has no notion what role delta V plays in the rocket equation.<br />
<br />
Mass propellant / mass payload = e<sup>(delta V/Vexhaust)</sup> - 1.<br />
<br />
Exhaust velocity of hydrogen/oxygen bipropellant is about 4.4 km/s. Now 3/4.4 is very close to ln(2).<br />
<br />
That means when using oxygen/hydrogen, every 3 km/s added to the delta V budget doubles over all mass.<br />
<br />
Starting with 1 tonne rocket dry mass plus payload,<br />
For 3 km/s you’d need 1 tonne propellant.<br />
For 6 km/s you’d need 3 tonnes propellant.<br />
For 9 km/s you’d need 7 tonnes propellant.<br />
And so on.<br />
<br />
Overall mass grows exponentially with increasing delta V. <a href="https://www.deviantart.com/hop41/art/The-legend-of-Paal-Paysam-188153459">The legend of Paal Paysam</a> illustrates the dramatic quantities exponential growth can give. Krishna challenged a king to a game of chess wagering a chess board with 1 grain of rice on the the first square, 2 grains on the second, 4 on the third and doubling each subsequent square. The king calculated the numbers for the first few squares and accepted. Here’s an illustration of Krishna’s wager:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie49GX4ptNmfyV5sJWNlj5c3Sag8dR1lMxT2SqzMQJbSi4O2l7l4Qp2OYsa3h3WqzAlX8hU0domtJwXMpIIOrCgoJ5j3ueBddSYKsZau1tsqOOXWXMjXuXmVjXJdvpzTbe32onkqAFZFLb/s1600/PaalPaysam.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="650" data-original-width="541" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie49GX4ptNmfyV5sJWNlj5c3Sag8dR1lMxT2SqzMQJbSi4O2l7l4Qp2OYsa3h3WqzAlX8hU0domtJwXMpIIOrCgoJ5j3ueBddSYKsZau1tsqOOXWXMjXuXmVjXJdvpzTbe32onkqAFZFLb/s640/PaalPaysam.jpg" width="532" /></a></div>
<br />
<br />
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; caret-color: rgb(0, 0, 0); color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-decoration: none; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
Breaking the rocket equation’s exponent into chunks has a dramatic effect on the amount of propellant used. With each propellent depot, the delta V budget starts over:</div>
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; caret-color: rgb(0, 0, 0); color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-decoration: none; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgo2yT52cKr933JuT9cwf0388CJuCXDF3276vJycwiui-lRXDBJZQ-fzILN3zP1Vmhvaz4YxpWTjGy8pzdBat9dSvVVjxmyuLa1PjxPQDbD73LEAvZNFBm4TpF9D-LJSDGjtGQO3g-SC2x5/s1600/RiceWithPropellantDepots-01.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1353" data-original-width="1128" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgo2yT52cKr933JuT9cwf0388CJuCXDF3276vJycwiui-lRXDBJZQ-fzILN3zP1Vmhvaz4YxpWTjGy8pzdBat9dSvVVjxmyuLa1PjxPQDbD73LEAvZNFBm4TpF9D-LJSDGjtGQO3g-SC2x5/s640/RiceWithPropellantDepots-01.jpg" width="532" /></a></div>
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; caret-color: rgb(0, 0, 0); color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-decoration: none; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<br /></div>
<div style="text-align: center;">
We can start back to 1 grain of rice at each propellant depot.</div>
<div style="text-align: center;">
Mount Everest is visible in this version, no longer covered with rice.</div>
<br />
<br />
Delta V from earth’s surface to LEO is about 9.5 km/s. LEO to lunar surface is about 6 km/s. The additional 6 km/s boosts four fold the mass that needs to be parked in LEO.<br />
<br />
If the ship could refuel in LEO, that would cut GLOW (Gross Lift Off Weight) four fold.<br />
<br />
Here’s a delta V map focusing on EML2 and LEO. Moon to LEO is about 3 km/s using aerobraking.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOYleSvEaVkb1yRgRk2MIb82oFXVE7X4w0-hjCPsqL89R_k9rGys2C54_5VrFiMU8G3SzQMTSL7Qi8AQgrqfEb-rAsZVYeNat1DwuNYjI2zbMBHlES_meZN5gSXmMmQTNIcLomZycXVQMG/s1600/DeltaVEML2toLEO.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="978" data-original-width="642" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOYleSvEaVkb1yRgRk2MIb82oFXVE7X4w0-hjCPsqL89R_k9rGys2C54_5VrFiMU8G3SzQMTSL7Qi8AQgrqfEb-rAsZVYeNat1DwuNYjI2zbMBHlES_meZN5gSXmMmQTNIcLomZycXVQMG/s640/DeltaVEML2toLEO.jpg" width="420" /></a></div>
<div style="text-align: center;">
<br /></div>
<div>
<br /></div>
<br />
But savings on propellent isn’t the chief advantage here. With an extraterrestrial propellant source, inter orbital tankers and ferries could move between orbits without ever suffering the extreme conditions of an 8 km/s re-entry into earth’s atmosphere.<br />
<br />
Also with delta V budgets on the order of 4 km/s, inter orbital vehicles can devote a higher <a href="http://hopsblog-hop.blogspot.com/2012/08/mf-is-mofo-tyranny-of-rocket-equation_21.html">mass fraction</a> to structure. Present day upper stages have less mass fraction than an aluminum Coke can. Which makes durable structure and adequate thermal protection very difficult if not impossible.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQdxO6vD4gAmANvtGRo6HpkbO0PFMNgL9go1jxLthEc1kGV_5-g3fuR6F-EcnKnme3o-xDwwfWEuUnCEhJTIltlSv2QyvZNz5vXQq9hTD5zEC73pvEP-NGt3aGrlfpkYOUIlZ4VzHntJXI/s1600/RacingVsMtnBike.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1389" data-original-width="1166" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQdxO6vD4gAmANvtGRo6HpkbO0PFMNgL9go1jxLthEc1kGV_5-g3fuR6F-EcnKnme3o-xDwwfWEuUnCEhJTIltlSv2QyvZNz5vXQq9hTD5zEC73pvEP-NGt3aGrlfpkYOUIlZ4VzHntJXI/s640/RacingVsMtnBike.jpg" width="536" /></a></div>
<br />
<div style="text-align: center;">
A racing bike vs a mountain bike.</div>
<div style="text-align: center;">
With a racing bike we want to minimize mass.</div>
<div style="text-align: center;">
But a racing bike is fragile while a mountain bike is durable and rugged.</div>
<div style="text-align: center;">
When an upper stage has a 4% dry <a href="http://hopsblog-hop.blogspot.com/2012/08/mf-is-mofo-tyranny-of-rocket-equation_21.html">mass fraction</a>, durability is not an option.</div>
<br />
Elon Musk and Jeff Bezos seem well on their way to developing economical, reusable booster stages. <a href="https://www.geekwire.com/2018/jeff-bezos-blue-origin-space-venture-go-moon-settlements/">Bezos wants to help establish lunar propellant mines</a>. If Bezos, Bridenstine et al successfuly export lunar propellant to LEO, upper stages could refuel before re-entry into the atmosphere. Reuse of upper stages is much more plausible if re-entry velocity is 4 km/s or less.<br />
<br />
<b>Space Elevators</b><br />
<br />
Stross mentions the possibility of <a href="http://hopsblog-hop.blogspot.com/2012/09/beanstalks-elevators-clarke-towers.html">Space Elevators</a>.<br />
<br />
Arthur C. Clarke popularized the notion with his novel <i>Fountains of Paradise</i>. Clarke, Asimov and Heinlein were writers from the great generation. They had some physics and tech savvy as well as an optimistic can-do attitude.<br />
<br />
Baby boomer SF writers are more about bleak dystopias and cautionary tales. Like main stream pop culture they rely on sex and glorifying substance abuse to sell their product. With a few exceptions, SF writers from my generation tend to suck at math and physics. Hopefully younger science fiction writers will pick up the mantles of Heinlein and Clarke.<br />
<br />
A space elevator was a good idea in the time of Clarke. Since then we’ve massive amounts of junk into Low Earth Orbit (LEO). Here is a panel from the Hubble telescope that spent 14 years in LEO:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEjrL-y6ZekWurdlQqxXLYvcXcOj_4UQQYxkQqjNrMjtD84vL1Eh2dqz6vY5329BEgnX5mwE1ZYunemibnMwNR007MP6OlSXVF_cNDe_MMNWhhvzbXi5WagwpR8gqWljP31MsXO8MQuueB/s1600/Hubble+Panel+debris+impacts.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="667" data-original-width="1000" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEjrL-y6ZekWurdlQqxXLYvcXcOj_4UQQYxkQqjNrMjtD84vL1Eh2dqz6vY5329BEgnX5mwE1ZYunemibnMwNR007MP6OlSXVF_cNDe_MMNWhhvzbXi5WagwpR8gqWljP31MsXO8MQuueB/s640/Hubble+Panel+debris+impacts.jpg" width="640" /></a></div>
<br />
<br />
See <a href="https://space.stackexchange.com/questions/4858/why-havent-more-spacecraft-satellites-been-hit-by-debris/4861">this Space Stack Exchange discussion on orbital debris</a>.<br />
<br />
The extreme height of a space elevator gives it enormous cross sectional area. Much more cross section than the panel pictured above. So even if we could manufacture long strands of Bucky tubes with insanely high tensile strength, the elevator would be severed by impacts.<br />
<br />
However full blown Clarke towers have smaller cousins: orbital tethers. Being a lazy baby boomer writer, Stross seems content to rehash tired 1970s SF ideas. It is possible Stross has never heard of orbital tethers.<br />
<br />
Orbital tethers can be placed in orbits relatively free of debris. They would be much shorter than a full blown Clarke Tower and would suffer much less stress. They could be made from existing materials like Zylon. I talk about orbital tethers at <a href="http://hopsblog-hop.blogspot.com/2016/08/tran-cislunar-railroad.html">Trans Cislunar Railroad</a>. Given two way traffic, a tether could harvest up momentum from higher orbits and trade it with the down momentum of lower orbits. Thus with two way traffic a tether could impart delta V with little expenditure of energy and propellant.<br />
<br />
Orbital tethers could also be anchored on Phobos and Deimos.<br />
<br />
Given tethers of modest mass, payloads can be exchanged between Phobos and Deimos via a Zero Relative Velocity Transfer Orbit (<a href="http://hopsblog-hop.blogspot.com/2016/01/deimos-tether.html#ZRVTO">ZRVTO</a>).<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8pdq9EjVtOIUE1n4VUSZQpv5iiA_wzjbxoHx-TVryWdr6xuGEr_93Jh3rnS8ZS4H_ryEMB5P5XZaWIYbuS8glakt4Ckbxs5D5ez_FLwBfxwBtiCTCBbMer6Gcycft-kBCYkL0yZafoGe-/s1600/PhobosToDeimos.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1302" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8pdq9EjVtOIUE1n4VUSZQpv5iiA_wzjbxoHx-TVryWdr6xuGEr_93Jh3rnS8ZS4H_ryEMB5P5XZaWIYbuS8glakt4Ckbxs5D5ez_FLwBfxwBtiCTCBbMer6Gcycft-kBCYkL0yZafoGe-/s400/PhobosToDeimos.jpg" width="325" /></a></div>
<br />
<br />
Given a somewhat more substantial tether, a Phobos tether could throw payloads down to a 1 A.U. perihelion (in other words, a transfer orbit to earth) or to a 3 A.U. aphelion (in other words a transfer orbit to the Main Belt).<br />
<br />
An upper Phobos tether capable of launching payloads to various regions of our solar system <a href="http://hopsblog-hop.blogspot.com/2016/01/upper-phobos-tether.html">needn't be that massive</a>.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJRa9V1t-m1lNWxV39ZRJZNv92o4Hyt6hjcnmF-K95BJGKI1ROnl2Dyjv9rdQsO9x2DRgrcWykgW-Up0pOBc7iOYtP8VpZzZqoavfR988ouZNi4RvYRRnE8edm0-tRN74BopDVxH4UMOjA/s1600/TetherPhobos.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1455" data-original-width="1600" height="582" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJRa9V1t-m1lNWxV39ZRJZNv92o4Hyt6hjcnmF-K95BJGKI1ROnl2Dyjv9rdQsO9x2DRgrcWykgW-Up0pOBc7iOYtP8VpZzZqoavfR988ouZNi4RvYRRnE8edm0-tRN74BopDVxH4UMOjA/s640/TetherPhobos.jpg" width="640" /></a></div>
<br />
<br />
A Phobos tether extending to Mars upper atmosphere would drop payloads into Mars atmosphere at .6 km/s. About mach two, the Concorde Jet would routinely do this through a much thicker atmosphere. This about 1/10 the velocity landers from earth normally enter Mars' atmosphere. A Phobos tether descending to Mars' upper atmosphere isn’t practical using Zylon but would certainly be doable if they manage to manufacture long lengths of Bucky tubes.<br />
<br />
<b>Summary of Stross' Errors</b><br />
<br />
Stross gives us numbers assuming all propellant and hab mass comes from earth's surface.<br />
<br />
Using in situ resources most of the hab mass can be made from materials at hand.<br />
<br />
More importantly there's the possibility of in situ propellant. This can drastically cut delta V budgets. Which cuts propellant and energy needed. It also makes robust, reusable vehicles possible.<br />
<br />
Momentum exchange tethers are doable. This would further reduce energy and propellant needed to travel between space destinations.<br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="Frontier">
<b><span style="font-size: large;">Opening A New Frontier Is Doable</span></b></div>
<br />
<br />
It is possible to establish infrastructure that would greatly reduce the cost of traveling about in space.<br />
<br />
Yes, it would be expensive but it is doable. Dennis Wingo's book <a href="https://www.amazon.com/Moonrush-Improving-Earth-Resources-Apogee/dp/1894959108">Moonrush</a> documents several examples of government/private enterprise partnerships establishing massive transportation and communication infrastructure. The trans continental railroad was such a collaboration.<br />
<br />
NASA administrator Jim Bridenstine has expressed his desire to work with SpaceX and Blue Origin to establish lunar and cislunar infrastructure. It is possible this could come to pass.<br />
<br />
But the effort would have better prospects for adequate funding if the public perceived it as possible. The space meow boys have used bad math and silly straw man arguments to strengthen the public perception that this is pie in the sky.<br />
<br />
The first steps towards opening the space frontier would be establishing infrastructure on other bodies. Semi-autonomous tele-robots are dropping in price while becoming more capable. British Petroleum has used R.O.V.s to build oil wells on the sea floor. It is possible to build the initial space infrastructure without a human presence.<br />
<br />
Once robots have established infrastructure to extract propellant and keep humans alive, the cost of human presence plummets.<br />
<br />
Why does Murphy argue so vehemently against a new frontier? He's worried that we'd be okay with trashing the earth if we had the option to move. <a href="https://www.youtube.com/watch?v=mrGFEW2Hb2g">Bill Maher makes the same argument</a>.<br />
<br />
Maher and Murphy are giving us a false dichotomy. We can do both. We need to work to preserve our home as well as open new frontiers. Space advocates are more aware than the average person that our precious planet is finite and fragile.<br />
<br />
For example Musk is also working on solar energy and electric cars in addition to his rockets. Bezos is advocating moving destructive mining and manufacturing out of our ecosphere.<br />
<br />
Musk and Bezos are doing more for a sustainable future than a million space meow boys.<br />
<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com6tag:blogger.com,1999:blog-3596550435682943926.post-53635635330279922962018-04-25T08:50:00.001-07:002018-04-25T08:50:12.346-07:00Tahoe recreational math conferenceI've been invited to talk at a recreational math conference at Lake Tahoe April 28.<br />
<br />
I will talk about the family of conics associated with a space elevator or a vertical orbital tether.<br />
<br />
The presentation combines stuff from a number of my earlier blog posts. <a href="http://cunews.info/TetherConicsBooklet.pdf">Here</a> is the pdf I will use for this talk.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz8pe1ctoe2XU7DVGRQ8XGEBF4bXairSv-nqQPCdCOzVMqR0WmnGF-iZUb6V2Eu2sfHXHUNHgTB2YoSJb9FgaU2lsQNI1Z8McaLOcvAK1V9xulXVwPJ6m6Rn3TsmEikNObA8YeJ3Wrpc94/s1600/Screen+Shot+2018-04-25+at+8.22.15+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="863" data-original-width="706" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz8pe1ctoe2XU7DVGRQ8XGEBF4bXairSv-nqQPCdCOzVMqR0WmnGF-iZUb6V2Eu2sfHXHUNHgTB2YoSJb9FgaU2lsQNI1Z8McaLOcvAK1V9xulXVwPJ6m6Rn3TsmEikNObA8YeJ3Wrpc94/s640/Screen+Shot+2018-04-25+at+8.22.15+AM.png" width="522" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
A screenshot from the cover of the booklet.</div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Pages 2 — 5 -- includes the visualizations I use to remember expressions for gravity and centrifugal acceleration. Which I use to show how canonical units are a whole lot easier to use than kilograms, kilometers and so on. For example the orbital periods or an orbit whose semi-major axis is k A.U. will have period k<sup>3/2</sup> years. An asteroid whose semi-major axis is 4 A.U. will have a period of 8 years. A 9 A.U. semi-major axis gives a period of 27 years.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Pages 13 — 14 -- I believe my general method for finding a ZRVTO orbit between tethers is new and original. If anyone knows of this method appearing in earlier publications, please give me a heads up.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Page 14 -- Most moons we know of are in nearly circular tide locked orbits. For such moons beanstalks through Planet-Moon L1 and L2 are plausible. I believe this would be a wonderful science device. But today's science fiction writers seems oblivious to any of the Lagrange points other than L4 and L5.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Pages 15 and 16 -- Shameless self promotion. I don't get any royalties on the Dover coloring books, I was paid a straight fee of $100 per page. Regardless, I'd like to see the books sell. A Dover editor placed his bets on me and I hope he is rewarded for this gamble. I do make money on T-shirt sales though. My T-shirts are available at <a href="http://ajo-copper-news.com/">Ajo-Copper-News.com</a> .</div>
<br />
<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com0tag:blogger.com,1999:blog-3596550435682943926.post-19324809233164242022017-06-09T11:30:00.000-07:002020-04-13T12:44:24.861-07:00Zylon Mars Elevator<div class="separator" style="clear: both;">
<br /></div>
<b><span style="font-size: large;">Mars Elevator With Conventional Materials</span></b><br />
<br />
Mars spins nearly the same rate as earth (about a 24.62 hour day). Mars has about 1/9 earth's mass. At 17,000 kilometers, altitude of Mars synchronous orbit is less than half the altitude of geosynchronous orbit (about 36,000 kilometers).<br />
<br />
These considerations have led some Mars enthusiasts to claim a Mars elevator made of conventional materials is possible. No bucky tubes or other science fiction material is needed, Kevlar will do. Is this true? I will take a look using <a href="http://hopsblog-hop.blogspot.com/2015/12/how-wolfes-tether-spreadsheet-works.html">Chris Wolfe's spreadsheet</a>.<br />
<br />
<b><span style="font-size: large;">Safety Factor</span></b><br />
<br />
In earlier blog posts using Wolfe's spreadsheet I used a safety factor of 1, a razor thin margin. The slightest scrape or nick will make the tether break. This is like drawing a pentagram to summon the demon Murphy's Law. No sensible entity would risk expensive payloads on such a narrow margin. Much less human lives. I hope to revise my earlier blog posts to include more sensible safety margins.<br />
<br />
In later blog posts I looked at scenarios using a safety factor of 3. With this margin a portion of tether can lose up to 2/3 of it's mass without breaking.<br />
<br />
In this post I'll use tables looking at a range of safety factors. With a safety factor of 2, I cut tensile strength in half. A safety factor of 3 cuts tensile strength to a third. Which is a lot like cutting exhaust velocity in the rocket equation. Increasing an exponent can make tether thickness sky rocket.<br />
<br />
<b><span style="font-size: large;">Mars Equator to Mars Synchronous Orbit</span></b><br />
<br />
This is the lower part of a Mars elevator. It exerts downward newtons that need to be balanced with upward newtons from elevator mass above Mars synchronous orbit.<br />
<br />
<table>
<tbody>
<tr>
<td><div style="text-align: center;">
<b>Safety</b></div>
<div style="text-align: center;">
<b> Factor </b></div>
</td><td><div style="text-align: center;">
<b>Zylon</b></div>
<div style="text-align: center;">
<b>Taper</b></div>
<div style="text-align: center;">
<b>Ratio</b></div>
</td><td><div style="text-align: center;">
<b>Tether to</b></div>
<div style="text-align: center;">
<b>Payload</b></div>
<div style="text-align: center;">
<b> Mass Ratio </b></div>
</td>
</tr>
<tr>
<td><div style="text-align: right;">
<div style="text-align: center;">
1</div>
</div>
</td><td><div style="text-align: right;">
13</div>
</td><td><div style="text-align: right;">
154</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
2</div>
</div>
</td><td><div style="text-align: right;">
162</div>
</td><td><div style="text-align: right;">
3191</div>
</td>
</tr>
<tr>
<td><div style="text-align: right;">
<div style="text-align: center;">
3</div>
</div>
</td><td><div style="text-align: right;">
2016</div>
</td><td><div style="text-align: right;">
51824</div>
</td>
</tr>
</tbody></table>
<br />
<div>
Payload is mass of elevator car as well as elevator car's contents. The elevator car will need to include motors and power source.<br />
<br />
<b><span style="font-size: large;">Mars Synchronous to Sub Deimos Elevator Top</span></b><br />
<br />
Elevator top is set 50 kilometers below Deimos' periapsis. This is to avoid collision. The counterweight and tether above Mars synchronous orbit must counterbalance the downward force of the lower elevator.<br />
<br />
<table><tbody>
<tr><td><div style="text-align: center;">
<b>Safety</b></div>
<div style="text-align: center;">
<b> Factor </b></div>
</td><td><div style="text-align: center;">
<b>Zylon</b></div>
<div style="text-align: center;">
<b>Taper</b></div>
<div style="text-align: center;">
<b>Ratio</b></div>
</td><td><div style="text-align: center;">
<b>Tether to</b></div>
<div style="text-align: center;">
<b>Payload</b></div>
<div style="text-align: center;">
<b> Mass Ratio </b></div>
</td>
<td><div style="text-align: center;">
<b>Counterweight</b></div>
<div style="text-align: center;">
<b>to Payload</b></div>
<div style="text-align: center;">
<b> Mass Ratio </b></div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
1</div>
</div>
</td><td><div style="text-align: right;">
1.02</div>
</td><td><div style="text-align: right;">
38</div>
</td>
<td><div style="text-align: right;">
1200</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
2</div>
</div>
</td><td><div style="text-align: right;">
1.03</div>
</td><td><div style="text-align: right;">
955</div>
</td>
<td><div style="text-align: right;">
14800</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
3</div>
</div>
</td><td><div style="text-align: right;">
1.05</div>
</td><td><div style="text-align: right;">
1761</div>
</td>
<td><div style="text-align: right;">
180000</div>
</td></tr>
</tbody></table>
<br />
<div>
</div>
<br />
<div style="color: black; font-style: normal; letter-spacing: normal; margin: 0px; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">
<b><span style="font-size: large;">The Whole Shebang</span></b><br />
<div style="font-weight: normal;">
<br /></div>
<b>Safety Factor 1</b><br />
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
Assuming lifting a 10 tonne elevator car and contents from Mars' surface and given a safety factor of 1, we'd need 10 * (38 + 154) tonnes of tether material. That'd be 1,920 tonnes of Zylon. Perhaps worthwhile if the elevator had a vigorous through put. I think these are the numbers Mars enthusiasts are talking about when they talk about Mars beanstalks made of Kevlar.</div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
Also needed would be a 12,000 tonne counterweight. That's about thirty times the mass of the I.S.S.. This to lift a 10 tonne elevator car from Mars' surface? The need for a stud hoss counterweight sinks the argument for a Mars elevator, in my opinion.</div>
<div style="font-weight: normal;">
<br /></div>
<b>Safety Factor 2</b><br />
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
10 * (162 + 955) = 11170. About 11 thousand tonnes of Zylon to lift a 10 tonne elevator car and contents.</div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
We'd need a nearly 150,000 tonne counterweight.</div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
I think it's pretty obvious a Zylon Mars elevator with a safety factor of two isn't worthwhile. I'm not going to bother looking at a safety factor of 3.</div>
<div style="font-weight: normal;">
<br /></div>
<b><span style="font-size: large;">Benefits</span></b><br />
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
The elevator top is moving at about 1.7 km/s. It needs another 1.6 km/s to achieve Trans Earth Insertion (TEI). From the surface of Mars it takes about 6 km/s for TEI. So the elevator cuts saves about 4.4 km/s off of trips to earth.</div>
<div style="font-weight: normal;">
<br /></div>
<b><span style="font-size: large;">Obstacles</span></b><br />
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
Given a sensible safety factor, a Zylon tether would need to be much more massive than the payload. The counterweight mass would dwarf the payload mass.</div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
Mars neighbors the main asteroid belt. Some rocks from the belt make their way to Mars neighborhood. Collision with asteroidal debris could cut the tether. Given this elevator's 20,000 km length and healthy taper ratio, there is a large cross sectional area. This increases likelihood of an impact.</div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
Also there is a chunk of Debris named Phobos which crosses the elevator's path every 10 hours or so.</div>
<div style="font-weight: normal;">
<br /></div>
<b><span style="font-size: large;">Comparison to Phobos Elevator</span></b><br />
<div style="font-weight: normal;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMCtOJyWqAAu7K33rYsXg02nK6hC-XF64OzQQX7tFkjvjp-imCowMOqJqw64Jx434M34jY5C86Poksy8Qqxqb_vi9zSIMToi0fXQMLIoraT1jh4g8MemDoJC6lD9nTwy9AR-4TBbHYxx6p/s1600/TetherPhobos.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1455" data-original-width="1600" height="582" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMCtOJyWqAAu7K33rYsXg02nK6hC-XF64OzQQX7tFkjvjp-imCowMOqJqw64Jx434M34jY5C86Poksy8Qqxqb_vi9zSIMToi0fXQMLIoraT1jh4g8MemDoJC6lD9nTwy9AR-4TBbHYxx6p/s640/TetherPhobos.jpg" width="640" /></a></div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
A Phobos elevator dropping to Mars' upper atmosphere and extending to Trans Ceres insertion is about 13,700 km. This about 6,000 km shorter than the Mars elevator described above. It also has a smaller taper ratio. This makes for a smaller cross sectional area to intercept debris. Being anchored at Phobos, this elevator won't collide with Phobos. The top is well below Deimos. orbit.</div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
This tether can provide Trans Ceres Insertion as well as Trans Earth Insertion.</div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
It takes about a .6 km/s suborbital hop for a Mars ascent vehicle to rendezvous with this tether foot.</div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
Using a safety factor of 1, the <a href="http://hopsblog-hop.blogspot.com/2016/01/upper-phobos-tether.html">upper Phobos tether</a> has a 3.21 payload to mass ratio. The <a href="http://hopsblog-hop.blogspot.com/2015/12/lower-phobos-tether.html">lower Phobos tether</a> has a tether to payload mass ratio of about 16.1. So from top to bottom, about twenty times the payload mass is needed in Zylon.</div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
<div style="font-weight: normal;">
The Phobos takes about 1/10 of the Zylon mass for a mars elevator with a safety factor of one.</div>
<div style="font-weight: normal;">
<br /></div>
<div class="separator" style="clear: both; font-weight: normal; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYX1desonhnMZLPhkmWd5TJZXT3au85KfYTTUfo0UILiVIIPaE0YYJXPqy43RHFpQSdvTYrZLkncZy753lNFWh-L7oqp6Gsyd0ZJpUeYiXJLcjwAq6F6arc7Z61ciaez9fCid4TwfDjvT2/s1600/Screen+Shot+2017-06-09+at+11.15.14+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="739" data-original-width="1172" height="402" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYX1desonhnMZLPhkmWd5TJZXT3au85KfYTTUfo0UILiVIIPaE0YYJXPqy43RHFpQSdvTYrZLkncZy753lNFWh-L7oqp6Gsyd0ZJpUeYiXJLcjwAq6F6arc7Z61ciaez9fCid4TwfDjvT2/s640/Screen+Shot+2017-06-09+at+11.15.14+AM.png" width="640" /></a></div>
<div style="font-weight: normal; text-align: center;">
A sub Deimos Mars elevator can't throw payloads above Mars escape velocity.</div>
<div style="font-weight: normal; text-align: center;">
But with higher taper ratio, it'd take ten times as much zylon mass than a Phobos elevator.</div>
<div style="text-align: center;">
<b>This is with a safety factor of 1.</b></div>
<div style="font-weight: normal; text-align: center;">
A Zylon Mars elevator with better safety factors is impractical.</div>
</div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
I hope to revisit the <a href="http://hopsblog-hop.blogspot.com/2016/01/upper-phobos-tether.html">upper Phobos tether</a> and <a href="http://hopsblog-hop.blogspot.com/2015/12/lower-phobos-tether.html">lower Phobos tether</a> pages and include safety factors of 2 and 3. I suspect with a higher safety factor that a Zylon tether from Phobos to Mars upper atmosphere may not be feasible.</div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
<br /></div>
<div style="font-weight: normal;">
<br /></div>
</div>
</div>
Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com10tag:blogger.com,1999:blog-3596550435682943926.post-40712795776878225602017-02-01T09:09:00.000-08:002020-04-13T12:45:20.783-07:00Matrices<div class="separator" style="clear: both;">
<b><span style="font-size: large;">Vectors</span></b></div>
<br />
<b><a href="http://hopsblog-hop.blogspot.com/2017/02/matrices.html#Rotation">Rotation Matrix</a></b><br />
<b><a href="http://hopsblog-hop.blogspot.com/2017/02/matrices.html#ProportionalScaling">Proportional Scaling Matrix</a></b><br />
<b><a href="http://hopsblog-hop.blogspot.com/2017/02/matrices.html#NonProportionalScaling">Non Proportional Scaling Matrix</a></b><br />
<b><a href="http://hopsblog-hop.blogspot.com/2017/02/matrices.html#Shear">Shear Matrix</a></b><br />
<b><a href="http://hopsblog-hop.blogspot.com/2017/02/matrices.html#Reflect">Reflect Matrix</a></b><br />
<b><br /></b>
<b><a href="http://hopsblog-hop.blogspot.com/2017/02/matrices.html#Determinant">Determinant of a Matrix</a></b><br />
<b><br /></b>
<b><a href="http://hopsblog-hop.blogspot.com/2017/02/matrices.html#Lorentz">Lorentz Transform Matrix</a></b><br />
<b><span style="font-size: large;"><br /></span></b>
<b><span style="font-size: large;"></span></b><br />
<div id="Rotation">
<b><span style="font-size: large;">Vectors</span></b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhCIfzauF1sxLDpSnBa7qHVxrUqgQcK-4ll47eiILF_kpsFC-TAQdLBdaYMSXSfvyu8l2X073OZsJjvIbp9clWcKJxQB5AXQAyCIq8AoDyTTGOf0mrpputIhcrcD4vpxga-G5pD03W9Iyc/s1600/VectorDog.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhCIfzauF1sxLDpSnBa7qHVxrUqgQcK-4ll47eiILF_kpsFC-TAQdLBdaYMSXSfvyu8l2X073OZsJjvIbp9clWcKJxQB5AXQAyCIq8AoDyTTGOf0mrpputIhcrcD4vpxga-G5pD03W9Iyc/s640/VectorDog.jpg" width="640" /></a></div>
<br />
Vectors are a way to describe point locations with numbers. Vectors can be used to build simple shapes like a cube or just about any shape you can imagine.<br />
<br />
We do lots of stuff to these vectors with <b>matrix multiplication</b>. We can grow, shrink, spin, stretch, squeeze, tilt and flip these guys.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRxkYa7jT3amzdlDX-XeqRw-tdIujTP_yRkW-5rLw7hcOHOCrIE5dDO2RkTKKK2SSmUHi88nrd1y7vFqNSBymb8YlKcplrreZVt7JHjO5Wo958wha3Gxfhc5RLOfXUBitFi_6MVmoR-b39/s1600/Dog+Transfomrations.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="228" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRxkYa7jT3amzdlDX-XeqRw-tdIujTP_yRkW-5rLw7hcOHOCrIE5dDO2RkTKKK2SSmUHi88nrd1y7vFqNSBymb8YlKcplrreZVt7JHjO5Wo958wha3Gxfhc5RLOfXUBitFi_6MVmoR-b39/s400/Dog+Transfomrations.jpg" width="400" /></a></div>
<br />
<br />
First we'll look at the things you can do to vectors on a plane with computer drawing programs like Adobe Illustrator. Below are some items from the Illustrator tool box that employ matrices.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8URffOkmHjxbOqsYmAtwv6snno2I_DTW_OsmKulJSD_Z9vVVc2sDV-hKY2IIFNsInxFDS8bKf-ZFhvViAKyJPzj7SMN_Nha0aig1en6SmpD8PWsmtn2AYW5OGffyPS11nl7dot9BQ_cTY/s1600/IllustratorMatrixTools.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="262" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8URffOkmHjxbOqsYmAtwv6snno2I_DTW_OsmKulJSD_Z9vVVc2sDV-hKY2IIFNsInxFDS8bKf-ZFhvViAKyJPzj7SMN_Nha0aig1en6SmpD8PWsmtn2AYW5OGffyPS11nl7dot9BQ_cTY/s400/IllustratorMatrixTools.png" width="400" /></a></div>
<br />
<b><span style="font-size: large;"><br /></span></b>
<b><span style="font-size: large;">Rotation Matrix</span></b></div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjf5jF6QkScFCbtTXOkm_X2sPLfDpexHZh1cW6siCIQEq2FZ3k55hyNkY45OxP-XU1rkxaqAIW4g_51gWqdDMXjwwYWWwtPSHrm1IvfBMSstxYL3JVAWevRtoAsL0jxICHw1etOVUmlHuTq/s1600/RotationMatrix.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="616" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjf5jF6QkScFCbtTXOkm_X2sPLfDpexHZh1cW6siCIQEq2FZ3k55hyNkY45OxP-XU1rkxaqAIW4g_51gWqdDMXjwwYWWwtPSHrm1IvfBMSstxYL3JVAWevRtoAsL0jxICHw1etOVUmlHuTq/s640/RotationMatrix.jpg" width="640" /></a></div>
<br />
Rotating a polygon doesn't change it's area. The area remains the same. The determinant of this matrix is 1.<br />
<br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="ProportionalScaling">
<b><span style="font-size: large;">Proportional Scaling Matrix</span></b></div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHPioja5jtJYUkJBen9De4xziFAxzwSQCr2o0LRgnDdlVFQ5CV4TdKDphoqEV9Lhg-a0K5dd5a3jh3CjXXTLJj-Dj87euu17uzOatDBWRuXql-BSX4M0tYbdrUq8UjuJXHGAQd6BZIasq0/s1600/ScalingMatrix.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="340" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHPioja5jtJYUkJBen9De4xziFAxzwSQCr2o0LRgnDdlVFQ5CV4TdKDphoqEV9Lhg-a0K5dd5a3jh3CjXXTLJj-Dj87euu17uzOatDBWRuXql-BSX4M0tYbdrUq8UjuJXHGAQd6BZIasq0/s640/ScalingMatrix.jpg" width="640" /></a></div>
<br />
Doubling size as well as height boosts a polygon's area by a factor of four. This determinant of this matrix is 4.<br />
<br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="NonProportionalScaling">
<b><span style="font-size: large;">Non Proportional Scaling Matrix</span></b></div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwDQvaMpq1CY7AEIRqs5bIOVnv9b7VS0wM5Fe0Ln9c2b8OKmM5_q_9RGocojFeyG81KIEjYtyTeqF8BKMidtifDKwj-GjWiOjA4w8QxXe09TVeEhpKbnxYiS90UNEcgmjqiDEb8o6E8W8O/s1600/NonProportionalScalingMatrix.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="340" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwDQvaMpq1CY7AEIRqs5bIOVnv9b7VS0wM5Fe0Ln9c2b8OKmM5_q_9RGocojFeyG81KIEjYtyTeqF8BKMidtifDKwj-GjWiOjA4w8QxXe09TVeEhpKbnxYiS90UNEcgmjqiDEb8o6E8W8O/s640/NonProportionalScalingMatrix.jpg" width="640" /></a></div>
<br />
This matrix stretches the width to twice the original and squeezes the height to half of what it was. Overall the area is unchanged. The determinant of this matrix is 1. However the determinant of a non proportional scaling matrix can be more or less than 1.<br />
<br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="Shear">
<b><span style="font-size: large;">Shear or Skew Matrix</span></b></div>
<br />
<br />
When I was using Macromedia Freehand, the graphics program called this transformation "skew". Then Adobe ate Macromedia and I was forced to use Adobe Illustrator. Illustrator calls it "shear".<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1YvTdYLhKNjYMQtOPaEj7rQ1j7k8LUCS9SeREkSIM0gkSNoh_2NpU-2La4bNSkYHRicLfiOqORpwkItyIv84KwnqICw2eeSr_RrrFy5jH29yOGRXZODqhDgRmodXDpDo2fuSvmhedpEFn/s1600/SkewMatrix.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="356" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1YvTdYLhKNjYMQtOPaEj7rQ1j7k8LUCS9SeREkSIM0gkSNoh_2NpU-2La4bNSkYHRicLfiOqORpwkItyIv84KwnqICw2eeSr_RrrFy5jH29yOGRXZODqhDgRmodXDpDo2fuSvmhedpEFn/s640/SkewMatrix.jpg" width="640" /></a></div>
<br />
This transformation transforms a horizontally aligned rectangle to a parallelogram with same base and height. Area remains unchanged. The determinant of this matrix is 1.<br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="Reflect">
<b><span style="font-size: large;">Flip Matrix</span></b></div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh1aEdfJp-UFMtj4llTYs8inXGUKaz0FGGTBvkSdqRcBRP_1gpgc_K6Mde6ocj3l1AbXqUgZlEEP1RbDB1CLhMxUN5FObZiYm3dAcHmUqUONdXuNC1ogR4d_-Mep-6knCKMUoFwNG7ZdD8/s1600/FlipMatrix.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="380" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh1aEdfJp-UFMtj4llTYs8inXGUKaz0FGGTBvkSdqRcBRP_1gpgc_K6Mde6ocj3l1AbXqUgZlEEP1RbDB1CLhMxUN5FObZiYm3dAcHmUqUONdXuNC1ogR4d_-Mep-6knCKMUoFwNG7ZdD8/s640/FlipMatrix.jpg" width="640" /></a></div>
<br />
Making the first term in the main diagonal negative flips polygons about the y axis. Making the lower right term negative would flip polygons about the x axis.<br />
<br />
Determinant is -1. Not sure what that means geometrically but absolute value of the area remains the same.<br />
<br />
Illustrator Tool Box<br />
<br />
<br />
<b><span style="font-size: large;"></span></b>
<br />
<div id="Determinant">
<b><span style="font-size: large;">Determinant of a Matrix</span></b></div>
<br />
<br />
Below is a general 3x3 matrix multiplied by each of the usual basis vectors in 3-space.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju7t6h9zW6pRZI9WcixqG3CWls7xI-dfcJF5EnDJNddQ_sFfPhc7bmPsidnQOf5BUy0TQAwyrVA24OcWEGu7LgQijrA-cM6p11g7dB9gT68CGl7QlDHMIXi1gIpl4PsoivS3pD_SkaSdlv/s1600/Matrix+columns.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju7t6h9zW6pRZI9WcixqG3CWls7xI-dfcJF5EnDJNddQ_sFfPhc7bmPsidnQOf5BUy0TQAwyrVA24OcWEGu7LgQijrA-cM6p11g7dB9gT68CGl7QlDHMIXi1gIpl4PsoivS3pD_SkaSdlv/s320/Matrix+columns.jpg" width="247" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
Notice the first basis vector is transformed into the first column of the matrix, the 2nd basis vector is transformed into the second column, and so on.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The 3 basis vectors form edges of a unit cube. Multiplying each of the vertices of this unit cube by our general matrix, we get a parallelepiped with edges <span style="color: red;">(a, b, c)</span>, <span style="color: #6aa84f;">(l, m, n)</span> and <span style="color: blue;">(x, y, z)</span>.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkbozVH0eLEEyPxxIzbSLl4Qb9CXZ92xwS6KnV2F-pGM0TDNfRsM7FrWo8VuEo4GGKkR8CjMxTVxDiB11bnSgUyqZ1a04fNc5Vj8ludPnI9LKZ5mVY-le69670QsygUSAmNzGp63nvFTwA/s1600/Transformed+cube.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="384" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkbozVH0eLEEyPxxIzbSLl4Qb9CXZ92xwS6KnV2F-pGM0TDNfRsM7FrWo8VuEo4GGKkR8CjMxTVxDiB11bnSgUyqZ1a04fNc5Vj8ludPnI9LKZ5mVY-le69670QsygUSAmNzGp63nvFTwA/s640/Transformed+cube.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
Of course the volume of the unit cube is one cubic unit. To find the volume of the transformed parallelepiped we take the <a href="https://en.wikipedia.org/wiki/Determinant">determinant of the matrix</a>. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
There are some matrices that don't change the size or shape of the objects they transform. Rotation matrices, for example. These have a determinant of 1. Matrices that don't change the size but flip the chirality of an object (say, change a left shoe into a right shoe), have a determinant of -1.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://www.youtube.com/watch?v=Ip3X9LOh2dk">Here is a nice vid</a> on the determinant of a matrix.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="Lorentz">
<b><span style="font-size: large;">Lorentz Transformation</span></b></div>
<br />
<br />
In ordinary Euclidean space, a point (x, y, x)'s distance from the origin would be<br />
sqrt(x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> ), a metric easily arrived at with the Pythagorean theorem.<br />
<br />
But the time space manifold we dwell in is a little strange. The metric is<br />
sqrt(-t<sup>2</sup> + x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> ). One of these dimensions is not like the other one.<br />
<br />
In ordinary Euclidean space, changing Point Of View (POV) entails a translation and/or a rotation. In our space time, changing POV entails a Lorentz Transformation.<br />
<br />
Adam Zalcman did a nice job of portraying the Lorentz transformation as a matrix. Here is a screen capture from his <a href="http://physics.stackexchange.com/a/30168/44119">physics stack exchange answer</a>:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4VzS1Ba5aLBKCIQDq0gpmjFdxqvjdLmUMrIWVgHXw7AplvkVIn_kghjnT0EC3gNaqHDjsnEuDo7jgd4z_vVrGPuuVj8mUDYy3CXILzO07hugDJ9ya2Fxsy0fKBSiUSkNQtE-TR_CuJf90/s1600/Lorentz+matrix.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="333" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4VzS1Ba5aLBKCIQDq0gpmjFdxqvjdLmUMrIWVgHXw7AplvkVIn_kghjnT0EC3gNaqHDjsnEuDo7jgd4z_vVrGPuuVj8mUDYy3CXILzO07hugDJ9ya2Fxsy0fKBSiUSkNQtE-TR_CuJf90/s400/Lorentz+matrix.png" width="400" /></a></div>
<br />
A Lorentz matrix for a 2 dimensional Minkowski space looks like this:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW0Ypi63QBBz_DfWnGz04p4txwF3bmSGEfXonc7ua3vQBoFKc4hYEkBl5C4TGRhyphenhyphenrycJdUSpk4dMe_hnyX3BUhB2W0Xc_ltQI-3pSQTmavGLvR8pD_3Uh7uZtTdU6_blLhK7Yp23QhYacg/s1600/2+D+Lorentz+matrix.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW0Ypi63QBBz_DfWnGz04p4txwF3bmSGEfXonc7ua3vQBoFKc4hYEkBl5C4TGRhyphenhyphenrycJdUSpk4dMe_hnyX3BUhB2W0Xc_ltQI-3pSQTmavGLvR8pD_3Uh7uZtTdU6_blLhK7Yp23QhYacg/s1600/2+D+Lorentz+matrix.png" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtJlTW6Q3DwgyUx18Po871ZY2M54kkqCafMt728aE4pSNpKLAp_LsYnEewPvTjmWICFi1qvITNYvfVQcUiHzve9PVSkNMsoZiKmO8KUCUC_r_P8tGspum3p4j2XId-ssTZhPCewj0pAVaC/s1600/Lorentz+matrix+half+a+c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtJlTW6Q3DwgyUx18Po871ZY2M54kkqCafMt728aE4pSNpKLAp_LsYnEewPvTjmWICFi1qvITNYvfVQcUiHzve9PVSkNMsoZiKmO8KUCUC_r_P8tGspum3p4j2XId-ssTZhPCewj0pAVaC/s640/Lorentz+matrix+half+a+c.jpg" width="640" /></a></div>
<br />
Above is our two dimensional Minkowski space. As they move through time inhabitants can move either right or left. The ship leaves earth in the present. A year later it has moved half a light year to the right. It is moving .5 c.<br />
<br />
Pluggin .5 c into our Lorentz transform matrix we get:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrX_dYdpu6G02fF-zCVZwITmHfLwXz_y7YELxbV5WgK2I1UG3yyegMhimFoPWeeEvyrSPgoGIBQrko_oVn_gj_JvvLR4b-1_vdqcrJmzVirxsYYa6HZCDsxkksIMgUd16VpDk9HWw4s5aL/s1600/2+D+Lorentz+Matrix+columns.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrX_dYdpu6G02fF-zCVZwITmHfLwXz_y7YELxbV5WgK2I1UG3yyegMhimFoPWeeEvyrSPgoGIBQrko_oVn_gj_JvvLR4b-1_vdqcrJmzVirxsYYa6HZCDsxkksIMgUd16VpDk9HWw4s5aL/s1600/2+D+Lorentz+Matrix+columns.jpg" /></a></div>
Transforming our Minkowski space with this matrix we get:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJtYqGOimCiCT1VkeaC7WjppIfd7nd6bi2k7xjSfFJEqYPtJXCmTTalt24biMvquWYJcw9XtzgB_h8a5dcJBuwJ_0LouBMolc14wA7WXM8mqvpXSnR0-k5jp9hI2uP7-0KwfJVGQpF_fse/s1600/Lorentz+matrix+half+a+c2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJtYqGOimCiCT1VkeaC7WjppIfd7nd6bi2k7xjSfFJEqYPtJXCmTTalt24biMvquWYJcw9XtzgB_h8a5dcJBuwJ_0LouBMolc14wA7WXM8mqvpXSnR0-k5jp9hI2uP7-0KwfJVGQpF_fse/s640/Lorentz+matrix+half+a+c2.jpg" width="640" /></a></div>
The ship's world line has been shoved to the left. From the ship passengers' point of view, they aren't moving. Also they perceive .866 years have elapsed, not a full year. The earth's world line has also been shoved to the left. From the ship's POV the earth is moving .5 c to the left.<br />
<br />
Note that the diagonals remain in the same place. Earth folks as well as ship passengers both perceive light photos to be traveling at 1 c (c is the speed of light).<br />
<br />
While the transformation stretches along one diagonal, it also squeezes along another diagonal. So the area remains the same. Determinant of this matrix is one.<br />
<br />
When I first saw the transformed coordinate system I was thinking "Wait a minute. Earth is now more than half a light year away and only .866 years have passed on the ship. Seems like earth is going more than .5 c. My mistake was in using the word "now". What were simultaneous events from one frame are no longer simultaneous.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFRe2v_ZNkhHrAdIGSRDw1FXMxLNEVi1K5HsRpKaMaz3dxEUV4Z1cy2g16FJWY4yqYyQvk_9my0jGlZ-5qA7XQNfIj2A7qSvfP-cl-YjLmauzNyUcSRud8qMXj7qGx05GQ52NrzZI1rcK5/s1600/Simultaneous+events.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFRe2v_ZNkhHrAdIGSRDw1FXMxLNEVi1K5HsRpKaMaz3dxEUV4Z1cy2g16FJWY4yqYyQvk_9my0jGlZ-5qA7XQNfIj2A7qSvfP-cl-YjLmauzNyUcSRud8qMXj7qGx05GQ52NrzZI1rcK5/s640/Simultaneous+events.jpg" width="640" /></a></div>
<br />
Note that from the ship's P.O.V. Earth's clock is running slower. This is possible because simultaneous events along worldlines change depending on which frame the viewer's in.<br />
<br />
<br />
Here is an animation showing different transforms where the ship's speed varies from -.9 c to .9 c.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh02PdJBbZWVprhYBFOAI8u73u8TnV5JaAReFg0gfPZX6_vVwY6R1SDs5riCXhvwAazaIl3ZdoIdO08LJAmgqNyCDlbHVqAbvE3VUeYNObNjoNdZuGfOAUEIq0TOpfvAiGXavqgCZYPZhL/s1600/Lorentz_Animation.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh02PdJBbZWVprhYBFOAI8u73u8TnV5JaAReFg0gfPZX6_vVwY6R1SDs5riCXhvwAazaIl3ZdoIdO08LJAmgqNyCDlbHVqAbvE3VUeYNObNjoNdZuGfOAUEIq0TOpfvAiGXavqgCZYPZhL/s640/Lorentz_Animation.gif" width="640" /></a></div>
<br />
Winchell Chung of Atomic Rockets <a href="http://www.projectrho.com/public_html/rocket/slowerlight.php#farmsky">describes a scene from a Heinlein novel </a>where a student asks:<br />
<br />
<blockquote class="tr_bq">
“Mr. Ortega, admitting that you can’t pass the speed of light, what would happen if the <em>Star Rover</em> got up close to the speed of light—and then the Captain suddenly stepped the drive up to about six g and held it there?”<br />
“Why,
it would—No, let’s put it this way—” He broke off and grinned; it made
him look real young. “See here, kid, don’t ask me questions like that.
I’m an engineer with hairy ears, not a mathematical physicist.” He
looked thoughtful and added, “Truthfully, I don’t know what would
happen, but I would sure give a pretty to find out. Maybe we would find
out what the square root of minus one looks like—from the inside.”</blockquote>
<br />
Let's take a look at world lines where one rocket is moving .5 c to the left and the other is moving .5 c to the right. At first glance it'd seem like the rocket moving to the left would be moving the speed of light with regard to the other rocket.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghp1YG-64HPvJZbpCwgImJLwqqcTEBdL2wbnM-_pKE4PJN9VMpiIxEKyILcypvDAc-LvikSE6hxqV6jeqXcbBKoW9gKccW8gJckgsXqFjY0bQEQhd7h93WyStagf6T0RlOuGP9-PUdcs0_/s1600/Lorentz+matrix+Accel.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghp1YG-64HPvJZbpCwgImJLwqqcTEBdL2wbnM-_pKE4PJN9VMpiIxEKyILcypvDAc-LvikSE6hxqV6jeqXcbBKoW9gKccW8gJckgsXqFjY0bQEQhd7h93WyStagf6T0RlOuGP9-PUdcs0_/s640/Lorentz+matrix+Accel.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
Transform the scene on the left to the orange ship's point of view. From the orange ship's P. O. V., the purple ship is moving .8 c to the left. The Lorentz transformation doesn't shift the purple ship all the way to the edge of the light cone. (Click on image to get a larger version).<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjURDiBm4H9KN0zMhe6PH0l-C5nQZ4mR01XRQbKUaTrKTth_maUZKmq8xenxPlB_FM3txOoBVlt5MjSmCoE2j06e_CG2l3Swaro-_R4WHbalOiA2sKXgiM76BQ0oiPs15h5QLPL3kD_X3RH/s1600/Hyperboloid+of+two+sheets.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="436" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjURDiBm4H9KN0zMhe6PH0l-C5nQZ4mR01XRQbKUaTrKTth_maUZKmq8xenxPlB_FM3txOoBVlt5MjSmCoE2j06e_CG2l3Swaro-_R4WHbalOiA2sKXgiM76BQ0oiPs15h5QLPL3kD_X3RH/s640/Hyperboloid+of+two+sheets.jpg" width="640" /></a></div>
<br />
From the point of view of each world line, his immediate neighbors are moving either .5 c to the left or .5 c to the right. The arrowhead on each line corresponds to the passage of one year from that world line's point of view. The horizontal line indicates simultaneous events from the P.O.V of the central world line after one year. These trace out a hyperbola with the edges of the light cone as asymptotes.<br />
<br />
If the above lines were a cone, plane of simultaneous events would cut the cone along a circle and the world lines would pierce that circle in points closer and closer the edge as the world lines approached c. This would be a <a href="https://en.wikipedia.org/wiki/Poincar%C3%A9_disk_model">Poincare disk</a>.<br />
<br />
M. C. Escher's Circle Limit prints are based on Poincare disks.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhP7oUfdMOYcPK3LKIoR1QFdpwxKD6wOlyAnIyMmvJKaOzXfm1BTf2zQUryV0L670_Z_6ghGWxyD2oJ87IHl-24fk96M9tHtw4QVl2Kb4V-X-pRr-8x9MktFCtKnxJfXA87fLxg7yJVZ3SK/s1600/EscherAngelDevilCircleLimit.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhP7oUfdMOYcPK3LKIoR1QFdpwxKD6wOlyAnIyMmvJKaOzXfm1BTf2zQUryV0L670_Z_6ghGWxyD2oJ87IHl-24fk96M9tHtw4QVl2Kb4V-X-pRr-8x9MktFCtKnxJfXA87fLxg7yJVZ3SK/s640/EscherAngelDevilCircleLimit.jpg" width="640" /></a></div>
<div style="text-align: center;">
Image from the <a href="http://www.mcescher.com/gallery/recognition-success/circle-limit-iv/">official M. C. Escher website</a>.</div>
<br />
Each angel or demon on this disk perceives themselves to be at the center while their neighbors shrinking towards the boundary of this world as they grow more distant. So it would be with Mr. Ortega's student who would step on the gas when he's moving .999 c. He'd just shift his position to the another part of the disk and he would be no closer to the edge.<br />
<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com8tag:blogger.com,1999:blog-3596550435682943926.post-68831595623991883992016-11-26T11:45:00.000-08:002020-04-13T12:45:38.426-07:00Lamentable Lagrange articles<div class="separator" style="clear: both;">
<b><span style="font-size: large;">Gravity doesn't cancel at the Lagrange points</span></b></div>
<br />
<blockquote class="tr_bq">
"There are places in the Solar System where the forces of gravity balance out perfectly. Places we can use to position satellites, space telescopes and even colonies to establish our exploration of the Solar System. These are the Lagrange Points."</blockquote>
<br />
From <a href="https://www.youtube.com/watch?v=foyJzvpeaBE">Fraser Cain's video on Lagrange points</a>. A lot of pop sci Lagrange articles repeat and spread this bad meme. It just ain't so.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKKCfky_iejPr7VnnjG-jECiJDSuGgh0UVnf99LzmFYdF-kqFMKJIbbMYX50iyKL-ENTs4JIRZfqauQc_OjB5Ai3R0_mo253UDuyE2PB7VABa4MI9varv5vqUl3m9sZVX6f31GojHVk36g/s1600/Screen+Shot+2016-11-26+at+10.22.35+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="572" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKKCfky_iejPr7VnnjG-jECiJDSuGgh0UVnf99LzmFYdF-kqFMKJIbbMYX50iyKL-ENTs4JIRZfqauQc_OjB5Ai3R0_mo253UDuyE2PB7VABa4MI9varv5vqUl3m9sZVX6f31GojHVk36g/s640/Screen+Shot+2016-11-26+at+10.22.35+AM.png" width="640" /></a></div>
The 5 Lagrange points can be found in many two body systems. They can be Sun-Jupiter, Earth-Moon, Jupiter, Europa -- Any pair of dancers has this retinue of 5 Lagrange regions moving along with them. Above are the 5 Pluto-Charon Lagrange points. Also pictured are the gravity vectors these bodies exert. Pluto's gravity is indicated with purple vectors and these point towards Pluto's center. Charon's gravity is indicated with orange vectors and these point towards Charon's center.<br />
<br />
For the gravity vectors to cancel each other, they need to be equal and pointing in opposite directions.<br />
<br />
<b>L1</b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzQS4S9BsYC3cU8eUN5AwxwQU5imjmsUo7oQ2mKhkyCbUygzVh9Pks3N5bmPhBMWUI1meacZOxAmp4dIZD8c4o9aSlhLiD6744Mq4cJykjZkhT_V-imYmyRLImC7u7bi6J8IfU5xUIHJh3/s1600/Screen+Shot+2016-11-26+at+10.45.48+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="176" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzQS4S9BsYC3cU8eUN5AwxwQU5imjmsUo7oQ2mKhkyCbUygzVh9Pks3N5bmPhBMWUI1meacZOxAmp4dIZD8c4o9aSlhLiD6744Mq4cJykjZkhT_V-imYmyRLImC7u7bi6J8IfU5xUIHJh3/s640/Screen+Shot+2016-11-26+at+10.45.48+AM.png" width="640" /></a></div>
<br />
The only L-Point where the gravity vectors pull in opposite directions is L1. And here the central body (Pluto) pulls harder than Charon. These two gravities don't balance out.<br />
<br />
<br />
<b>L3 and L2</b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTgukUWxPYbFmKgHQyXYrqZwo2EIKxgj5SF87B2TxG20yol8zag5nLazJlJLQyM-gmf2J8IQBnmJIXNCbtPMETUqVeGPYp245tiRSCJlvh_3PZA8fNncuKzplf0yD_pd_LmvM-H2TuU1i0/s1600/Screen+Shot+2016-11-26+at+11.01.40+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="74" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTgukUWxPYbFmKgHQyXYrqZwo2EIKxgj5SF87B2TxG20yol8zag5nLazJlJLQyM-gmf2J8IQBnmJIXNCbtPMETUqVeGPYp245tiRSCJlvh_3PZA8fNncuKzplf0yD_pd_LmvM-H2TuU1i0/s640/Screen+Shot+2016-11-26+at+11.01.40+AM.png" width="640" /></a></div>
<br />
Zooming in on the L3 and L2 points, we can see both bodies pull the same direction. These don't balance.<br />
<br />
<br />
<b>L4 and L5</b><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsZtukxoIPz34Uv5Iw1_84aCsF6MNSFK9FCMNa_ehLo4fKL03O7sRdwOORSrkZPNHib6GkLoPZybXPPzwEafrVYLfny5zhYzrYQEPqI9h4ma3utWDkTnEhz4lIqOl__8dwx2u1ypMl7jyR/s1600/Screen+Shot+2016-11-26+at+11.22.55+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsZtukxoIPz34Uv5Iw1_84aCsF6MNSFK9FCMNa_ehLo4fKL03O7sRdwOORSrkZPNHib6GkLoPZybXPPzwEafrVYLfny5zhYzrYQEPqI9h4ma3utWDkTnEhz4lIqOl__8dwx2u1ypMl7jyR/s640/Screen+Shot+2016-11-26+at+11.22.55+AM.png" width="306" /></a></div>
<br />
<br />
Zooming in on the L4 and L5 points. Pluto pulls much harder. The angle between these vectors is 60º<br />
<br />
<b><span style="font-size: large;">The So-Called Centrifugal Force</span></b><br />
<br />
There is a third player in these Lagrange tug of wars. What we used to call centrifugal force. This is not truly a force but rather inertia in a rotating frame. Here is an <a href="https://xkcd.com/123/">XKCD</a> cartoon on this so called force:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsQqiR7x6gnaBpxX5XM60MWsRyn0tv-02JQScKp5bsSQY3R_X4ut-RfEXZTYrqXQTIqBcnWMyseJH5_IEBDIhj9d7CBCcB1e2JDBYkUdjmRPze6YFtkrpjw31ijb_IbdzfMmfT8yTSjbUt/s1600/centrifugal_force.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsQqiR7x6gnaBpxX5XM60MWsRyn0tv-02JQScKp5bsSQY3R_X4ut-RfEXZTYrqXQTIqBcnWMyseJH5_IEBDIhj9d7CBCcB1e2JDBYkUdjmRPze6YFtkrpjw31ijb_IbdzfMmfT8yTSjbUt/s640/centrifugal_force.png" width="430" /></a></div>
<br />
Indeed, in a rotating frame, inertia sure feels like a force. The pseudo acceleration can be described as ω<sup>2</sup>r where ω is angular velocity in radians per time and r is distance from center of rotation. The vector points away from the center of rotation.<br />
<br />
<b><span style="font-size: large;">Putting Gravity and Centrifugal Force Together</span></b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0ickUdX-kz_GNUIBNmtaxDzXn6c0i7H_iv-Tc70L7eEjnLjEjq9R-IRCfl__O1dppaSZxOlxrVC4AFQv6fvRnBxGSUfbdkJ6q6c_5u_qYcLoby4DK1_nyIBjKz4xBGgAR4xONb65MMnz8/s1600/Screen+Shot+2016-11-26+at+12.10.04+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="574" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0ickUdX-kz_GNUIBNmtaxDzXn6c0i7H_iv-Tc70L7eEjnLjEjq9R-IRCfl__O1dppaSZxOlxrVC4AFQv6fvRnBxGSUfbdkJ6q6c_5u_qYcLoby4DK1_nyIBjKz4xBGgAR4xONb65MMnz8/s640/Screen+Shot+2016-11-26+at+12.10.04+PM.png" width="640" /></a></div>
<br />
<br />
Here's the same diagram but with centrifugal force thrown in (the blue vectors). Also the foot of the Charon gravity vectors are placed on the head of the Pluto gravity vectors -- this is a visual way to carry out vector addition.<br />
<br />
For L1, Charon and Centrifugal Force are on the same team and they perfectly balance Pluto's gravity.<br />
<br />
For both L2 and L3, Pluto and Charon are on the same team and they neutralize their opponent Centrifugal Force.<br />
<br />
But what about L4 and L5? An observant reader may notice that the centrifugal force vector doesn't point away from Pluto's center. Adding Charon's tug to Pluto's tug moves the direction to the side a little bit.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0SjVEi_vsLWGGxexiKZwkWym2LIDMz5iXQApXfPs3JeA5F6lQioAY7lymgMHkr1z7eM_3zv7246cvJCprAYW8ND_HPZXNemzuFnOaW2O53sxfUJNW__wSpQuhZJD8BxEke-NM6BGQf6k8/s1600/Screen+Shot+2016-11-26+at+12.28.43+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="638" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0SjVEi_vsLWGGxexiKZwkWym2LIDMz5iXQApXfPs3JeA5F6lQioAY7lymgMHkr1z7eM_3zv7246cvJCprAYW8ND_HPZXNemzuFnOaW2O53sxfUJNW__wSpQuhZJD8BxEke-NM6BGQf6k8/s640/Screen+Shot+2016-11-26+at+12.28.43+PM.png" width="640" /></a></div>
<br />
<br />
Now the centrifugal force vector points from the barycenter. This is the common point of rotation around which both Pluto and Charon rotate. The same applies to L5.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJnpTMmrZRoFc7lhTayr6I3lYarX8XoBRCcWbzvqr99HbBKFtE8kHNMWbDilfBPO1PtVuZz2B73ZAqiohJw35J6b5rN-MSnH5KpvhRBwLE-yx7HxZgp8gKgYuCJPZju2HJqAFRmzdEiOfQ/s1600/Screen+Shot+2016-11-28+at+8.54.53+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="380" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJnpTMmrZRoFc7lhTayr6I3lYarX8XoBRCcWbzvqr99HbBKFtE8kHNMWbDilfBPO1PtVuZz2B73ZAqiohJw35J6b5rN-MSnH5KpvhRBwLE-yx7HxZgp8gKgYuCJPZju2HJqAFRmzdEiOfQ/s400/Screen+Shot+2016-11-28+at+8.54.53+AM.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
L4, Charon's center and Pluto's center form an equilateral triangle.</div>
<div class="separator" style="clear: both; text-align: center;">
The barycenter lies on the corner of a non-equilateral triangle.</div>
<br />
<br />
And so it is with all the orbiting systems in our neighborhood. It is a 3 way way tug-of-war between centrifugal force, gravity of the orbiting body and gravity of the central body. Sometimes two players are on the same team, other places they switch. In L4 and L5 everyone pulls in a different direction. But in all 5 Lagrange points, the sum of the three accelerations is zero.<br />
<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com14tag:blogger.com,1999:blog-3596550435682943926.post-54348025717125081552016-09-15T14:38:00.000-07:002020-04-13T12:45:59.224-07:00Xenon<div class="separator" style="clear: both;">
<b><span style="font-size: large;">Xenon The Noble Gas</span></b></div>
<br />
<a href="https://en.wikipedia.org/wiki/Xenon">Xenon</a> is one of heavier Noble Gases<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjA8jtxoia6V9lmPZ5vvmFxggiPSk0X-wr0qczzjtMq8ABfqlPjizO6Y1pE45XYth0FwSfg9B4azWMTfgXFbocDSvFfAEdko3eA2lFtnWd55Ni2l4wCzD6on23StY7yuyngmkTtMR1LEWq2/s1600/Xenon+Periodic+Table.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjA8jtxoia6V9lmPZ5vvmFxggiPSk0X-wr0qczzjtMq8ABfqlPjizO6Y1pE45XYth0FwSfg9B4azWMTfgXFbocDSvFfAEdko3eA2lFtnWd55Ni2l4wCzD6on23StY7yuyngmkTtMR1LEWq2/s640/Xenon+Periodic+Table.png" width="640" /></a></div>
<div style="text-align: center;">
Screen capture from <a href="http://www.chemicalelements.com/show/mass.html">ChemicalElements.com</a></div>
<br />
The noble gases are the orange column on the right of the periodic table. These are chemically inert. Which means they're not corrosive. This makes them easier to store or use.<br />
<br />
<b><span style="font-size: large;">Low Ionization Energy</span></b><br />
<br />
Per this graph is from <a href="https://en.wikipedia.org/wiki/Ionization_energy">Wikipedia</a>, Xenon has a lower ionization energy than the lighter noble gases.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5G368TBiupCVd8opU-9NdRysdzidSrUKpBzYbK9_RVQLGYUon6fQoHuTggakjMN2qRNebsm5YhoQB9Mz28DktbndkmwSSgnPsGN8h8ta15ysczAcjx0hvy8ys3c7J4janD60z1wVV6rut/s1600/Ionization+Energy.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="252" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5G368TBiupCVd8opU-9NdRysdzidSrUKpBzYbK9_RVQLGYUon6fQoHuTggakjMN2qRNebsm5YhoQB9Mz28DktbndkmwSSgnPsGN8h8ta15ysczAcjx0hvy8ys3c7J4janD60z1wVV6rut/s640/Ionization+Energy.png" width="640" /></a></div>
<br />
Ionization energy for xenon (Xe) is 1170.4 kJ/mol. Ionization for krypton (Kr) is 1350.8 kJ/mol. Looks like about a 15% difference, right?<br />
<br />
But a mole of the most common isotope of xenon is 131.3 grams, while a mole of krypton is 82.8 grams. So it takes 181% or nearly twice as much juice to ionize a gram of krypton.<br />
<br />
Likewise it takes nearly 4.5 times as much juice to ionize a gram of argon.<br />
<br />
The reaction mass must be ionized before it can be pushed by a magnetic field. Xenon takes less juice to ionize. So more of an ion engine's power source can be devoted to imparting exhaust velocity to reaction mass.<br />
<br />
<b><span style="font-size: large;">Big Atoms, Molar Weight</span></b><br />
<br />
Low molar weight makes for good ISP but poor thrust. And pathetic thrust is the Achilles heel of <a href="https://en.wikipedia.org/wiki/Hall-effect_thruster">Hall Thruster</a>s and other ion engines. The atomic weight of xenon is 131.29 (see periodic table at the top of the page).<br />
<br />
Tiny hydrogen molecules are notorious for leaking past the tightest seals. Big atoms have a harder time squeezing through tight seals. Big whopper atoms like xenon can be stored more easily.<br />
<br />
Around 160 K, xenon is a liquid with a density of about 3 grams per cubic centimeter. In contrast, oxygen is liquid below 90 K and a density of 1.1. So xenon is a much milder cryogen than oxygen and more than double (almost triple) the density.<br />
<br />
<b><span style="font-size: large;">Abundance</span></b><br />
<br />
Ordinary atmosphere is 1.2 kg/m<sup>3</sup> while xenon is about 5.9 kg/m<sup>3</sup> at the same pressure. Xenon has about 4.8 times the density of regular air.<br />
<br />
By volume earth's atmosphere is .0000087% xenon. 4.8 * .000000087 = 4.2e-7. Earth's atmosphere is estimated to mass 5e18 kg. By my arithmetic there is about 2e12 kg xenon in earth's atmosphere. In other words, about 2 billion tonnes.<br />
<br />
Page 29 of the <a href="http://www.lpi.usra.edu/sbag/documents/Final%20Report%20Asteroid%20Retrieval%20Study%20EXTERNAL%20RELEASE%20version%2020120412a_docx.pdf">Keck asteroid retrieval proposal</a> calls for 12.9 tonnes of xenon. Naysayers were aghast: "13 tonnes is almost a third of global xenon production for year! It would cause a shortage." Well, production is determined by demand. With 2 billion tonnes in our atmosphere, 13 tonnes is a drop in the bucket. We throw away a lot of xenon when we liquify oxygen and nitrogen from the atmosphere.<br />
<br />
In fact ramping up production of xenon would lead to economies of scale and likely cause prices to <b><i>drop</i></b>. TildalWave makes such an argument in this <a href="http://space.stackexchange.com/a/8700/2848">Space Stack Exchange answer</a> to the question "How much does it cost to fill an ion thruster with xenon for a spacecraft propulsion system?" TildalWave argues ramped up production could result in a $250,000 per tonne price. That's about a four fold cut in the going market price of $1.2 million per tonne.<br />
<br />
<b>Radon</b><br />
<br />
If you examined the periodic table and ionization tables above you might have noticed there's a heavier noble gas that has an even lower ionization energy: <a href="http://education.jlab.org/itselemental/ele086.html">Radon</a> a.k.a. Rn. Radon is radioactive. Radon 222, the most stable isotope, has a half life of less than 4 days. If I count the zeros on the <a href="http://education.jlab.org/itselemental/ele086.html">Radon page</a> correctly, our atmosphere is about 1e-19% radon -- what you'd expect for something with such a short half life. Besides being rare, it wouldn't last long in storage.<br />
<br />
Scott Manley did <a href="https://www.youtube.com/watch?v=Cb_U_CbQ5sc">a great video on xenon</a>.<br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="IonHohmann">
<b><span style="font-size: large;">Where xenon excels</span></b></div>
<br />
<br />
<b>Great for moving between heliocentric orbits</b><br />
<br />
Ion thrusters can get 10 to 80 km/s exhaust velocity, 30 km/s is a typical exhaust velocity. That's about 7 times as good as hydrogen/oxygen bipropellent which can do 4.4 km/s. But, as mentioned, ion thrust and acceleration are small. It takes a looong burn to get the delta V. To get good acceleration, an ion propelled vehicle needs good <a href="http://hopsblog-hop.blogspot.com/2015/05/the-need-for-better-alpha.html">alpha</a>. In my opinion, 1 millimeter/second<sup>2</sup> is doable with near future power sources.<br />
<br />
If the vehicle's acceleration is a healthy fraction of local gravity field, the accelerations resemble the impulsive burns to enter or exit an elliptical transfer orbit. But if the acceleration is a tiny fraction of the local gravity field, the path is a slow spiral.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglKjSo6eSGJTfg4MXNUVVUIS88wh1txZ-XQ6O6PKArwFPmdTVtLhKfOTsI3t04MkqQ9hltaYH-8JMy9lt52_btL85O6eiRCji8TuVCK6vmtvebyZ95GHM4dBblW47UguxFDsVvyvLyua0t/s1600/sun+acceleration.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglKjSo6eSGJTfg4MXNUVVUIS88wh1txZ-XQ6O6PKArwFPmdTVtLhKfOTsI3t04MkqQ9hltaYH-8JMy9lt52_btL85O6eiRCji8TuVCK6vmtvebyZ95GHM4dBblW47UguxFDsVvyvLyua0t/s640/sun+acceleration.jpg" width="598" /></a></div>
<br />
Earth's distance from the sun, the sun's gravity is around 6 millimeters/second<sup>2</sup>. At Mars, sun's gravity is about 2.5 mm/s<sup>2</sup> and in the asteroid belt 1 mm/s<sup>2</sup> or less. Ion engines are okay for moving between heliocentric orbits, especially as you get out as far as Mars and The Main Belt.<br />
<br />
<b>Sucks for climbing in and out of planetary gravity wells</b><br />
<br />
At 300 km altitude, Earth's local gravity field is about 9000 millimeters/second<sup>2</sup>. About 9 thousand times the 1 mm/s<sup>2</sup> acceleration a plausible ion vehicle can do. At the altitude of low Mars orbit, gravity is about 3400 millimeters/sec<sup>2</sup>. So slow gradual spirals rather than elliptical transfer orbits. There's also no Oberth benefit.<br />
<br />
At 1 mm/sec<sup>2</sup> acceleration, it would take around 7 million seconds (80 days) to climb in or out of earth's gravity well and about 3 million seconds (35 days) for the Mars well.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYpMqHY2yY3BIBH-mzgylgsSsdoigJO2045R8-dT5xOMUVLh4QiBppUZvZN6ZzZxgu5Duwur8tqQ5IvlUZ5796QLK7sRrs1_qThXGJZD81RKVBWaw4TyPu5NYvKsnDh2gWv84e_Fr_GtE5/s1600/AdlerIonSpiral.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="496" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYpMqHY2yY3BIBH-mzgylgsSsdoigJO2045R8-dT5xOMUVLh4QiBppUZvZN6ZzZxgu5Duwur8tqQ5IvlUZ5796QLK7sRrs1_qThXGJZD81RKVBWaw4TyPu5NYvKsnDh2gWv84e_Fr_GtE5/s640/AdlerIonSpiral.png" width="640" /></a></div>
<div style="text-align: center;">
Mark Adler's rendition of an ion spiral</div>
<div style="text-align: center;">
where the thruster's acceleration is 1/000 that of local gravity at the start.</div>
<div style="text-align: center;">
From a <a href="http://space.stackexchange.com/questions/8420/general-guidelines-for-modeling-a-low-thrust-ion-spiral">stack exchange answer on how to model low thrust trajectories</a>. </div>
<br />
The general rule of thumb for calculating the delta V needed for low thrust spirals: subtract speed of destination orbit from speed of departure orbit.<br />
<br />
Speed of Low Earth Orbit (LEO) is about 7.7 km/s. But you don't have to go to C3 = 0, getting past earth's Hill Sphere suffices. So about 7 km/s to climb from LEO to the edge of earth's gravity well.<br />
<br />
It takes about 5.6 km/s to get from earth's 1 A.U. heliocentric orbit to Mars' 1.52 A.U. heliocentric orbit.<br />
<br />
Speed of Low Mars Orbit (LMO) is about 3.4 km/s. About 3 km/s from the edge of Mars' Hill Sphere to LMO.<br />
<br />
7 + 5.6 + 3 = 15.6. A total of 15.6 km/s to get from LEO to LMO.<br />
<br />
With the Oberth benefit it takes about 5.6 km/s to get from LEO to LMO. The Oberth savings is almost 10 km/s.<br />
<br />
10 km/s is nothing to sneeze at, even if exhaust velocity is 30 km/s. Climbing all the way up and down planetary gravity wells wth ion engines costs substantial delta V as well as a lot of time.<br />
<br />
<b>Elevators and chemical for planet wells, ion for heliocentric</b><br />
<br />
So in my daydreams I imagine infrastructure at the edge of planetary gravity wells. Ports where ion driven driven vehicles arrive and leave as they move about the solar system. Then transportation from the well's edge down the well would be accomplished by chemical as well as orbital elevators.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYSDbnOB_tFy_8pGx4SjGKK9466fSZv3UJQnf9_J0K9c_s5Q6JilYMYfY4c9S_f4vqKom2xjbumc9GHAm_VuFi2kguxlQz3VxJpfNLRpEcsxXC4ZwLqbWx9ucunPAVgosEnRpRza3n3k6o/s1600/XenonVehicles3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="432" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYSDbnOB_tFy_8pGx4SjGKK9466fSZv3UJQnf9_J0K9c_s5Q6JilYMYfY4c9S_f4vqKom2xjbumc9GHAm_VuFi2kguxlQz3VxJpfNLRpEcsxXC4ZwLqbWx9ucunPAVgosEnRpRza3n3k6o/s640/XenonVehicles3.jpg" width="640" /></a></div>
<br />
<br />
<b><span style="font-size: large;">Other possible sources of ion propellent.</span></b><br />
<br />
Another possible propellent for ion engines is argon. Also a noble gas. Ionization energy isn't as good as xenon, but not bad. Mars atmosphere is about 2% argon. Mars is next door to The Main Belt. I like to imagine Mars will supply much of the propellent for moving about the Main Belt.Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com14tag:blogger.com,1999:blog-3596550435682943926.post-51864293488016604382016-09-10T11:36:00.002-07:002020-04-13T12:46:14.278-07:00General template for space elevators<div class="separator" style="clear: both;">
<b><span style="font-size: large;">A Family of Conic Sections</span></b></div>
<br />
Below is a general vertical space elevator. The conic sections are the paths payloads would follow if released from a point on the tether a distance r from body center.<br />
<br />
We choose our units so radius of the balance point is 1. Centrifugal acceleration matches gravity at the balance point and net acceleration is zero. For tether locations above the balance point, centrifugal force exceeds gravity and net acceleration is up (away from the planet). For locations below the balance point, gravity is greater than centrifugal acceleration and the net acceleration is down.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6GYkdlO1PtBZUG8SwjhtTDrxm38WoTQEijqAlEvMICeQoXMXcxkSa0Bw2yUNuuHIm-GVVvRk-TiLb2robQufEykZts-LKDOJbMSuSoey1GaJwkxxRzWSLj4eJW-Rv0Pd7_1D64fKNgZ5-/s1600/Tether+conics2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6GYkdlO1PtBZUG8SwjhtTDrxm38WoTQEijqAlEvMICeQoXMXcxkSa0Bw2yUNuuHIm-GVVvRk-TiLb2robQufEykZts-LKDOJbMSuSoey1GaJwkxxRzWSLj4eJW-Rv0Pd7_1D64fKNgZ5-/s640/Tether+conics2.jpg" width="596" /></a></div>
<br />
This family of conic sections are coplanar, coaxial and confocal. Eccentricity is r<sup>3</sup>-1, setting r = 1 at the circular orbit of the balance point. (See <a href="http://space.stackexchange.com/questions/5253/whats-the-path-of-something-dropped-from-a-space-elevator">this stack exchange answer</a> for the math).<br />
<br />
In the yellow region are hyperbolic orbits. In the blue region are are elliptical orbits higher than the circular orbit at the balance point. In the orange region, the tether drops payloads into elliptical orbits lower than the circular orbit at the balance point.<br />
<br />
A circle of eccentricity zero separates the orange and blue regions, radius of circle = 1.<br />
A parabola of eccentricity 1 separates the blue and gold regions, radius of parabola's periapsis = 2<sup>1/3</sup> <br />
<br />
Here is the same graphic zoomed in:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXlP-y6HeJHmCswrB9J9Em3drSTzANfAYhf3KmXi53uaMDz_uNWu5yXWuIhnuaHj4wENkYm1oFnabfGIq7z55kQ7jDDY-QuB9CIRzJrric8DHbtnxbWo-wPP_3AFPLkn72V2VVKgtmkOhM/s1600/Tether+conics4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXlP-y6HeJHmCswrB9J9Em3drSTzANfAYhf3KmXi53uaMDz_uNWu5yXWuIhnuaHj4wENkYm1oFnabfGIq7z55kQ7jDDY-QuB9CIRzJrric8DHbtnxbWo-wPP_3AFPLkn72V2VVKgtmkOhM/s640/Tether+conics4.jpg" width="640" /></a></div>
<br />
<a href="http://clowder.net/hop/railroad/Tether%20conics2.svg">Here</a> is the graphic as a Scalable Vector Graphic. I am hoping science fiction writers and illustrators will download this resource and use it.<br />
<br />
Scaling this graphic for a variety of scenarios:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwAlQcOxigDt_BMwP2BoVo3z3MApWzF0-kczq9ut1VDM56Pqlyd7T6ureih4M_mk00gSzsxQNsqkfWvcgmefYTaPIUIOS2sz92BXzLPwysHHyiaY8OdNWDuVIHAZNUxHF0io0ndSe87T0H/s1600/Tether+conics+Small.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="186" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwAlQcOxigDt_BMwP2BoVo3z3MApWzF0-kczq9ut1VDM56Pqlyd7T6ureih4M_mk00gSzsxQNsqkfWvcgmefYTaPIUIOS2sz92BXzLPwysHHyiaY8OdNWDuVIHAZNUxHF0io0ndSe87T0H/s640/Tether+conics+Small.jpg" width="640" /></a></div>
<br />
The numbers are in kilometers. In the case of earth, the circular orbit is the geosynchronous orbit at an altitude of about 36,000 kilometers.<br />
<br />
In general, radius of a synchronous orbit can be described as:<br />
<br />
r = (Gm / ω<sup>2</sup>)<sup>1/3</sup><br />
<br />
Where ω is the body's angular velocity in radians, 2 pi radians/sidereal day.<br />
<br />
<b><span style="font-size: large;">Orbital Elevators</span></b><br />
<br />
We usually think of an a space elevator anchored at the body's equator. An elevator can also be in a non synchronous orbit. Here the template is scaled to match the orbits of Phobos or Deimos:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpk-sTXQgFl4OTIMtymdkjTf4ANSMBPHsJ0oZAATNPr2KH1Wb7dgtlPrQBSZcdwFDkwvDCeOUJMHgHZgLQvXajAf1liI9NQ_oHTZGtgCcJ-tT-83p3Ihi_JqqcafA5c_AdBnlnvAiCvI9n/s1600/TetherPhobosDeimos.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="372" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpk-sTXQgFl4OTIMtymdkjTf4ANSMBPHsJ0oZAATNPr2KH1Wb7dgtlPrQBSZcdwFDkwvDCeOUJMHgHZgLQvXajAf1liI9NQ_oHTZGtgCcJ-tT-83p3Ihi_JqqcafA5c_AdBnlnvAiCvI9n/s640/TetherPhobosDeimos.jpg" width="640" /></a></div>
<br />
<br />
Notice Phobos' tether foot is above Mars surface. The foot is moving about .5 km/s with regard to Mars surface and therefore can't be anchored to Mars. Neither could a Deimos elevator be attached to Mars.<br />
<br />
Orbital radius of Phobos is about 40% that of Deimos. So I cloned and shrunk Deimos' tether conics by 40%. I rotated the cloned family of conics by 180º. The result is an interesting moiré pattern:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixqsqi3gFeWTvYnZ1xq7Jc-IG-XvY-NL1UrO_4rS-MCF4cVW9zIzW1-O_leOP5Tslnts0UlOPQRSGqZ7Ivhdz6rhZhEmRUWRW4CP2d8uc7SEuxokQ64uGvUiGNNwGT3SYJb4sgsv_vQzyS/s1600/PhobosDeimos3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="396" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixqsqi3gFeWTvYnZ1xq7Jc-IG-XvY-NL1UrO_4rS-MCF4cVW9zIzW1-O_leOP5Tslnts0UlOPQRSGqZ7Ivhdz6rhZhEmRUWRW4CP2d8uc7SEuxokQ64uGvUiGNNwGT3SYJb4sgsv_vQzyS/s640/PhobosDeimos3.jpg" width="640" /></a></div>
<br />
It was this pattern that led me to search for a common ellipse.<br />
<br />
Eccentricity of the common ellipse:<br />
<br />
e = (1 - (ω<sub>Deimos</sub>/ω<sub>Phobos</sub>)<sup>1/2</sup>) / (1 + ω<sub>Deimos</sub>/ω<sub>Phobos</sub>)<sup>1/2</sup>)<br />
<br />
Periapsis and apoapsis of the common ellipse:<br />
<br />
r<sub>periapsis</sub> = (1 + e)<sup>1/3</sup> r<sub>Phobos</sub><br />
r<sub>apoapsis</sub> = (1 - e)<sup>1/3</sup> r<sub>Deimos</sub><br />
<br />
<div class="separator" id="ZRVTO" style="clear: both;">
<b><span style="font-size: large;">ZRVTOs</span></b></div>
<div class="separator" style="clear: both;">
<br /></div>
Here's a pic of the ellipse Phobos and Deimos share:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdnB5tHiszis0qe1YmfTIGakXLdbbSFSFOlJoA571_D_R7kfY1Ik63VRmkxctN8m10eCl1RIU-mhKnP4nBGpYY9Vv3r2F1PoBGWOrAbPtzQ6tuQdYrqSwT1gRh8lcbiiFo194lGlJ-7lvz/s1600/PhobosToDeimos.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdnB5tHiszis0qe1YmfTIGakXLdbbSFSFOlJoA571_D_R7kfY1Ik63VRmkxctN8m10eCl1RIU-mhKnP4nBGpYY9Vv3r2F1PoBGWOrAbPtzQ6tuQdYrqSwT1gRh8lcbiiFo194lGlJ-7lvz/s640/PhobosToDeimos.jpg" width="520" /></a></div>
<br />
This is an example of a Zero Relative Velocity Transfer Orbits (ZRVTO) - a term coined by <a href="https://www.researchgate.net/profile/Marshall_Eubanks">Marshall Eubanks</a>. In Marshall's words: "locations (and times, say for a Lunar and Terrestrial space elevator) where you drop things from one space elevator and they approach and hang motionless (for an instant) at a location on the other elevator. ... what you would want for large scale movement of material."<br />
<br />
Eubanks goes on to say "In practice, you might need a little bit of course correction delta-V to make up for radiation pressure, etc."<br />
<br />
Also it would be rare for the elevators playing catch to be perfectly coplanar. So a small plane change delta V expense will be the rule rather than the exception. Still the delta V budgets would be a small fraction of what it would take for normal lift off and insertion to Hohmann transfers.<br />
<br />
<b><span style="font-size: large;">Not just Phobos and Deimos</span></b><br />
<br />
To be an anchor for a vertical elevator, a moon needs to be in a near circular orbit and tide locked to its planet. This describes most of the moons in our solar solar system. For two moons to share an ellipse, they need to be nearly coplanar. Again, most the moons in our solar system.<br />
<br />
Here are the common ellipses between the moons of Saturn:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7bv5uFZ_EnpJaC5BD1e2_15RzV4YK7766zRH1NmAAaAVIOyj3T8OSGHqsqldiB-osZZ344NApHKmh4CbbzTPGUYt6T-AYiE6yffs8Ioxf1fMg_lqS-F_zzWfL-jyYhY6bVtNIZRNkr4Vc/s1600/SaturnMoonTethers.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7bv5uFZ_EnpJaC5BD1e2_15RzV4YK7766zRH1NmAAaAVIOyj3T8OSGHqsqldiB-osZZ344NApHKmh4CbbzTPGUYt6T-AYiE6yffs8Ioxf1fMg_lqS-F_zzWfL-jyYhY6bVtNIZRNkr4Vc/s640/SaturnMoonTethers.jpg" width="578" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Judging by the two gas giants and two ice giants in our solar system, families of coplanar, tidelocked moons are common.</div>
<br />
<b><span style="font-size: large;">Mini Solar Systems</span></b><br />
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Earlier <a href="http://hopsblog-hop.blogspot.com/2013/01/mini-solar-systems.html">I had looked at Mini Solar Systems</a>, a notion I stole from <a href="https://retrorockets.wordpress.com/2012/06/28/designing-a-miniature-solar-system-part-1/">Retrorockets</a>. In our solar system Hohmann trip times between planets are on the order of months or years. Launch windows are typically years apart. But for a system of moons around a gas giant, trip times and launch windows are days or weeks. So a Flash Gordon paced story could take place without wildly improbable engineering.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>GIELO and ELM</b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
GIELO - Giant In Earth Like Orbit. ELM - Earth Like Moon. I have long been infatuated with this setting. Here is a painting I had done in 2001:</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7fBoiAauYryAaSQMnEfyox_q93Bx2oPGTdkFChPV_Z_YkDs4LU1yO9KJhbr_VSqPyI3ZY5-iXUtG9QP6rrer8pOjAyGuLhwV_D0HVMG-dILMJr_s30vhs0H_LbNXhXInyBKGzkrhM6oF4/s1600/ELMandGIELO.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7fBoiAauYryAaSQMnEfyox_q93Bx2oPGTdkFChPV_Z_YkDs4LU1yO9KJhbr_VSqPyI3ZY5-iXUtG9QP6rrer8pOjAyGuLhwV_D0HVMG-dILMJr_s30vhs0H_LbNXhXInyBKGzkrhM6oF4/s640/ELMandGIELO.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
ELM the earth like moon is in the upper right. In the foreground a generation star ship is sending quad pod scout probes to investigate an artifact at the GIELO-ELM L4 region.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
James Cameron's Avatar uses such a setting. Pandora is an ELM. I believe this setting could be developed a lot more. If ELM had sister moons and they were all tide locked, it would be a nice mini-solar system setting.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Icey moons with hospitable interiors.</b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Gas giants in Goldilocks zones aren't the only possibility. Temperature and pressure rise as we burrow deeper into a body. Earth might not be the only location in the solar system that has liquid water at a livable pressure. Thus the icey moons of our own solar system might eventually become "mini solar systems".</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Planets of red dwarfs</b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
And recently <a href="http://www.centauri-dreams.org/?p=36210">an approximately earth sized planet was found in the goldilocks zone of Proxima Centauri</a>. Proxima Centauri is a small red dwarf star. The possibly earth like planet has an orbital radius of about 7.5 million kilometers and an orbital period of about 12 days. Planets about small red dwarfs are yet another possible "mini solar system" setting. Planets so close are likely tide locked to the star. Would atmospheric convection mitigate the temperature extremes between the night side and day side? I'm not sure. In any case, I believe there would be a comfortable region hugging the planet's frozen terminator. (By "frozen" I mean stationary).</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Delta V and the rocket equation</b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The <a href="https://retrorockets.wordpress.com/2012/12/17/buidling-a-miniature-solar-system-part-2/">Retrorockets guy took a second look at mini solar systems</a>. While trip times are short and launch windows frequent, it still takes a lot of delta V to insert to a Hohmann transfer. I was annoyed he used the <a href="http://hopsblog-hop.blogspot.com/2014/02/the-most-common-delta-v-error.html">incorrect Tom Murphy method of patching conics</a>. But most his math is sound. He is correct that Tsiolkovsky's rocket equation would be a major pain in the mini solar system just as it is in ours. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
This is where a tether system comes into play. Given elevators on tide locked bodies and assuming most the bodies are nearly coplanar, travel between bodies could be done with very little reaction mass. It'd still take a lot of energy to move stuff up and down the elevators. But the <a href="http://hopsblog-hop.blogspot.com/2012/08/mf-is-mofo-tyranny-of-rocket-equation_21.html">difficult mass fractions imposed by the Tsiolkovsky's equation</a> would no longer be a consideration.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Summary</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Similar mathematical models and drawings can be used for a wide range of vertical tethers.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
A popular misconception is that elevators are only good for getting off the ground. So it's a waste to build an elevator from a small body. But an elevator not only gets the payload off the ground, it can fling a payload towards a destination. The hyperbolic orbits portrayed in this post are especially interesting.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Space elevators would be especially useful in a system of tide locked moons. Or tide locked planets about a small star.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
So far the only elevators I see portrayed in science fiction are from major planets. Like Kim Stanley Robinson's elevators in his Mars trilogy. Or Clarke's earth elevator in Fountains of Paradise. There are far more plausible elevators that could be very useful. These doable elevators could also provide many interesting settings.</div>
Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com2tag:blogger.com,1999:blog-3596550435682943926.post-2388888642818180372016-08-27T12:08:00.001-07:002020-04-13T12:46:31.695-07:00Pluto Charon Elevator<div class="separator" style="clear: both;">
<b><span style="font-size: large;">Double Tidal Locking</span></b></div>
<div>
<br /></div>
<div>
Pluto and Charon are mutually tidally locked. That is, they both present the same face to the other planet all the time. They hover motionless in each other's sky. Pluto is in Charon synchronous orbit and Charon is in Pluto synchronous orbit.</div>
<div>
<br /></div>
<div>
What is more, <a href="http://iopscience.iop.org/article/10.1088/0004-6256/144/1/15/meta;jsessionid=2CE6401D6B25577CF8E58A3F0B1D4AA5.c1.iopscience.cld.iop.org">the orbit is very nearly circular</a>.<br />
<br />
From <a href="https://arxiv.org/pdf/1510.07704.pdf">Stern et al's 2015 paper</a>:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimLP2OTkfb8SJMD_Sl2zbRrpoQ3XxnSJC_7BqrdzbWvAHOqojf5FcLX_0qm6vtssSgEj5I9u6ljYSjtANFNHTO2A4jmP2YXVpN7owkdTxxZNqZ6gqaFKsvM9qsvv2RoEynA-NVjCyrou3K/s1600/Screen+Shot+2019-03-09+at+11.41.47+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="224" data-original-width="818" height="174" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimLP2OTkfb8SJMD_Sl2zbRrpoQ3XxnSJC_7BqrdzbWvAHOqojf5FcLX_0qm6vtssSgEj5I9u6ljYSjtANFNHTO2A4jmP2YXVpN7owkdTxxZNqZ6gqaFKsvM9qsvv2RoEynA-NVjCyrou3K/s640/Screen+Shot+2019-03-09+at+11.41.47+AM.png" width="640" /></a></div>
<br /></div>
<div>
(Thank you to Dr. Kirby Runyon for pointing me to this paper).<br />
<br /></div>
<div>
A tether could be extended from Pluto's near point to Charon's near point. Since the orbit is so nearly circular and obliquity is tiny, there would very very little flexing of this tether.</div>
<div>
<br /></div>
<div>
<b><span style="font-size: large;">Minimum Tether to Remain Aloft</span></b></div>
<div>
<br /></div>
<div>
To remain aloft, a tether anchored to Charon would need to extend past the L1 point more than 10,000 kilometers to within nearly 2,500 kilometers of Pluto's surface.</div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJIcPMAqegXy0O0nEVQA1lnS2VkLSsfgNwcSMVTQlcdZaUOqyc0vntKaznFdtCLf6-p-bO_Ws88tWhMUe_aiVFHioXLOAGtTf-j9arE7_ULo5neGc2dE0os5ypNEXpeuswmCEymR7PF9pS/s1600/Pluto+Charon+Graphic.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="144" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJIcPMAqegXy0O0nEVQA1lnS2VkLSsfgNwcSMVTQlcdZaUOqyc0vntKaznFdtCLf6-p-bO_Ws88tWhMUe_aiVFHioXLOAGtTf-j9arE7_ULo5neGc2dE0os5ypNEXpeuswmCEymR7PF9pS/s640/Pluto+Charon+Graphic.jpg" width="640" /></a></div>
<div>
<br /></div>
<div>
This tether would be more than 15,000 kilometers long. Using <a href="http://hopsblog-hop.blogspot.com/2015/12/how-wolfes-tether-spreadsheet-works.html">Wolfe's Spreadsheet </a>we find Zylon taper ratio is 1.13. Tether to Payload mass ratio is .88. This is with a safety factor of 3.<br />
<br />
<b><span style="font-size: large;">All The Way To Pluto</span></b><br />
<br />
Extending the tether an additional 2,500 kilometers anchors it to Pluto's surface.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5qqBr_d02nVGHj4N-Z5hVn8calO4J26D_ciztJXTbgZT_3j-1sAAJelxTKe1B1Yih7Z7tID0A6VJiIameV_gS44Qw-fgapNtu2la_FN-p8hhYCos2sdXikmLTieyZV5IENp8Z5EFHnq_p/s1600/Pluto+Charon+Graphic2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="144" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5qqBr_d02nVGHj4N-Z5hVn8calO4J26D_ciztJXTbgZT_3j-1sAAJelxTKe1B1Yih7Z7tID0A6VJiIameV_gS44Qw-fgapNtu2la_FN-p8hhYCos2sdXikmLTieyZV5IENp8Z5EFHnq_p/s640/Pluto+Charon+Graphic2.jpg" width="640" /></a></div>
<br />
Taper ratio is about 1.7 and Tether to Payload mass ratio is 14.36.<br />
<br />
Still acceptable but dramatically different from a tether only 2,500 shorter. This is because we dropped the tether foot into a much steeper part of Pluto's gravity well.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEit50h0UC65ulD4yUTT4ljQmrfwgBcI1axoCrvSqIdhEEkn3rZ6lxzY0nhDur7t6ZjhDDsrSY_nm7DLTFm6cIFyv04OZyHTiDbUn_HnPr6aDT0M3AsgvFwM_qFUlPHApBFTE4lwTLljz67g/s1600/Pluto+Charon+Acceleration.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEit50h0UC65ulD4yUTT4ljQmrfwgBcI1axoCrvSqIdhEEkn3rZ6lxzY0nhDur7t6ZjhDDsrSY_nm7DLTFm6cIFyv04OZyHTiDbUn_HnPr6aDT0M3AsgvFwM_qFUlPHApBFTE4lwTLljz67g/s640/Pluto+Charon+Acceleration.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Net acceleration is .62 meters/second<sup>2</sup> at the Pluto end of the elevator. Very close to Pluto's surface gravity. At the Charon anchor net acceleration is -.28 meters/second<sup>2</sup>. Very close to Charon's surface gravity. It is negative to indicate it's in the opposite direction from Pluto's gravity.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
At L1 net acceleration is zero.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
It's easy to see most of the stress newtons come from the close neighborhoods of Pluto or Charon. It might be worthwhile to build standard compressive towers at the elevator anchor points.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">What's The Point?</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Pluto's surface escape velocity is 1.2 km/s. Charon's surface escape velocity is .6 km/s. It's not that hard to get off the surface of Pluto or Charon. So what's the point of an elevator?</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Space craft with very good ISP have meager thrust. With such space craft soft landings on Pluto or Charon would not be possible. Nor could they leave the surface of these planets.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
But a low thrust craft could dock with the elevator at L1. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
From L1 a small nudge could send passengers or cargo towards Pluto or Charon. And gravity would pull it the rest of the way down.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
I believe Pluto Charon L1 would become a major metropolis on the corridor between two major city states as well as a port to the rest of the solar system.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Will humans reach Pluto?</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>The Edge of Sunlight</b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Sunlight falls with inverse square of distance from sun. Asteroids 3 A.U. from from the sun will receive 1/9 of the insolation we enjoy on earth. Sun Jupiter Trojans at 5 A.U. will get 1/25 the sunlight. We could compensate by constructing large parabolic mirrors to harvest sunlight.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmF7M0U_C0YvbOWkiVxDvmwkMi2HsIDzFh0Et-JRXvX9tc2LuTSYmDeybjKzMk6MphqgTxi0ppb_vDLtYX3U1vqBPHrna-GFD8DtVYETlIdWp-Ny3yjtuLEIKBqwq-90ALagb9XwBP88BF/s1600/Parabolic+Mirror.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="522" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmF7M0U_C0YvbOWkiVxDvmwkMi2HsIDzFh0Et-JRXvX9tc2LuTSYmDeybjKzMk6MphqgTxi0ppb_vDLtYX3U1vqBPHrna-GFD8DtVYETlIdWp-Ny3yjtuLEIKBqwq-90ALagb9XwBP88BF/s640/Parabolic+Mirror.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
Giant parabolic mirrors could harvest sunlight for spin habs.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
But Pluto has a 30 A.U. by 49 A.U. orbit. And most of the time it dwells in the neighborhood of aphelion. 1/49<sup>2</sup> = about 1/2400. Mirrors for the KBO nation states would need to be vast. Mike Combs wrote a <a href="http://www.nss.org/settlement/MikeCombs/eyeshine.htm">neat story</a> featuring these sorts of mega mirrors. As much as I enjoy Mike's story, I don't think such monster mirrors are practical.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Fusion Power?</b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Will our technology achieve practical fusion power plants? Maybe. If so, that would vastly expand our possible frontiers.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>The 4th Space Frontier</b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
There's nothing like <a href="http://hopsblog-hop.blogspot.com/2016/02/limits-to-growth-logistic-vs-exponential.html">logistic growth ceilings</a> to motivate opening a new frontier. As we settle and fill up one frontier, we start looking over the horizon. I'm going to make some wildly speculative predictions. This is a science fiction blog, after all.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
1st space frontier: NEAs, Luna, Mars, Phobos and Deimos. This would give us one or two millennia of unrestrained growth.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
2nd space frontier: The Main Belt. Three millennia of exponential growth. Ceres will be the capital of this United Federation of Main Belt Nation States. This frontier will open within a century or two after we establish a strong foothold on Mars/<a href="http://hopsblog-hop.blogspot.com/2015/06/phobos-panama-canal-of-inner-solar.html">Phobos</a>/Deimos.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
3rd space frontier: The Sun Jupiter Trojans. The <a href="http://hopsblog-hop.blogspot.com/2016/07/hildas-as-cyclers.html">Hildas</a> will be our ride from the Main Belt to the Trojans. It will take five hundred years to fill the Trojan petri dish.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
4th space frontier: The Kuiper Belt as well as the icey moons of Saturn, Uranus and Neptune. As mentioned earlier, this would require practical power sources other than sunlight. Pluto will be the capital of the United Federation of Kuiper Belt Nation States. This frontier will take 10 millennia to expand into.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
5th space frontier: The Oort. The nation states of the Oort will be separated by vast distances. They will be more isolated than even the nation states of the Kuiper. There is a strong incentive to become less reliant on trade and more self sufficient. 20 millennia of unrestrained growth. By the time we reach the outer Oort, nation states will be self sufficient biomes. There would be nothing preventing an outer Oort nation state from achieving solar escape velocity and leaving our sun's sphere of influence.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The Outer Oort Nation States will be natural generation star ships.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Charon Elevator through L2</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Enough wild eyed fantasy. Back to mundane stuff like space elevators in the Kuiper Belt.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
To maintain tension and remain , an elevator from Charon's far point through the Pluto Charon L2 would need to extend 41,000 kilometers. With a safety factor of 3, Zylon taper ratio would be 1.14. Tether to Payload mass ratio would be about .3.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Small Problem: Styx</b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Pluto's moon Styx orbits at a distance of 42,600 kilometers from Pluto. Charon orbits at about 20,000 kilometers from Pluto. So a tether from Charon's far point can only extend about 22,000 kilometers before it runs the risk of an impact with Styx.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
A counterweight would need to be placed on the elevator somewhere below the orbit of Styx. If placed just below the orbit of Styx, the tether top could impart a velocity of about .5 km/s. Which would be helpful for injection into heliocentric transfer orbits to other destinations in the solar system.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
This elevator could also help with transportation between Charon and the other <a href="https://en.wikipedia.org/wiki/Moons_of_Pluto">moons of Pluto</a>: Styx, Nix, Kerboros and Hydra. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
An ion craft could also dock with Pluto Charon L2, so L2 could also serve as a port to the rest of the solar system. There are <a href="http://www.gg.caltech.edu/~mwl/publications/papers/heteroclinic.pdf">heteroclinic paths</a> between L1 and L2 so transportation between the two elevators would be easy.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Pluto And I Share An Annivesary</span></b></div>
<br />
Clyde Tombaugh discovered Pluto on February 18, 1930. February 18 is my birthday! So I guess it's only natural I'm interested in this body, we're practically twins.</div>
Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com7tag:blogger.com,1999:blog-3596550435682943926.post-4381851852668661102016-08-17T13:11:00.001-07:002020-04-13T12:46:59.871-07:00Tran Cislunar Railroad<div class="separator" style="clear: both;">
<b><span style="font-size: large;">Three Orbital Tethers</span></b></div>
<span style="font-size: large;"><b><br /></b></span>
This post revisits <a href="http://hopsblog-hop.blogspot.com/2015/05/orbital-momentum-as-commodity.html">Orbital Momentum As A Commodity</a>. But now I will examine these tethers using <a href="http://hopsblog-hop.blogspot.com/2015/12/how-wolfes-tether-spreadsheet-works.html">Wolfe's spreadsheet</a>.<br />
<br />
I envision 3 equatorial tethers to move stuff back and forth between LEO and the lunar neighborhood:<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioWBg_bsHpXXl3shrGV686bzaLXJ2mobE0A0JYxniYWa2q11FMjJu1GjTbeyKvpfi0umQiXM37fmYza7iiAGiVDRjK0HK6iaDggtNfqsXTj6E6ExBCKL6F7mPvHlw92xla2vwdPcGyQaJJ/s1600/Screen+Shot+2015-05-27+at+5.23.23+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioWBg_bsHpXXl3shrGV686bzaLXJ2mobE0A0JYxniYWa2q11FMjJu1GjTbeyKvpfi0umQiXM37fmYza7iiAGiVDRjK0HK6iaDggtNfqsXTj6E6ExBCKL6F7mPvHlw92xla2vwdPcGyQaJJ/s640/Screen+Shot+2015-05-27+at+5.23.23+PM.png" width="587" /></a><br />
<br />
<br />
The location of these vertical tethers avoids zones of <a href="https://en.wikipedia.org/wiki/Space_debris">orbital debris</a>:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIRWdP2nml1AodWPHowm7TEHTsdR_bTGtbbhKMCglYqKHx2jZKha3k0MkNQ8Znh7M0BgRsPS8mAR35Lx75VrrQwvRsS7j-Lce5YAjpu-m2IYJ0x3GOuAjGEfGEU6YWJTW09nEWBZ8hlo4z/s1600/Screen+Shot+2015-05-27+at+4.49.29+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIRWdP2nml1AodWPHowm7TEHTsdR_bTGtbbhKMCglYqKHx2jZKha3k0MkNQ8Znh7M0BgRsPS8mAR35Lx75VrrQwvRsS7j-Lce5YAjpu-m2IYJ0x3GOuAjGEfGEU6YWJTW09nEWBZ8hlo4z/s640/Screen+Shot+2015-05-27+at+4.49.29+PM.png" width="534" /></a></div>
<br />
The orange regions, LEO, MEO and GEO, have high satellite and/or debris density. Thus tethers in those regions would be more vulnerable to damage from impacts.<br />
<b><span style="font-size: large;"><br /></span></b>
<b><span style="font-size: large;">Dead Sats for tether anchors</span></b><br />
<br />
Unless elevator mass is lot more than the payloads, the acts of catching or throwing could destroy the tether orbit. At first it looks like the need for a substantial anchor mass is a show stopper. But there are a large number of dead sats in equatorial orbits. By one estimate, <a href="http://space.stackexchange.com/questions/9185/how-many-dead-sats-near-geo/9705#9705">there's 670 tonnes in the graveyard orbit above geosynch</a>.<br />
<br />
The dead sats gathered might have functioning solar arrays. According to <a href="http://space.stackexchange.com/questions/13482/whats-salvageable-from-a-dead-satellite">this stack exchange</a> discussion, solar arrays degrade by 2 to 3% a year due to radiation, debris impacts and thermal degradation. Thus a 20 year old array could still be providing 50% to 66% of the power it delivered at the beginning of its life. The parabolic dishes for high gain antennas might also be salvageable.<br />
<br />
Whether functioning or not, solar arrays as well as other paneling might be used as shades to keep propellent cold. If our tethers receive propellent from the moon or from asteroids parked in lunar orbit, shades would help with cryogenic storage.<br />
<br />
Consolidating dead equatorial satellites would reduce their cross sectional area and help solve the problem of orbital debris.<br />
<br />
<b><span style="font-size: large;">Super GEO tether</span></b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUoN7nrV5S6hni07CvM3w8ZuynNVMrNUMeFjNqWyKBWYNuutwz4mn2T-okVk_Lg-BXevp-aLJ5-ULUbLwQ6qls2eIjGyrIEBTpGevQ94VOCXU19s-0g7pD7H7spoAudAvCY57ng8IJibxv/s1600/Screen+Shot+2016-08-15+at+8.13.13+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="484" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUoN7nrV5S6hni07CvM3w8ZuynNVMrNUMeFjNqWyKBWYNuutwz4mn2T-okVk_Lg-BXevp-aLJ5-ULUbLwQ6qls2eIjGyrIEBTpGevQ94VOCXU19s-0g7pD7H7spoAudAvCY57ng8IJibxv/s640/Screen+Shot+2016-08-15+at+8.13.13+PM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The circular orbit pictured above is 10,000 km above Geosynchronous Earth Orbit (GEO). The lower part of the tether has a length of 7,000 km and the upper tether is 10,340 km in length.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
A Space Stack Exchange answer estimates there are <a href="http://space.stackexchange.com/a/9705/2848">670 tonnes of dead sats</a> in the geosynch graveyard orbit. <a href="http://www.esa.int/Our_Activities/Operations/Space_Debris/Space_debris_by_the_numbers">Here</a> is a page that tries to estimate total mass in earth orbit.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Delta V to raise the dead sats to this higher orbit is about .28 km/s. This might be accomplished with ion engines. Also the elevator could be used to send some to the sats towards the lower MEO tether. This would help with the .28 km/s delta V budget.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Upper Super GEO Tether, 10,340 km long</b></div>
<table border="0" style="width: 360px;">
<tbody>
<tr>
<td>Safety Factor</td>
<td>3</td>
</tr>
<tr>
<td>Zylon taper ratio:</td>
<td>1.38</td>
</tr>
<tr>
<td>Tether to payload mass ratio:</td>
<td>.78</td>
</tr>
<tr>
<td>Tether top radius</td>
<td>62,504 km</td>
</tr>
<tr>
<td>Tether top speed:</td>
<td>3.3 km/s</td>
</tr>
<tr>
<td>Tether top net acceleration:</td>
<td>.07 m/s<sup>2</sup> (.007 g)</td>
</tr>
<tr>
<td>Payload apogee:</td>
<td>384,400 km</td>
</tr>
<tr>
<td>Payload apogee speed:</td>
<td>.53 km/s</td></tr>
</tbody></table>
<br />
The payload apogee is at lunar altitude and the payload's moving .53 km/s. The moon moves at about 1 km/s. So Vinf with regard to the moon is about .47.<br />
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Lower Super GEO tether, 7,100 km long</b></div>
<div class="separator" style="clear: both; text-align: left;">
</div>
<table border="0" style="width: 360px;">
<tbody>
<tr>
<td>Safety Factor</td>
<td>3</td>
</tr>
<tr>
<td>Zylon taper ratio:</td>
<td>1.21</td>
</tr>
<tr>
<td>Tether to payload mass ratio:</td>
<td>.47</td>
</tr>
<tr>
<td>Tether foot distance from earth</td>
<td>45,000 km</td>
</tr>
<tr>
<td>Tether foot speed:</td>
<td>2.4 km/s</td>
</tr>
<tr>
<td>Tether foot net acceleration:</td>
<td>.07 m/s<sup>2</sup> (.007 g)</td>
</tr>
<tr>
<td>Payload perigee:</td>
<td>21,450 km</td>
</tr>
<tr>
<td>Payload perigee speed:</td>
<td>5 km/s</td>
</tr>
</tbody></table>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The tether foot drops a payload to rendezvous with the MEO tether.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Sub MEO Tether</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijygokYfULz0od5d32awOAAcAb2zROLFt0NqtAzTKOw8khklmnV83SNV693u9zRxkrvg4X1BgB6QmnLPGsBQplyZRbKH2mQc3uEs11AaTk0pUe4R6NIjM93oY3h08iOmGLJH34AoFpbFf4/s1600/Screen+Shot+2016-08-15+at+8.34.20+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijygokYfULz0od5d32awOAAcAb2zROLFt0NqtAzTKOw8khklmnV83SNV693u9zRxkrvg4X1BgB6QmnLPGsBQplyZRbKH2mQc3uEs11AaTk0pUe4R6NIjM93oY3h08iOmGLJH34AoFpbFf4/s640/Screen+Shot+2016-08-15+at+8.34.20+PM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="text-align: left;"><br /></span></div>
<div class="separator" style="clear: both;">
The circular orbit of the Sub MEO anchor mass is has a radius of 19,425 km. To get satellites from the super synchronous graveyard orbit to this orbit takes about 1.4 km/s. Some of that 1.4 km/s might be accomplished with the super GEO tether. Sending mass downward would help push the remaining GEO sats upward.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
<b>Upper Sub MEO Tether, 2,050 km long</b></div>
<table border="0" style="width: 360px;">
<tbody>
<tr>
<td>Safety Factor</td>
<td>3</td>
</tr>
<tr>
<td>Zylon taper ratio:</td>
<td>1.30</td>
</tr>
<tr>
<td>Tether to payload mass ratio:</td>
<td>.61</td>
</tr>
<tr>
<td>Tether top distance from earth</td>
<td>21,450 km</td>
</tr>
<tr>
<td>Tether top speed:</td>
<td>5 km/s</td>
</tr>
<tr>
<td>Tether top net acceleration:</td>
<td>.3 m/s<sup>2</sup> (.03 g)</td>
</tr>
<tr>
<td>Payload apogee:</td>
<td>45,000 km</td>
</tr>
<tr>
<td>Payload apogee speed:</td>
<td>2.4 km/s</td>
</tr>
</tbody></table>
<br />
The payload apogee radius and speed matches the foot of the super GEO tether's radius and speed.<br />
The top of this tether's radius and speed matches the payload perigee and speed sent from super GEO tether. The Sub MEO and Super GEO tethers can exchange payloads with minimal delta V at tether/payload rendezvous.<br />
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Lower Sub MEO tether.</b></div>
<div class="separator" style="clear: both; text-align: left;">
</div>
<table border="0" style="width: 360px;">
<tbody>
<tr>
<td>Safety Factor</td>
<td>3</td>
</tr>
<tr>
<td>Zylon taper ratio:</td>
<td>1.35</td>
</tr>
<tr>
<td>Tether to payload mass ratio:</td>
<td>.78</td>
</tr>
<tr>
<td>Tether foot radius</td>
<td>17,375 km</td>
</tr>
<tr>
<td>Tether foot speed:</td>
<td>4.1 km/s</td>
</tr>
<tr>
<td>Tether foot net acceleration:</td>
<td>.38 m/s<sup>2</sup> (.038 g)</td>
</tr>
<tr>
<td>Payload perigee:</td>
<td>9,680 km</td>
</tr>
<tr>
<td>Payload perigee speed:</td>
<td>7.3 km/s</td>
</tr>
</tbody></table>
<br />
<div>
The Low Sub MEO tether sends and receivse payloads to and from the upper Super LEO tether.</div>
<div>
<br /></div>
<div>
<b><span style="font-size: large;">Super LEO Tether</span></b></div>
<div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXpXUzxkNcpcpMGeA5YBwLDvZyl13u7KuGXsm2pCAoFnigGPd3zJEPgcaVBbzkoWhUEG_TNCB20nG3UHsB7arQQVQe4aDEr-ShAxWRFYJGZdDm3GlhdjQ0_6QqYxABtHZNNHizkHyj0hUo/s1600/Screen+Shot+2016-08-16+at+9.36.55+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="472" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXpXUzxkNcpcpMGeA5YBwLDvZyl13u7KuGXsm2pCAoFnigGPd3zJEPgcaVBbzkoWhUEG_TNCB20nG3UHsB7arQQVQe4aDEr-ShAxWRFYJGZdDm3GlhdjQ0_6QqYxABtHZNNHizkHyj0hUo/s640/Screen+Shot+2016-08-16+at+9.36.55+PM.png" width="640" /></a></div>
<br />
The anchor mass is in a circular orbit of radius 9300 km.<br />
<b><br /></b>
<b>Upper Super LEO Tether, 765 km long</b></div>
<table border="0" style="width: 360px;">
<tbody>
<tr>
<td>Safety Factor</td>
<td>3</td>
</tr>
<tr>
<td>Zylon taper ratio:</td>
<td>1.4</td>
</tr>
<tr>
<td>Tether to payload mass ratio:</td>
<td>.84</td>
</tr>
<tr>
<td>Tether top radius</td>
<td>10,065 km</td>
</tr>
<tr>
<td>Tether top speed:</td>
<td>7.1 km/s</td>
</tr>
<tr>
<td>Tether top net acceleration:</td>
<td>.11 m/s<sup>2</sup> (.011 g)</td>
</tr>
<tr>
<td>Payload apogee:</td>
<td>17375 km</td>
</tr>
<tr>
<td>Payload apogee speed:</td>
<td>4.1 km/s</td>
</tr>
</tbody></table>
<br />
The payload apogee is at lunar altitude and the payload's moving .53 km/s. The moon moves at about 1 km/s. So Vinf with regard to the moon is about .47.<br />
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Lower Super LEO tether, 450 km long</b></div>
<div class="separator" style="clear: both; text-align: left;">
</div>
<table border="0" style="width: 360px;">
<tbody>
<tr>
<td>Safety Factor</td>
<td>3</td>
</tr>
<tr>
<td>Zylon taper ratio:</td>
<td>1.13</td>
</tr>
<tr>
<td>Tether to payload mass ratio:</td>
<td>.29</td>
</tr>
<tr>
<td>Tether foot distance from earth</td>
<td>8,844 km</td>
</tr>
<tr>
<td>Tether foot speed:</td>
<td>6.2 km/s</td>
</tr>
<tr>
<td>Tether foot net acceleration:</td>
<td>.7 m/s<sup>2</sup> (.07 g)</td>
</tr>
<tr>
<td>Payload perigee:</td>
<td>6,778 km</td>
</tr>
<tr>
<td>Payload perigee speed:</td>
<td>8.3 km/s</td>
</tr>
</tbody></table>
<br />
<div>
Perigee altitude is about 300 km. Circular orbital speed at this atltitude is about 7.7 km/s. To send a LEO payload on it's way to the Super LEO tether would take about .6 km/s.<br />
<br />
Sending a payload from the tether to LEO can take less than .6 km/s as the delta v needed for circularizing can be provided by aerobraking.<br />
<br />
<b><span style="font-size: large;">Total Tether Mass to Payload Ratio</span></b><br />
<br />
We've looked at a total of 6 tether lengths, the upper and lower parts of 3 vertical tethers.<br />
<br />
<b>Tether Mass to Payload Mass Ratios & Lengths</b><br />
<table border="0" style="width: 300px;">
<tbody>
<tr>
<td><br /></td>
<td><div style="text-align: right;">
T/P</div>
</td>
<td style="text-align: right;">Length (km)</td>
</tr>
<tr>
<td>Upper Super GEO</td>
<td><div style="text-align: right;">
.78</div>
</td>
<td style="text-align: right;">10340</td>
</tr>
<tr>
<td>Lower Super GEO</td>
<td><div style="text-align: right;">
.47</div>
</td>
<td style="text-align: right;"> 7100</td>
</tr>
<tr>
<td>Upper Sub MEO</td>
<td><div style="text-align: right;">
.61</div>
</td>
<td style="text-align: right;"> 2050</td>
</tr>
<tr>
<td>Lower Sub MEO</td>
<td><div style="text-align: right;">
.78</div>
</td>
<td style="text-align: right;"> 2050</td>
</tr>
<tr>
<td>Upper Super LEO</td>
<td><div style="text-align: right;">
.84</div>
</td>
<td style="text-align: right;"> 765</td>
</tr>
<tr>
<td>Lower Super LEO</td>
<td><div style="text-align: right;">
.29</div>
</td>
<td style="text-align: right;"> 450</td>
</tr>
<tr>
<td><b>Total:</b></td>
<td><div style="text-align: right;">
<b>3.77</b></div>
</td>
<td style="text-align: right;"><b>22,755</b></td>
</tr>
</tbody></table>
<br />
Thus 38 tonnes of Zylon could accommodate 10 tonnes of payload. That's not too bad.<br />
<br />
A much larger problem is the anchor mass needed for each tether. There are lots of dead sats just above GEO that could be gathered for the Super GEO tether anchor mass. But anchor masses for the sub MEO and super LEO tethers will be more expensive. This is a possible show stopper.<br />
<br />
<b><span style="font-size: large;">Facilitating Momentum Exchange</span></b><br />
<br />
<b>Using Hall Thrusters to restore momentum.</b><br />
<br />
Sending mass from LEO to a lunar height apogee saps our tethers' orbital momentum. The momentum hit is somewhere around payload mass * 4 km/s. Orbital momentum can be restored gradually with ion thrusters. Hall Thrusters can expel xenon with a 30 km/s exhaust velocity.<br />
<br />
Plugging these numbers into the rocket equation:<br />
<br />
Propellent mass fraction = 1 - e <sup>-4/30</sup> = ~.125.<br />
<br />
About 1/8. So to make up for the momentum lost throwing 7 tonnes of payload, we'd need a tonne of xenon. Better than chemical but still expensive.<br />
<br />
<b>Lunar or NEA propellent as a source of up momentum.</b><br />
<br />
Some Near Earth Asteroids (NEAs) can be parked in lunar orbit for as little as .2 km/s. Carbonaceous asteroids can be up to 40% water by mass (in the form of hydrated clays). There may be rich water ice deposits in the lunar cold traps. So far as I know, these are the most accessible potential sources of extra terrestrial propellent.<br />
<br />
Catching propellent from higher orbits would boost a tether's momentum. Dropping this payload to a lower tether would also boost momentum.<br />
<br />
Thus up momentum can be traded for down momentum. Xenon reaction mass to maintain tether orbits can be cut drastically with two way traffic.<br />
<br />
<b>Jon Goff's gear ratios</b><br />
<br />
Jon Goff has pointed out it take some delta V to get propellent from the moon's surface to LEO. Thus only ~10% of propellent mined lunar cold traps would make it LEO. See his blog post <a href="http://selenianboondocks.com/2013/12/the-slings-and-arrows-of-outrageous-lunar-transportation-schemes-part-1-gear-ratios/">The Slings And Arrows of Outrageous Lunar Transportation Schemes Part-1 Gear ratios</a>.<br />
<br />
Well, lunar propellent could be a source of down momentum for the <a href="http://hopsblog-hop.blogspot.com/2016/08/lunar-sky-hook.html">Lunar Sky Hook</a> I described recently. And a source of up momentum for the Trans Cislunar Railroad this blog post looks at. NEA propellent could also be a source of up momentum for the Trans Cislunar Railroad.<br />
<br />
Using propellent as a source of tether up momentum I believe it's plausible for 40% of the lunar propellent to make it to LEO. In which case it becomes plausible to use reaction mass to mitigate the extreme conditions of re-entry.<br />
<br />
<b><span style="font-size: large;">Breaking the Genie's Bottle</span></b><br />
<br />
The human race is a genie in a bottle. Given Tsiolkovsky's rocket equation, it's enormously difficult to cross the boundaries that confine us. But given infrastructure and resources at our disposal, we can build bridges to larger frontiers.<br />
<br />
<br />
<br /></div>
Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com9tag:blogger.com,1999:blog-3596550435682943926.post-42655506582680444882016-08-08T21:00:00.000-07:002020-04-13T12:47:18.714-07:00Lunar Sky Hook<div class="separator" style="clear: both;">
Kim Holder has been urging me to do this blog post. Her comments in various forums have been helpful in thinking about this.</div>
<br />
<b><span style="font-size: large;">Vertical Lunar Tether In A Polar Orbit</span></b><br />
<br />
This sky hook is a gravity gradient stabilized vertical tether. It's in a polar orbit so it will pass over the poles as well as the lower lunar latitudes.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimbBagBIzufLaUPpUDmzLAxuCkhMea1C_W406AMg2w_OqKK_Bm3Y-yAR8MWOMC2zs80Zqwqa5gTG0zipbFbGErA1WALVYGfznhXDmds1VwiQs_3gqsD-KaTACh8Z9_qF9I6LxrlagmvIBa/s1600/Screen+Shot+2016-08-08+at+4.00.09+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="434" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimbBagBIzufLaUPpUDmzLAxuCkhMea1C_W406AMg2w_OqKK_Bm3Y-yAR8MWOMC2zs80Zqwqa5gTG0zipbFbGErA1WALVYGfznhXDmds1VwiQs_3gqsD-KaTACh8Z9_qF9I6LxrlagmvIBa/s640/Screen+Shot+2016-08-08+at+4.00.09+PM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="text-align: left;"><br /></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="text-align: left;">Unlike an equatorial orbit, there are only two occasions during a lunar orbit where a tether's Vinf velocity vector is anti-parallel to the moon's velocity vector. So launch windows to earth would only occur each two weeks. That's still pretty often. These occasions are also good times to rendezvous with the tether.</span></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Playing with earth moon three body simulations, polar orbits seem to remain stable up to a radius of around 20,000 kilometers. That is where I will set the anchor mass at the balance point of this sky hook. I believe this is far enough above the lunar surface that the <a href="https://en.wikipedia.org/wiki/Mass_concentration_(astronomy)">mascons</a> won't damage this tether's orbit.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG5mAfnk2xIIRDMrrj5nQcnOWvEMCfwDGIKYPwM_MJO4wQTXowxu2O8js6yfyZrl7P4xlhi484Zy-u4K2WjCLKOsNMDByqKrD7YTAb741AVVVGQuQRL9EWuNDpyF9ffbxXIp5USCn0V20l/s1600/Lunar+Sky+Hook.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG5mAfnk2xIIRDMrrj5nQcnOWvEMCfwDGIKYPwM_MJO4wQTXowxu2O8js6yfyZrl7P4xlhi484Zy-u4K2WjCLKOsNMDByqKrD7YTAb741AVVVGQuQRL9EWuNDpyF9ffbxXIp5USCn0V20l/s640/Lunar+Sky+Hook.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Asteroid Anchor Mass Via a Keck vehicle</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
What to use for the anchor mass? With the asteroid retrieval vehicle proposed in the <a href="http://www.nss.org/settlement/asteroids/Asteroid_Retrieval_Feasibility_Study_2012.pdf">Keck Report</a>, it is possible for a vehicle of moderate mass to retrieve a much larger mass to the earth moon neighborhood. The Keck authors believe a rock could be placed in high lunar orbit for around .17 km/s. A lunar orbit with a 20,000 km radius has a speed of around .5 km/s. I believe it would take around .7 km/s to park a rock in the orbit we want.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The Keck vehicle includes solar panel arrays and Hall ion thrusters. These would be great to have on a vertical tether. It takes awhile for ion engines to impart momentum, but given time they're about ten times as efficient as the best chemical rockets. A tether can build up momentum over time but release it suddenly. Thus they are a good way to enjoy an ion engine's great ISP <b><i>and</i></b> an Oberth benefit.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
As well as adjusting the tether's orbit the Keck vehicle's solar arrays might also power elevator cars moving up and down the tether. If water is exported from from the lunar cold traps to the tether, the arrays might also crack water into oxygen and hydrogen bipropellent. There are a number of possible uses for this power source.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b><span style="font-size: large;">Upper Tether</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The tether length above the anchor mass can be built in increments. I imagine the tether growing longer and more able with time. Here are three possible stages:</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>To EML2 or EML1</b></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHKUpdN5S9Yax4aN6czEImPdmVawZsSNc_ZvrDbSvesUs6yLtXQNhhavGXXpmP9C6OM_adp9MSr9FDpvAJNfX_2fX-90spfX4BqaMgA22fNGMQ-kW5oSlbMHf_9h_6Ebmdy9fDiP_cDdFz/s1600/To+EML2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHKUpdN5S9Yax4aN6czEImPdmVawZsSNc_ZvrDbSvesUs6yLtXQNhhavGXXpmP9C6OM_adp9MSr9FDpvAJNfX_2fX-90spfX4BqaMgA22fNGMQ-kW5oSlbMHf_9h_6Ebmdy9fDiP_cDdFz/s640/To+EML2.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
EML1 and 2 are about 65,000 km from the moon. To reach this apolune, we'd need an upper tether length of about 2700 kilometers. Using <a href="http://hopsblog-hop.blogspot.com/2015/12/how-wolfes-tether-spreadsheet-works.html">Wolfe's spread sheet</a>, this tether length has a taper ratio of 1. With a safety factor to 3, tether mass to payload ratio is about .02.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
This is pretty good. I believe this low stress tether length could accommodate copper wires to transmit power to the elevator cars.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Once at apolune, I believe it would take about .3 km/s to park the payload at EML2 or EML1.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="http://hopsblog-hop.blogspot.com/2015/05/eml2.html">EML2</a> is a good staging location should we want to travel to and from destinations beyond the earth-moon neighborhood.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<b>To a Perigee at Geosynchronous Orbit</b> </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5dIvmacv7G7428K4L1qOA1ObvNMcconmZlUdi0FkDn5JXlJc97u6eNBKi7INZgiQbX6nzelVRaQT3hvOmoMfNQQqOiDYqyiFWIA_FZ1kcsh_rnP9ftlzaBt8GORVh8P_PaSm7BMJzOSlU/s1600/To+GEO.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="259" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5dIvmacv7G7428K4L1qOA1ObvNMcconmZlUdi0FkDn5JXlJc97u6eNBKi7INZgiQbX6nzelVRaQT3hvOmoMfNQQqOiDYqyiFWIA_FZ1kcsh_rnP9ftlzaBt8GORVh8P_PaSm7BMJzOSlU/s640/To+GEO.jpg" width="640" /></a></div>
<br />
<br />
Transfer orbit from GEO to the moon is about a an ~36,000 x 378,000 ellipse. Apogee speed is about .45 km/s. The moon's speed is about 1.02 km/s. So the tether needs to hurl a payload to a Vinf of (1.02-.45) km/s or about .57 km/s.<br />
<br />
To achieve this Vinf our tether needs to be 12,200 km. Zylon taper ratio is 1.09. With a safety factor of three, Tether to payload mass ratio is about .167. So a ten tonne tether could accommodate a sixty tonne payload. This is still pretty good. A power cable along this length is also doable.<br />
<br />
Perigee velocity of our transfer orbit is ~4.13 km/s. Geosynch orbit velocity is ~3.07 km/s. If the transfer orbit and destination geosynch orbit are coplanar, geosynch circularization would be about 1.06 km/s. But I expect that would be the exception rather than the rule. If the orbit inclinations differ by 20º, 1.6 km/s would be needed to park in geosynch.<br />
<br />
<b>To a Perigee at Low Earth Orbit.</b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFtiQZC2wu01pg-jS0z9s12bX3IgfHkr-eYmHMiFwdK8clrQxG-aKC3mjhTM0q2FtX0pZmdP6HRybym0yfyBWZnYM0Mu3MyCrBfIh6iwbb6GWR96GdX6QBX1hPsPa0JD6j1BRv942W6gvx/s1600/To+LEO.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="274" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFtiQZC2wu01pg-jS0z9s12bX3IgfHkr-eYmHMiFwdK8clrQxG-aKC3mjhTM0q2FtX0pZmdP6HRybym0yfyBWZnYM0Mu3MyCrBfIh6iwbb6GWR96GdX6QBX1hPsPa0JD6j1BRv942W6gvx/s640/To+LEO.jpg" width="640" /></a></div>
<br />
<br />
A 300 x 378,000 km orbit has apogee velocity of ~.19 km/s. (1.02 - .19) km/s = .83 km/s.<br />
<br />
To throw a payload to a trans earth orbit, our tether needs to impart a Vinf of .83 km/s. This takes a tether length of 19,200 kilometers. With a safety factor of three, Zylon taper ratio is 1.2. Tether to payload mass ratio is .38.<br />
<br />
If perigee is through earth's upper atmosphere, aerobraking can provide a large part of the 3.1 km/s delta V for circularizing at LEO.<br />
<br />
<div class="separator" style="clear: both;">
<b><span style="font-size: large;">Lower Tether</span></b></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
Again, the tether length below the anchor mass can be built in increments. Incremental growth with time is more doable than trying to do the whole length in fell swoop. Here are some possible steps along the way.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
<b>To a Perilune at Low Lunar Orbit.</b></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmUYUDRK2eUOIMxAHt8AJJmDnzCfatT-XcfcrOl3CyO2mnNisnqMaDu7JsboLVJD96zCWRLyWFRxB2lnGDr8-_ueNRH6z5Kj42hyphenhyphengKBz0se0qW2kot3kirNzRiyI-yZue9DfcMvZfFIrBW/s1600/To+LLO.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmUYUDRK2eUOIMxAHt8AJJmDnzCfatT-XcfcrOl3CyO2mnNisnqMaDu7JsboLVJD96zCWRLyWFRxB2lnGDr8-_ueNRH6z5Kj42hyphenhyphengKBz0se0qW2kot3kirNzRiyI-yZue9DfcMvZfFIrBW/s640/To+LLO.jpg" width="640" /></a></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
To drop a payload to a 90 km altitude perilune, length needs to be 7360 km. Given a safety factor of 3, Zylon taper ratio is 1.06. Tether to payload mass ratio is .15.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
Velocity of transfer orbit's perilune is about 2.2 km/s. Low lunar orbit is about 1.6 km/s. It'd take about .6 km/s to circularize at low lunar orbit. </div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
<b>To the Moon's Surface, Impact Velocity 1 km/s.</b></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0HeXmMY-COvAt5CYztX14mODLCMcjdHIFPRJaZVjxvwasQ43ANGZtuG0gL9yi5VmpOlKQZBV2r8d4Gqfn_7e1snNrnCENH_9WV7M_wvnRYda1jxLwAg7I_KU-iresYvtgvkwfkxln34oC/s1600/1+km+s+impact.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="170" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0HeXmMY-COvAt5CYztX14mODLCMcjdHIFPRJaZVjxvwasQ43ANGZtuG0gL9yi5VmpOlKQZBV2r8d4Gqfn_7e1snNrnCENH_9WV7M_wvnRYda1jxLwAg7I_KU-iresYvtgvkwfkxln34oC/s640/1+km+s+impact.jpg" width="640" /></a></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
If the tether is extended to a length of 17890 km, tether foot altitude is about 370 km. Dropping a payload from this tether foot would result in a 1 km/s impact. </div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
Given a safety factor of <b><i>two</i></b>, Zylon taper ratio is 2.88. Tether to payload mass ratio is 26.87.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
<i>Note the safety factor is less than in the other scenarios</i>. As we descend further into the moon's gravity well, stress climbs more rapidly. It would be more difficult to include copper wires for power along the lower parts of the tether.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
<b>To a Tether Foot Just Above the Moon's Surface.</b></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhe4pr1FGRmHzGynZpVj3f-PJxOURJQaFT6PkYAxyQjwhTueHAkx8GJIO3o24euGLr-8OJ39JbBk3XNviAgo2pmQfehxAH-i1fBw5JMTMGW5UDRnBUpkvVyTt6yQ8zEAwEcR8pR5nunKW5-/s1600/Surface.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhe4pr1FGRmHzGynZpVj3f-PJxOURJQaFT6PkYAxyQjwhTueHAkx8GJIO3o24euGLr-8OJ39JbBk3XNviAgo2pmQfehxAH-i1fBw5JMTMGW5UDRnBUpkvVyTt6yQ8zEAwEcR8pR5nunKW5-/s640/Surface.jpg" width="640" /></a></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
Dropping the tether foot to an altitude of 10 kilometers gives us a length of 18,252 km. Safety factor of 2 and Zylon taper ratio is 3.72. Tether to payload mass ratio is about 51.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
Dropping from this tether foot, a payload would impact the lunar surface at .184 km/s. </div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
A .2 km/s payload delta V budget for soft landing seems quite doable. Likewise it would take about .2 km/s to launch a payload from the lunar to rendezvous with the tether foot.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
However dropping the tether foot this far is considerably more ambitious than the other scenarios described above.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
<b><span style="font-size: large;">Travel About The Moon</span></b></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
Kim Holder noted such a tether might serve as transportation between locations on the moon.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
Without a tether, going from pole to pole would take about 3.4 km/s: 1.7 km/s to launch and another 1.7 for soft landing. Going from equator to pole would take 1.53 km/s to launch and another 1.53 km/s for a soft landing, totaling 3.06 km/s. </div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
So a 18,000 km lower lunar tether length would make travel about the moon easier.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
<b><span style="font-size: large;">A Location to Process Asteroid Ore</span></b></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
It takes about .6 km/s to park ore from some of the more accessible asteroids in 20,000 km lunar orbit. If rendezvous with the tether top is doable, it could take considerably less.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
I envision infrastructure accreting about the tether anchor mass 18,262 km above the lunar surface. Water, platinum, gold, rare earth metals, and other materials could be extracted at the anchor. Refined commodities could climb to the top of the tether and then tossed earthward.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
<b><span style="font-size: large;">A Synergy Between The Moon and Near Earth Asteroids</span></b></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
Moon and asteroid enthusiasts are often at odds with one another. They should be allies. In terms of delta V, it's a lot easier to park asteroids in lunar orbit than lower earth orbits. And given growing infrastructure in lunar orbit, the moon's surface becomes more accessible.</div>
Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com12tag:blogger.com,1999:blog-3596550435682943926.post-6017159156668576912016-07-22T18:25:00.000-07:002020-04-13T12:47:36.233-07:00Hildas As Cyclers<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJvo7bAHOaOrj_kg4t5C3hSQEyaizr7VOyuCl-qSU7h6dCOeKdWwotOf9IEo-s9jrer20UHCmJcLk5rgIhZWbmqUpoP1in7i7B5FnUewhmMY5-jAevrZLZH29sbNYOeYDB7nNTowhk37Fw/s1600/Screen+Shot+2016-07-22+at+8.56.39+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJvo7bAHOaOrj_kg4t5C3hSQEyaizr7VOyuCl-qSU7h6dCOeKdWwotOf9IEo-s9jrer20UHCmJcLk5rgIhZWbmqUpoP1in7i7B5FnUewhmMY5-jAevrZLZH29sbNYOeYDB7nNTowhk37Fw/s640/Screen+Shot+2016-07-22+at+8.56.39+AM.png" width="618" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="background-color: white;"><span style="color: #cc0000;"><br /></span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="background-color: white;"><span style="color: #cc0000;">Hilda Asteroids - Red</span>, <span style="color: blue;">Sun Jupiter Trojans - Blue</span>, <span style="color: #45818e;">Main Belt - Green</span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="background-color: white;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;">The above image was made from screen captures of Scott Manley's beautiful animation <a href="https://www.youtube.com/watch?v=yt1qPCiOq-8">Asteroids In Resonance With Jupiter.</a></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;">Jupiter is the dot off to the left, the sun is the yellow dot in the middle. Within the Main Belt can be seen Mercury, Venus, Earth and Mars. I colored the different asteroid populations so we can tell them apart.</span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;">The <a href="https://en.wikipedia.org/wiki/Jupiter_trojan">Sun Jupiter Trojans</a> have a 1 to 1 resonance with Jupiter. They co-rotate with Jupiter. The leading Trojans remain in a neighborhood 60 degrees ahead of Jupiter and the trailing Trojans stay in a neighborhood 60 degrees behind.</span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;">The <a href="https://en.wikipedia.org/wiki/Hilda_family">Hildas</a> have have 3 to 2 resonance with Jupiter meaning they circle the sun three times for every two Jupiter orbits. Jupiter's orbital period is about 12 years and the Hildas have 8 year periods.</span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;">The Hilda orbits only look triangular in Manley's animation because they're being viewed in a rotating frame. You can see Jupiter remains on the left side of the image. In an inertial frame, a Hilda orbit is an ordinary elliptical orbit with aphelion passing through the Trojans and perihelion passing through the main belt.</span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO1xZ45ktGbI4MgL6-CEBu7VwywoQcfpXexqTPO7E8Gj569YqX9dG8vTefCWYVs6-7rFF1hA959jqa6qWMrXrZxAzkU5osTmdMQOD3a23ZT6u3ICNmWHuSZK0icARR2uhKJBFMH0EM-lA2/s1600/Jupiter+Hildas.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO1xZ45ktGbI4MgL6-CEBu7VwywoQcfpXexqTPO7E8Gj569YqX9dG8vTefCWYVs6-7rFF1hA959jqa6qWMrXrZxAzkU5osTmdMQOD3a23ZT6u3ICNmWHuSZK0icARR2uhKJBFMH0EM-lA2/s640/Jupiter+Hildas.jpg" width="604" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
I envision the Hilda biomes playing a similar role as Marco Polo's caravans shuttling people and goods between east and west. But the Hildas travel between the Trojans and the Main Belt.</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
The would be a series of regular fly bys for a Hilda Cycler</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
1) Main Belt to trailing Trojans — 4 years.</div>
<div class="separator" style="clear: both; text-align: justify;">
2) Trailing Trojans to Main Belt — 4 years.</div>
<div class="separator" style="clear: both; text-align: justify;">
3) Main Belt to leading Trojans — 4 years</div>
<div class="separator" style="clear: both; text-align: justify;">
4) Leading Trojans to Main Belt — 4 years</div>
<div class="separator" style="clear: both; text-align: justify;">
5) Main Belt to Sun Jupiter L3 — 4 years. But there is no asteroid population at SJL3.</div>
<div class="separator" style="clear: both; text-align: justify;">
6) From SJL3 to Main Belt 4 years</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
Then back to step 1). The cycle repeats itself.</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
So not only can a Hilda be a go between between the Main Belt and Trojans, but it can also move stuff between the trailing and leading Trojan populations. Trailing to leading takes 8 years and leading to trailing takes 16 years.</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
As can be seen from Manley's animation, there is a steady stream of Hildas traveling the circuit. </div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
<b><span style="font-size: large;">Delta V</span></b></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
The Hildas have a variety of eccentricities. I will look at a Hilda orbit having an eccentricity of .31. That would put the aphelion at 5.2 A.U. and the perihelion at 2.74 A.U. (The perihelion is in Ceres' neighborhood, Ceres' semi-major axis is 2.77 A.U.).</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
Assuming a circular, coplanar orbit at 2.74 A.U., it would take 2.6 km/s to leave a Main Belt Asteroid and board a Hilda.</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
Assuming a circular, coplanar orbit at 5.2 A.U., it would take 2.2 km/s to depart the Hilda and rendezvous with a Trojan.</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
However, coplanar orbits is a very optimistic assumption. Asteroids have a large variety of inclinations. Making a 10 degree plane change from a Hilda's orbit can cost 2 to 3 km/s.</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
<b>Ways to mitigate delta V expense</b></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
Many asteroids spin about pretty fast. This plus their shallow gravity wells make them amenable to <a href="http://hopsblog-hop.blogspot.com/2012/09/beanstalks-elevators-clarke-towers.html">bean stalks</a>, also known as space elevators. </div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
"Why would an asteroid need a space elevator?" I'm sometimes asked. The questioner will assert "It's very easy to get off an asteroid's surface, and getting off the body's surface is the only reason for an elevator." Which is wrong, of course.</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
Speed of a body on an elevator is <span style="background-color: white;">ωr where </span><span style="background-color: white;">ω is angular velocity in radians per time unit and r is distance from center of rotation. If r is large, the elevator can fling a payload at high velocity with regard to the asteroid. It is quite plausible for an asteroid's bean stalk to provide .5 to 1 km/s delta V.</span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="background-color: white;"><br /></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="background-color: white;">Also an asteroid bean stalk allows rendezvous with an ion propelled space craft. Ion ships have great ISP but minute thrust. Soft landings with an ion craft are not possible on larger asteroids like Ceres, or Vesta.</span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="background-color: white;"><br /></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="background-color: white;">And ion propelled ships are more viable in the outer system. When a ship's acceleration is a large fraction of the local gravity acceleration, an ion burn is more like a chemical impulsive burn. See <a href="http://space.stackexchange.com/a/8421/2848">General Guidelines for Modeling a Low Thrust Ion Spiral</a>. In the outer Main Belt, the sun's gravity is about 1 millimeter/sec<sup>2</sup>. Sun's gravity at the Trojans is about .2 millimeters/sec<sup>2</sup>.</span></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div :="" class="separator" id="JupiterTrojans" style="clear: both; text-align: justify;">
<b><span style="font-size: large;">Jupiter's Trojans</span></b></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
Not much is known about Jupiter's Trojans. <a href="http://www.japantimes.co.jp/news/2016/07/21/national/science-health/huge-sail-will-power-jaxa-mission-trojan-asteroids-back/#.V5K6buvFypP">Japan hopes to launch a mission in the early 2020's</a>. Another proposed mission is <a href="https://en.wikipedia.org/wiki/Lucy_(spacecraft)">Lucy</a> which would also launch in the early 2020's. </div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
These bodies are on average 5.2 A.U. from the sun and so receive only 1/27 the sunlight earth enjoys. For this reason I am hopeful they are rich in volatile ices. I'd give better than even odds they have lots of water and carbon dioxide ice. Nitrogen compounds like ammonia and cyano compounds are a possibility. Aside from earth, Nitrogen is in short supply throughout the inner solar system and these would be a great export to the Main Belt biomes.</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
Their numbers are speculation. According to <a href="https://en.wikipedia.org/wiki/Jupiter_trojan#Numbers_and_mass">Wikipedia</a>:</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<blockquote class="tr_bq">
Estimates of the total number of Jupiter trojans are based on deep surveys of limited areas of the sky.<sup class="reference" id="cite_ref-Yoshida2005_1-2" style="font-size: 11px; line-height: 1; unicode-bidi: -webkit-isolate; white-space: nowrap;"><a href="https://en.wikipedia.org/wiki/Jupiter_trojan#cite_note-Yoshida2005-1" style="background-image: none; color: #0b0080; text-decoration: none;">[1]</a></sup> The <a href="https://en.wikipedia.org/wiki/Lagrangian_point#L4_and_L5" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="Lagrangian point">L<sub style="font-size: 11px; line-height: 1;">4</sub></a> swarm is believed to hold between 160–240,000 asteroids with diameters larger than 2 km and about 600,000 with diameters larger than 1 km. If the <a href="https://en.wikipedia.org/wiki/Lagrangian_point#L4_and_L5" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="Lagrangian point">L<sub style="font-size: 11px; line-height: 1;">5</sub></a> swarm contains a comparable number of objects, there are more than <span class="nowrap" style="white-space: nowrap;">1 million</span> Jupiter trojans 1 km in size or larger. For the objects brighter than <a href="https://en.wikipedia.org/wiki/Absolute_magnitude#Solar_System_bodies_.28H.29" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="Absolute magnitude">absolute magnitude</a> 9.0 the population is probably complete. These numbers are similar to that of comparable asteroids in the asteroid belt. The total mass of the Jupiter trojans is estimated at 0.0001 of the mass of Earth or one-fifth of the mass of the asteroid belt.</blockquote>
<blockquote class="tr_bq">
Two more recent studies indicate, however, that the above numbers may overestimate the number of Jupiter trojans by several-fold. This overestimate is caused by (1) the assumption that all Jupiter trojans have a low <a href="https://en.wikipedia.org/wiki/Albedo" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="Albedo">albedo</a> of about 0.04, whereas small bodies may actually have an average albedo as high as 0.12;<sup class="reference" id="cite_ref-Fernandes2009_18-0" style="font-size: 11px; line-height: 1; unicode-bidi: -webkit-isolate; white-space: nowrap;"><a href="https://en.wikipedia.org/wiki/Jupiter_trojan#cite_note-Fernandes2009-18" style="background-image: none; color: #0b0080; text-decoration: none;">[16]</a></sup> (2) an incorrect assumption about the distribution of Jupiter trojans in the sky. According to the new estimates, the total number of Jupiter trojans with a diameter larger than 2 km is <span class="nowrap" style="white-space: nowrap;">6.3 ± 1.0<span style="margin: 0px 0.15em 0px 0.25em;">×</span>10<sup style="font-size: 11px; line-height: 1;">4</sup></span> and <span class="nowrap" style="white-space: nowrap;">3.4 ± 0.5<span style="margin: 0px 0.15em 0px 0.25em;">×</span>10<sup style="font-size: 11px; line-height: 1;">4</sup></span> in the <a href="https://en.wikipedia.org/wiki/Lagrangian_point#L4_and_L5" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="Lagrangian point">L<sub style="font-size: 11px; line-height: 1;">4</sub></a> and <a href="https://en.wikipedia.org/wiki/Lagrangian_point#L4_and_L5" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="Lagrangian point">L<sub style="font-size: 11px; line-height: 1;">5</sub></a>swarms, respectively. These numbers would be reduced by a factor of 2 if small Jupiter trojans are more reflective than large ones.<sup class="reference" id="cite_ref-Fernandes2009_18-1" style="font-size: 11px; line-height: 1; unicode-bidi: -webkit-isolate; white-space: nowrap;"><a href="https://en.wikipedia.org/wiki/Jupiter_trojan#cite_note-Fernandes2009-18" style="background-image: none; color: #0b0080; text-decoration: none;">[16]</a></sup></blockquote>
<blockquote class="tr_bq">
The number of Jupiter trojans observed in the <a href="https://en.wikipedia.org/wiki/Lagrangian_point#L4_and_L5" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="Lagrangian point">L<sub style="font-size: 11px; line-height: 1;">4</sub></a> swarm is slightly larger than that observed in <a href="https://en.wikipedia.org/wiki/Lagrangian_point#L4_and_L5" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="Lagrangian point">L<sub style="font-size: 11px; line-height: 1;">5</sub></a>. However, because the brightest Jupiter trojans show little variation in numbers between the two populations, this disparity is probably due to observational bias. However, some models indicate that the <a href="https://en.wikipedia.org/wiki/Lagrangian_point#L4_and_L5" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="Lagrangian point">L<sub style="font-size: 11px; line-height: 1;">4</sub></a> swarm may be slightly more stable than the <a href="https://en.wikipedia.org/wiki/Lagrangian_point#L4_and_L5" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="Lagrangian point">L<sub style="font-size: 11px; line-height: 1;">5</sub></a> swarm. </blockquote>
<blockquote class="tr_bq">
The largest Jupiter trojan is <a href="https://en.wikipedia.org/wiki/624_Hektor" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="624 Hektor">624 Hektor</a>, which has an average diameter of 203 ± 3.6 km. There are few large Jupiter trojans in comparison to the overall population. With decreasing size, the number of Jupiter trojans grows very quickly down to 84 km, much more so than in the asteroid belt. A diameter of 84 km corresponds to an absolute magnitude of 9.5, assuming an <a href="https://en.wikipedia.org/wiki/Albedo" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none;" title="Albedo">albedo</a> of 0.04. Within the 4.4–40 km range the Jupiter trojans' size distribution resembles that of the main-belt asteroids. An absence of data means that nothing is known about the masses of the smaller Jupiter trojans. The size distribution suggests that the smaller Trojans are the products of collisions by larger Jupiter trojans.
</blockquote>
<br />
I'd love to see science fiction stores set on 624 Hektor.<br />
<br />
This article written in memory of Hilda Alvarez May 5, 1929 - July 20, 2016<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com5tag:blogger.com,1999:blog-3596550435682943926.post-73372779742162233762016-05-26T13:34:00.000-07:002016-05-26T13:34:25.322-07:00Rotovator help with re-entryThere are proposals for rotovators to catch payloads in low earth orbit and then throw them to higher orbits.<br />
<br />
It occurs to me that rotovators used for throwing comm sats to GTO could also help the upper stage re-enter earth's atmosphere at a lower velocity.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Juict3Wr0_5hm9Uz2cBmEyl1AfN0jVCSpRGu00idw0OLUAXxt-IYV83uvkkloKRFU6kSuwl-nrXZ7rI0X240cki3T62Ksz2Deih_YMsyEC0HHWhrocERJgGU4i3cIVV81378WX4zTbSM/s1600/Rotovator+upper+stage.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Juict3Wr0_5hm9Uz2cBmEyl1AfN0jVCSpRGu00idw0OLUAXxt-IYV83uvkkloKRFU6kSuwl-nrXZ7rI0X240cki3T62Ksz2Deih_YMsyEC0HHWhrocERJgGU4i3cIVV81378WX4zTbSM/s640/Rotovator+upper+stage.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
1) Rotovator catches upper stage and payload in LEO.</div>
<div class="separator" style="clear: both; text-align: left;">
2) Rotovator throws payload to higher orbit.</div>
<div class="separator" style="clear: both; text-align: left;">
3) Rotovator drops upper stage into a suborbital orbit.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Step 3) accomplishes two things:</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
a) It restores some of the orbital momentum the tether lost in catching and tossing the payload.</div>
<div class="separator" style="clear: both; text-align: left;">
b) It reduces re-entry velocity of the upper stage. Slower re-entry velocities make recovery and reuse of the upper stage less difficult.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Is this a good idea? Or another hare brained scheme? I'm tossing this out in several venues hoping knowledgeable folks will review it.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com5tag:blogger.com,1999:blog-3596550435682943926.post-33766077261694734542016-04-16T13:00:00.000-07:002020-04-13T12:48:13.157-07:00Liftport Lunar Tether<div class="separator" style="clear: both;">
This is the fifth in a series of posts using <a href="http://hopsblog-hop.blogspot.com/2015/12/how-wolfes-tether-spreadsheet-works.html">Chris Wolfe's spreadsheet</a> to look at various elevators.</div>
<br />
<b><span style="font-size: large;">274,000 km Lunar Tether</span></b><br />
<br />
This is based on the <a href="http://www.lpi.usra.edu/meetings/leag2011/pdf/2043.pdf">Ladder PDF</a> written by <a href="https://en.wikipedia.org/wiki/LiftPort_Group">Liftport</a> founder Michael Laine and Marshall Eubanks.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPZlRs7YS762yQmcL6EEsLmewXLXu6xDsB6-HwfbQtkJHROxiz8tDENJshdBZHf8s_CLyIiBGbaE9LSjBGJzgc000bm0CMP9LACSAYPIYOPtnxsR0USlhai6FZX73rLFsMO-TzkrgoWb-N/s1600/LiftportLunarTether.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPZlRs7YS762yQmcL6EEsLmewXLXu6xDsB6-HwfbQtkJHROxiz8tDENJshdBZHf8s_CLyIiBGbaE9LSjBGJzgc000bm0CMP9LACSAYPIYOPtnxsR0USlhai6FZX73rLFsMO-TzkrgoWb-N/s640/LiftportLunarTether.jpg" width="307" /></a></div>
<br />
Eubanks and Laine suggest the use of Zylon or M5. This is why I've been using Zylon through out these tether posts. These gentlemen have invested a lot of time and effort researching elevators and tethers. If they like Zylon, I'll follow suit.<br />
<br />
They propose launching the tether to EML1. From EML1, the tether anchor would descend moonward towards Sinus Medii on the lunar surface, 0º, 0º. The spent upper stage would drop with the tether foot earthward.<br />
<br />
If the mass were tethers alone, the 264,000 length would be inadequate to keep the tether from collapsing to the moon. But spent upper stage acts as a counterweight to maintain tension.<br />
<br />
<b>Ratios earthside of EML1</b><br />
<br />
A spent Centaur upper stage is about 2250 kilograms. This is the quantity I used for foot station mass. These newtons subtract from newtons available for payload. The Ladder PDF calls for 11 tonnes of Zylon. By trial and error I entered payload quantities until tether mass in my spreadsheet came to 11 tonnes.<br />
<br />
In addition to foot station mass of 2250 kg, I got a maximum foot payload mass of 1640 kg.<br />
<br />
Zylon taper ratio: 1.61. Tether mass to payload mass ratio: 8.05<br />
<br />
Given the extreme the extreme length of this elevator, I expected a higher number than 8. But the net acceleration at the tether foot is only .0274 newtons per kilogram. With this acceleration, a 10 tonne mass would exert as much force as when my 62 pound dog sits on my lap.<br />
<br />
<b>Ratios moonside of EML1</b><br />
<br />
But what sort of payload can this elevator support moonside of EML1?<br />
<br />
At the anchor in Sinus Medii, my tether model's cross sectional area is 1.64e-8 square meters. Multipying this times Zylon's tensile strength gives ~95.4 newtons the tether can support. Net acceleration at this point is 1.4 meters/s^2 (mostly moon's gravity). 95.4 newtons/(1.4 m/s^2) = 68 kilograms. For a payload just above the moon's surface, the elevator can support 68 kilograms.<br />
<br />
Tether to payload mass ratio: 161.<br />
<br />
Let's say we wanted a 1 tonne elevator car capable of carrying 9 tonnes of cargo. We'd need a 1,610 tonne tether.<br />
<br />
<b>Benefits</b><br />
<b><br /></b>
Dropping a payload from 70,900 km earthward of EML1 would send a payload to to an atmosphere grazing orbit. Repeated perigee aerobraking passes could circularize the orbit. Shedding 3 km/s via repeated drag passes would require some thermal protection but not as much as the space shuttle which would shed 8 km/s over a very short time.<br />
<br />
Thus lunar materials could be delivered to Low Earth Orbit (LEO) without using reaction mass.<br />
<br />
Likewise, a 3 km/s LEO burn could deliver payloads to an apogee where orbit velocity matches tether velocity. Normal delta V from LEO to moon surface is about 6 km/s. So the elevator cuts about 3 km/s from the delta V budget for reaching the moon's surface. Cutting 3 km/s from delta V budget about doubles payload mass if using H/Lox bi-propellent.<br />
<br />
Dropping a payload 160,000 km earth of EML1 would send a payload to an orbit with perigee as geosynchronous orbit altitude. At perigee the circularization burn is .95 km/s. Thus delta V between GSO and lunar surface is less than kilometer per second.<br />
<br />
<b>Some drawbacks</b><br />
<br />
This is a very long tether. How fast can an elevator car move? Having copper wire along the length of the tether would boost taper ratio as well tether to payload mass ratio. For descent from EML1 to lunar surface, the tether to payload mass ratio is already 161.<br />
<br />
So in addition to carrying gripping wheels and a motor, the elevator car must carry it's own power source. Photovoltaic arrays? There are <a href="https://en.wikipedia.org/wiki/Solar_golf_cart">solar powered golf carts</a>. These aren't famous for their speed. There are <a href="https://en.wikipedia.org/wiki/Tesla_Motors">Tesla</a> cars whose lithium batteries can be charged by solar cells. These vehicles can move. It is also possible lithium batteries could be charged during an elevator cars down hill descent via <a href="https://en.wikipedia.org/wiki/Regenerative_brake">regenerative braking</a>. Downhill would be moonward or earthward from EML1. Movement towards EML1 would be uphill.<br />
<br />
Batteries, solar arrays and/or regenerative brakes would boost elevator car mass and thus subtract from cargo mass.<br />
<br />
Let's say the elevator car can move an average speed of 400 mph (644 kilometers/hour). A round trip along the length of this elevator and back would take about a month. If the elevator doubles payload mass delivered from LEO, it'd take about 160 months to recoup the investment of delivering tether mass from LEO.<br />
<br />
And what justifies this investment? What are the benefits of a facility at Sinus Medii?<br />
<br />
I'm a moon guy but it's the lunar poles I like. There are polar plateaus that enjoy near constant sunlight and very mild temperature swings. These plateaus neighbor permanently shadowed crater floors that might harbor rich volatile deposits. In situ CHON not only makes life support easier, but extra-terrestrial propellent could break the exponent in the rocket equation.<br />
<br />
But Sinus Medii is at the equator. It's as far from the lunar poles as a lunar surface point can possibly be. We're stuck with two week nights, severe temperature swings and regolith drier than a bone.<br />
<br />
Charles Radley has suggested mining He3. I'm not holding my breath but what if we achieved fusion power? <a href="http://www.transterrestrial.com/?p=41338#comment-271482">Here</a> is John Schilling's take on fusion and lunar He3:<br />
<blockquote class="tr_bq">
Helium-3 mining on the moon simply does not pass the arithmetic test. The highest 3He concentration ever recorded in lunar regolith is fifteen parts per billion, and the process by which it is deposited is inherently resistant to geologic concentration.<br />
Assuming someone manages to invent a 3He fusion reactor that operates at 50% efficiency (giggle), that translates to net energy output of 4.5E6 joules per kilogram of high-grade regolith.<br />
The energy output of a kilogram of the lowest grade of coal burned in a good 19th-century reciprocating steam engine, is about 4.5E6 joules per kilogram. And that doesn’t change if you substitute dried peat for the coal.<br />
So, the proposal is to set up an enormous mining infrastructure on the Moon, and invent a fundamentally new kind of engine backed by fifty years of failed promises, for the sake of an energy source roughly as good as burning high-grade dirt in a type of engine obsolete for over a century.<br />
And no, that analysis doesn’t change significantly if we include accessible reserves or environmental impact.<br />
I understand that you want desperately to believe that there are immense riches to be had in space, as soon as the suits see the light and come up with the money. The good news is, this is probably true. But the list of great riches to be had in space, does not include lunar helium-3 (or helium-4, for that matter). The numbers do not add up, no matter what the glossy magazine articles say, and math trumps faith.</blockquote>
<br />
Other than fuel for fusion it is hard to imagine He3 markets that would justify the expense of a lunar tether and mine.<br />
<br />
I admire Michael Laine. I believe tethers will play a part in making space transportation economical. I also like and admire Charles Radley as well as Marshall Eubanks. So it pains me to say this. At this point I am not enthusiastic about the Liftport Lunar elevator.<br />
<br />
But there are <a href="http://hopsblog-hop.blogspot.com/2016/08/lunar-sky-hook.html">other possible elevators</a> in the moon's neighborhood.<br />
<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com11tag:blogger.com,1999:blog-3596550435682943926.post-3653764703939194922016-02-11T11:50:00.000-08:002020-04-13T12:48:35.197-07:00Limits to growth, logistic vs exponential<div class="separator" style="clear: both;">
<b><span style="font-size: large;">Malthusian growth model</span></b></div>
<br />
The <a href="https://en.wikipedia.org/wiki/Malthusian_growth_model">Malthusian growth model</a> sees population growth as exponential.<br />
<br />
P(t) = P<sub>o</sub>e<sup>rt</sup><br />
where<br />
P<sub>o </sub>= P(0) is the initial population size,<br />
r = population growth rate<br />
t = time<br />
<br />
Growth of microbe populations are often used to illustrate this. Let's say an amoeba will grow and divide into two amoeba after an day of absorbing nutrients.<br />
<br />
Day 1: 1 amoeba<br />
Day 2: 2 amoeba<br />
Day 3: 4 amoeba<br />
Day 4: 8 amoeba<br />
<br />
And so on. Population doubles each day. <a href="http://hop41.deviantart.com/art/The-legend-of-Paal-Paysam-188153459">Exponential growth</a> is famous for starting out slow and then zooming through the roof.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHgK1RvEd7xdN78jEb5r3uaL26cxfvq2ropE5t-N9O2x76N4OhzGzUJzX8Ktv25w2RCHkdVgYHY2qEFTqUMwRqp_knmINx2fSv4uruw8Nf9BUAc6Me-iGgJejaWcw8BqoSdBigifGbr1N5/s1600/Screen+Shot+2016-02-08+at+7.06.13+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="406" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHgK1RvEd7xdN78jEb5r3uaL26cxfvq2ropE5t-N9O2x76N4OhzGzUJzX8Ktv25w2RCHkdVgYHY2qEFTqUMwRqp_knmINx2fSv4uruw8Nf9BUAc6Me-iGgJejaWcw8BqoSdBigifGbr1N5/s640/Screen+Shot+2016-02-08+at+7.06.13+PM.png" width="640" /></a></div>
<br />
On the left is exponential growth in cartesian coordinates. On the right in polar coordinates, radius doubles every circuit.<br />
<br />
Malthus imagined a rapidly growing population consuming all their available food supply and then starving to death.<br />
<br />
<b><span style="font-size: large;">Logistic growth</span></b><br />
<br />
Sometimes populations have suffered Malthusian disaster. More often rate of growth slows as the population approaches the limit that resources can support. This is <a href="https://en.wikipedia.org/wiki/Logistic_function">logistic growth</a>.<br />
<br />
P(t) = Le<sup>-rt</sup> / (L +( e<sup>-rt</sup> - 1))<br />
<br />
Where L is the maximum population local resources can support.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ0HuRfasYE87X1_oZcuZ2TVMcTdy0_HjK8_aq_FMieSu-EFn7h9gFI76uuH5Tbb4N9f3dTy6zNHPg3KNeqizO2Lpe-TFLLh-j4n6IOnrG3dfr5-81CmaDAA1hVlijZk8ZS9RSWI7g1crd/s1600/Screen+Shot+2016-02-09+at+9.10.35+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="402" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ0HuRfasYE87X1_oZcuZ2TVMcTdy0_HjK8_aq_FMieSu-EFn7h9gFI76uuH5Tbb4N9f3dTy6zNHPg3KNeqizO2Lpe-TFLLh-j4n6IOnrG3dfr5-81CmaDAA1hVlijZk8ZS9RSWI7g1crd/s640/Screen+Shot+2016-02-09+at+9.10.35+PM.png" width="640" /></a></div>
<br />
At the start, logistic growth resembles exponential growth. But as the population nears the logistic ceiling, growth tapers off. Above the blue boundary represents the limit to growth. In red is the logistic growth curve, the thinner black curve is exponential growth.<br />
<br />
<b><span style="font-size: large;">What slows growth?</span></b><br />
<br />
In Heinlein's science fiction, war limits growth. This was also the foundation idea of Niven and Pournelle's <i><a href="https://en.wikipedia.org/wiki/The_Mote_in_God%27s_Eye">The Mote In God's Eye</a></i> -- War is the inevitable result of burgeoning populations.<br />
<br />
<a href="https://en.wikipedia.org/wiki/Four_Horsemen_of_the_Apocalypse">The Four Horsemen of Apocalypse</a> -- plague, war, famine and death are seen as natural outcomes of uncontrolled population growth.<br />
<br />
A <a href="http://www.economist.com/node/14743589">declining fertility rate</a> is a less ominous way to step on the brakes. It is my hope most people will choose to have small families. And indeed, current trends indicate people are voluntarily having fewer kids. Still, there are skirmishes as various entities compete for limited resources.<br />
<br />
<span style="font-size: large;"><b>Bad vs worse</b></span><br />
<br />
A growing population, a growing consumer appetite, a limited body of resources. It doesn't take a rocket scientist to see growth must eventually level off.<br />
<br />
Whether it levels off via the 4 horsemen or moderation and voluntary birth control, either option sucks. It's disaster vs stagnation.<br />
<br />
<b><span style="font-size: large;">Alternatives?</span></b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhABZOe41Ij_mtgSjih2Hw5bDhmfqC0vDxZrSdy28axD0mC2joY-k7srD1sL-451L0mvj9KWVBq9z44PZdVIw4fNZwfb7_tmkjW38MmAECMLgPjR4q_Cs3y6b_PuWurhsrF78EtI6EJz72-/s1600/Johnny+Robinson+Cartoon.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="416" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhABZOe41Ij_mtgSjih2Hw5bDhmfqC0vDxZrSdy28axD0mC2joY-k7srD1sL-451L0mvj9KWVBq9z44PZdVIw4fNZwfb7_tmkjW38MmAECMLgPjR4q_Cs3y6b_PuWurhsrF78EtI6EJz72-/s640/Johnny+Robinson+Cartoon.gif" width="640" /></a></div>
<br />
Above is a <a href="http://johnnyrobinson.com/index.html">Johnny Robinson</a> cartoon. Used with permission.<br />
<br />
I believe our solar system is possibly the next frontier. That has been the thrust of this blog since the start. If we do manage to break our chains to earth, it will be a huge turning point in human history, more dramatic than the settling of the Americas. The potential resources and real estate dwarf the north and south American land masses.<br />
<br />
While settling the solar system allows expansion, it won't relieve population pressure on earth. Settlement of the Americas did not relieve population pressure in Europe, Asia and Africa. Mass emigration is impractical.<br />
<br />
Rather, pioneers jumping boundaries starts growth within the new frontiers. I like to view the logistic growth spiral in polar form as a petri dish. When a population within a petri dish has matured to fill its boundaries, it sends spores out to neighboring petri dishes. Then populations within neighboring petri dishes grow to their limits.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5KTFJ-TQ-cnx2Dge2IP2_XQlbNHELh3pw_Dhs3wsg1EqNSRTE139unO7gD2Cx-2Q0l7x5Twg3qll0Oq1AlSibVDkiE1UsDBYT0NWgVjyIOEvSaAKlLE2HlmL2JIGpy8Majpqpz19bBKii/s1600/Screen+Shot+2016-02-11+at+12.08.51+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5KTFJ-TQ-cnx2Dge2IP2_XQlbNHELh3pw_Dhs3wsg1EqNSRTE139unO7gD2Cx-2Q0l7x5Twg3qll0Oq1AlSibVDkiE1UsDBYT0NWgVjyIOEvSaAKlLE2HlmL2JIGpy8Majpqpz19bBKii/s640/Screen+Shot+2016-02-11+at+12.08.51+PM.png" width="580" /></a></div>
<br />
<br />
The first petri dish still has a population filling the limit. They have not escaped the need to live within their means. I take issues with critics who say space enthusiasts want to escape to a new planet after earth has been trashed. Space enthusiasts know earth is fragile, more so than the average person. It is noteworthy that Elon Musk is pioneering planet preserving technologies such as electric cars and solar energy.<br />
<br />
But even if mass emigration from Europe or Asia was not possible, the expansion into the Americas energized the economy and zeitgeist of the entire planet. It provided investment opportunities. Also an incentive to explore. This is the greatest benefit of a frontier. Curiosity is one of the noblest human qualities and I hope we will always want to see what lies over yonder hill. And that we will keep devising ways to reach the far side of the next hill. Satisfaction and contentment are for cattle. If we lose our hunger and wander lust we will no longer be human.<br />
<br />
<br />
<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com8tag:blogger.com,1999:blog-3596550435682943926.post-22456510046687353832016-01-17T12:45:00.046-08:002023-12-31T15:29:44.685-08:00Fact checking Neil deGrasse Tyson<div class="separator" style="clear: both; text-align: left;">
Tyson is well known for fact checking movies, comics and other pop culture stuff. Here's giving Tyson a taste of his own medicine.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
1. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#IdiotDoctors">Idiot doctors</a></div>
<div class="separator" style="clear: both; text-align: left;">
<b>2. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#GeorgeBush">George Bush and star names</a></b></div>
<div class="separator" style="clear: both; text-align: left;">
<b>3. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#HamidAlGhazali">Hamid al Ghazali: "Math is the work of the devil."</a></b></div>
<div class="separator" style="clear: both; text-align: left;">
<b>4. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Newton">Newton just stops when he cedes his brilliance to God.</a></b></div>
<div class="separator" style="clear: both; text-align: left;">
5. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Transcendental">There are more transcendental numbers than irrationals</a></div>
<div class="separator" style="clear: both; text-align: left;">
<b>6. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#FiveCenturies">Medieval Christians were Flat Earthers</a></b></div>
<div class="separator" style="clear: both; text-align: left;">
7. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Eiffel">Eiffel tower was the first structure taller than the pyramids</a></div>
<div class="separator" style="clear: both; text-align: left;">
8. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#BlindBat">Blind as a bat</a></div>
<div class="separator" style="clear: both; text-align: left;">
9. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#TheMartian">Tyson's trailer for The Martian</a></div>
<div class="separator" style="clear: both; text-align: left;">
10. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#GravityExponential">Gravity falls exponentially with distance</a></div>
<div class="separator" style="clear: both; text-align: left;">
11. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Clarke">Clarke was first to calculate altitude of geosynchronous orbits</a></div>
<div class="separator" style="clear: both; text-align: left;">
12. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Unhackable">Unhackable systems</a></div>
<div class="separator" style="clear: both; text-align: left;">
13. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#CoriolisNaval">Coriolis force in naval battles</a></div>
<div class="separator" style="clear: both; text-align: left;">
14. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#CoriolisFootball">Coriolis force in football</a></div>
<div class="separator" style="clear: both; text-align: left;">
15. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#2001">2001 Space Odyssey space station rotates too fast</a></div>
<div class="separator" style="clear: both; text-align: left;">
16. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#BrickHelicopters">Brick helicopters</a></div>
<div class="separator" style="clear: both; text-align: left;">
17. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#SpacePen">NASA's million dollar space pen</a></div>
<div class="separator" style="clear: both; text-align: left;">
18. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#GMOs">GMOs</a></div>
<div class="separator" style="clear: both; text-align: left;">
19. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Miniaturization">Nobody thought of miniaturization before NASA</a></div>
<div class="separator" style="clear: both; text-align: left;">
20. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Deflategate">Deflate Gate</a></div><div class="separator" style="clear: both; text-align: left;">
21. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#RocketEquation">Tyson's version of The Rocket Equation</a></div><div class="separator" style="clear: both; text-align: left;"><b>
22. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Copernicus">Copernicus kept his ideas secret for fear of The Church</a></b></div><div class="separator" style="clear: both; text-align: left;">
23. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#PainfulSex">Tyson: Painful sex would make a species go extinct</a>.</div><div class="separator" style="clear: both; text-align: left;">
24. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#JWST">James Webb Space Telescope is parked in Earth's shadow.</a></div><div class="separator" style="clear: both; text-align: left;">
25. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#SmoothEarth">Earth is smoother than a billiard ball</a></div><div class="separator" style="clear: both; text-align: left;">
26. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Curvature">Curvature isn't visible from Branson's flight.</a></div><div class="separator" style="clear: both; text-align: left;">
27. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Cordless">NASA invented cordless power tools.</a></div><div class="separator" style="clear: both; text-align: left;">
28. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#NoFallout">Modern nuclear weapons would have no nuclear fallout</a>.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;"><a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#OtherComplaints"><b><span style="font-size: medium;">Other Complaints Against Tyson</span></b></a></div><div class="separator" style="clear: both; text-align: left;">
<div>a. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Allegations">Allegations of Sexual Misconduct</a></div>
<div>b. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#NewYorker">Neil trashing an admiring writer from the New Yorker</a></div>
<div>c. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#BusinessPartner">Neil's former business partner alleges Neil misled him.</a></div>
<div>d. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#KickStarter">Investors sink $734,287 into Neil's vapor ware video game.</a></div>
<div>e. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Students">Students pay big bucks for a nothing burger appearance.</a></div>
<div>f. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Astrophysicist?">Is Tyson an astrophysicist?</a></div><div>
<div>g. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Vegans">Vegans lack the cosmic perspective</a></div>
<div>h. <a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Misinformation">Failing to correct misinformation</a></div></div></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">
Most of Tyson's misinformation is merely annoying. For example, who cares if he tells his listeners there are more transcendental numbers than irrationals? It's not as if the vast majority of his fans will ever actually study Cantor's ideas on infinite sets. But the examples of his bad math and science serve to demonstrate Tyson's comfortable talking with confidence on subjects he knows little about.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Much worse is when Tyson uses his poor memory and sloppy scholarship to invent history. And then uses his false history to push a narrative. Falsifying history is a serious offense. I have bolded examples of Tyson's bad history.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div id="IdiotDoctors">
<b><span style="font-size: x-large;">Tyson on "idiot doctors"</span></b><br />
<b><span style="font-size: x-large;"><br /></span></b></div>
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/f5X64QCDVnI/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/f5X64QCDVnI?feature=player_embedded" width="320"></iframe></div>
<br />
The first half of the video Tyson argues surviving cancer doesn't demonstrate divine intervention. I'm fine with that.<br />
<br />
But the <a href="https://www.youtube.com/watch?v=f5X64QCDVnI&feature=youtu.be&t=88">second half of the video</a> is a clueless rant against idiot doctors, the American Medical Association and Pre-Med students.<br />
<br />
A doctor doesn't just tell a patient "You've got six months." Rather a patient is given statistics on people in a similar condition. So a patient lives longer than the norm. Does this make the doctor an idiot? No. It demonstrates there are statistical outliers on a bell curve. It is..... astonishing. Astonishing that Tyson and the physics 101 prof are unfamiliar with entry level statistics.<br />
<br />
Also Tyson as well as the physics prof seem to believe someone who's failed freshman physics would go on to med school. There are idiot physicists, I assure you!<br />
<br />
Well known skeptic <a href="http://theness.com/neurologicablog/index.php/doctor-bashing/">Dr. Novella called Tyson out on this</a> (scroll to Those Darn Physicists). Novella noted this was <a href="https://www.youtube.com/watch?v=8vfOpZD4Sm8&feature=youtu.be&t=1074">part of the keynote speech at TAM6</a>, a 2008 conference for skeptics. Dr. Novella thought it was an excellent lecture except for the idiot doctor part. Which goes to show even self proclaimed skeptics are happy to swallow falsehoods if they seem to support their personal prejudices. Also from Tyson's TAM6 speech was his Bush and Star Names story.<br />
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div id="GeorgeBush">
<b><span style="font-size: x-large;">President Bush and Star Names</span></b></div>
<br />
<a href="https://www.youtube.com/watch?v=8vfOpZD4Sm8&feature=youtu.be&t=3007">Tyson tells us</a> President Bush attempted to "distinguish we from they" in the wake of the 9-11 attack. This routine was also included in the TAM6 keynote address.<br />
<br />
Stands to reason right? We all know a Republican would seize this emotionally charged moment to stir up hatred against Arabs.<br />
<br />
However Bush's <a href="http://georgewbush-whitehouse.archives.gov/news/releases/2001/09/20010917-11.html">actual 9-11 speech</a> called Islam the religion of peace. Bush was calling for inclusion and tolerance. Exactly the opposite of the xenophobic demagogue Tyson falsely portrays.<br />
<br />
In fact Bush and his administration have repeatedly condemned anti-Muslim rhetoric. Colin Powell was one of the first to bring Corporal Kareem Kahn's sacrifice to public attention:<br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/b6SKpv-MwXE" width="320" youtube-src-id="b6SKpv-MwXE"></iframe></div><br />
<br />Bush has made many comments urging tolerance and inclusion for Muslims. See <a href="https://georgewbush-whitehouse.archives.gov/infocus/ramadan/islam.html" target="_blank">this page from the Whitehouse Archives</a>.<br /><div><br /></div><div>
Tyson's shallow stereotype may apply to some Republicans, but not all.<br />
<br />
Jonathan Adler wrote a number of columns on this for The Washington Post:<br />
<a href="https://www.washingtonpost.com/news/volokh-conspiracy/wp/2014/09/22/does-neil-degrasse-tyson-make-up-stories/">Does Neil deGrasse Tyson make up stories?</a><br />
<a href="https://www.washingtonpost.com/news/volokh-conspiracy/wp/2014/09/27/neil-degrasse-tyson-admits-he-botched-bush-quote/">Neil deGrasse Tyson admits he botched Bush quote</a><br />
<a href="https://www.washingtonpost.com/news/volokh-conspiracy/wp/2014/09/24/what-makes-an-accusation-wiki-worthy/">What makes an accusation Wiki-worthy?</a> This column was interesting. Do information sources try to suppress information damaging to people they sympathize with? The winning clique of Wikipedia editors sure did. The successful effort to censor this information are well documented on the talk pages starting with <a href="https://en.wikipedia.org/wiki/Talk:Neil_deGrasse_Tyson/Archive_2">Archive 2</a>.<br />
<br />
Tyson <a href="https://www.washingtonpost.com/news/volokh-conspiracy/wp/2014/09/22/does-neil-degrasse-tyson-make-up-stories/">eventually admitted his story was false</a> and apologized to President Bush. However Tyson <a href="https://www.facebook.com/notes/neil-degrasse-tyson/partial-anatomy-of-my-public-talks/10152360009440869">qualifies his apology with these words:</a><br />
<br />
<blockquote class="tr_bq">
"Of course very little changes in that particular talk. I will still mention Islamic Extremists flying planes into buildings in the 21st century. I will still contrast it with the Golden Age of Islam a millennium earlier..."</blockquote>
Well, the rest of that particular talk is just as wrong Tyson's Bush and Star Names fantasy.<br />
<br />
<div id="HamidAlGhazali">
<b><span style="font-size: x-large;">Ghazali "Math is the work of the devil"</span></b></div>
<br />
The Bush quote confabulation segues into a non existent Hamid Al-Ghazali quote. Hamid Al Ghazali was a muslim cleric that supposedly ended the Islamic Golden Age. <a href="https://www.youtube.com/watch?v=8vfOpZD4Sm8&feature=youtu.be&t=3263">According to Tyson</a>, Ghazali wrote that math was the work of the devil. <a href="https://www.youtube.com/watch?v=tcHPU-aOJAY&feature=youtu.be&t=214">Tyson would make that claim</a> in other talks besides the TAM6 keynote speech. Tyson claims Islamic progress stopped and hasn't recovered since.<br />
<br />
<a href="http://blog.ghazali.org/archives/141">Ghazali would praise the disciplines of science and mathematics</a> saying they are necessary for a prosperous society. So I very much doubt that Ghazali ever demonized math. When challenged Tyson replied:<br />
<blockquote class="tr_bq">
"As for Al Ghazali, a more accurate representation of his views is that the manipulation of numbers was an earthly rather than a divine pursuit. And it was divine thoughts and conduct that were widely promoted -- to the exclusion of earthly conduct. Earthly conduct became associated with being anti-God, which I characterized as the devil. In later speeches (over the past year or so) I leave it as a simple split between earthly and divine pursuits, realizing that <b>I was misleading some people by mentioning the devil at all.</b>"</blockquote>
This quote is from <a href="http://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html?showComment=1458056847836#c5302117705517347439">Tyson's comment below</a>. In other words he admits there was no Ghazali text containing the assertion that math is the work of the devil.<br />
<br />
Did Islamic innovation end with Ghazali? No. There were <a href="https://en.wikipedia.org/wiki/List_of_Muslim_scientists">many Islamic scientists and mathematicians who came later</a>. Abu al-Hasan was born three centuries after Ghazali died. Hasan was the father of symbolic algebra.<br />
<br />
The Golden Age of Islam ended more in the 1400s when sea routes rendered land trading routes obsolete. At that time the mideast ceased to be a trading hub where diverse cultures would meet and exchange ideas.<br />
<br />
Tyson claims the once innovative civilization would surely have rebounded if not for Ghazali. He notes that the 1.3 billion Muslims alive today don't earn that many Nobel science prizes. Well, neither do the 1.3 billion people living in China. Nor the 1.3 billion people living in India. And these civilizations enjoyed periods of innovation. In fact our zero and numbering system comes from India, not the Arabs as Tyson falsely claims. Is Neil going to blame the Chinese lack of Nobel science prizes on Ghazali?<br />
<br />
Professor <a href="https://en.wikipedia.org/wiki/Joseph_E._B._Lumbard">Joseph Lumbard</a> made <a href="https://www.youtube.com/watch?v=1qLSzhuTCXc">an excellent video on this topic</a>.<br />
<br />
Physicist <a href="https://www.basilaltaie.com/about-1/">Basil Altaie</a> also made <a href="https://www.youtube.com/watch?v=fFrhOxXGgaw">a video calling out Tyson's wrong history</a>.<br />
<br />
Islamic Scholar Mohammed Hijab also calls out <a href="https://www.youtube.com/watch?v=nfRnYNig9jU">Tyson's sloppy scholarship and falsehoods on Islamic history</a>.<br />
<br />
People have been calling out Tyson's bad history on Islam <a href="https://thedailybanter.com/2010/08/12/neil-degrasse-tyson-and-the-myth-of-islamic-anti-science/">since at least 2010</a>.<div><br /></div><div>Tim O'Neill <a href="https://historyforatheists.com/2023/03/neil-degrasse-tyson-and-al-ghazali/" target="_blank">thoroughly examined Tyson's history on Ghazali</a>.<br />
<br />
<div id="Newton">
<b><span style="font-size: x-large;">Newton Just Stops When</span></b></div><div id="Newton"><b><span style="font-size: x-large;">He Cedes His Brilliance To God</span></b></div>
<br />Tyson's false history on Newton comes in two parts. The first part is actually flattering to Newton, Tyson claims Newton accomplished decades of collaborative efforts in just two months on a lark.</div><div><br /></div><div>But then Tyson uses his exaggeration of Newton's accomplishments to slam the great man. Tyson claims that Newton could have easily done Laplace's Traite de Mecanique Celeste in an afternoon. But supposedly Newton just stopped when he ceded his brilliance to God.</div><div><br /></div><div>The last part makes me angry. Newton did not just stop. And claiming Newton's faith hindered him? It was Newton's faith that sustained his passion for inquiry.</div><div><br /></div><div>In the following I look at each of these claims. </div><div><br /></div><div>
About an hour into his TAM6 lecture, Tyson portrays Newton as a super human saying <a href="https://www.youtube.com/watch?v=8vfOpZD4Sm8&feature=youtu.be&t=3740">Newton invented calculus on a dare</a>. Tyson frequently makes this claim and <a href="https://youtu.be/D6_UVBAfdHA?t=742">often says it took Newton two months</a> to establish this branch of mathematics.</div><div>
<br />
Well, no.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9Yvz4CztAKk2hKHf9Eojpphu4wJVcUxO7geC70M8lngagGW9z9KbHb_RUsBROw8lQ4qpxN9INATH3M_M3ytXeY891xD-D045oWSm49qMkz3M5jn1c0ZnvSK8QEip5upyYK1XPNGqLVdK5/s1600/TimeLineNewtonCalculus.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="513" data-original-width="1600" height="204" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9Yvz4CztAKk2hKHf9Eojpphu4wJVcUxO7geC70M8lngagGW9z9KbHb_RUsBROw8lQ4qpxN9INATH3M_M3ytXeY891xD-D045oWSm49qMkz3M5jn1c0ZnvSK8QEip5upyYK1XPNGqLVdK5/s640/TimeLineNewtonCalculus.jpg" width="640" /></a></div>
<br />
<br />
Two thousand years before Newton Eudoxus was slicing stuff into small bits to get more accurate approximations of volume and area.<br />
<br />
These methods were well known when Descartes and Fermat invented analytic geometry (also known as graph paper with an x and y axis). With this invention y=x<sup>2</sup> became a parabola. x<sup>2</sup> + y<sup>2</sup> = 1 became a circle with radius one. Descartes’ way of looking at things enabled us to scrutinize conic sections and other curves with symbolic algebra.<br />
<br />
After Descartes and Fermat invented analytic geometry, it was only a matter of time before someone used Eudoxus like methods to get good approximations of the slope of a curve or the area under a curve. Which was done by Fermat and Cavalieri among others.<br />
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
A screen capture from <a href="http://www.math.wpi.edu/IQP/BVCalcHist/calc2.html">History of the Differential from 17th Century:</a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUyC4NfdqYYcSTqT4JLMok6kFM2jbRPs_9QuqhiAcFVP6iVCfblFjUzwHGWRsyIojIRlmnhauldEdHtc-IhzSYeY2l1d27ZjjaaEeESsJk_MFN3Jzqk-AEniXoHDD4Q1IUSTnBUmxTUZUB/s1600/Screen+Shot+2017-12-16+at+12.44.52+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="583" data-original-width="662" height="562" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUyC4NfdqYYcSTqT4JLMok6kFM2jbRPs_9QuqhiAcFVP6iVCfblFjUzwHGWRsyIojIRlmnhauldEdHtc-IhzSYeY2l1d27ZjjaaEeESsJk_MFN3Jzqk-AEniXoHDD4Q1IUSTnBUmxTUZUB/s640/Screen+Shot+2017-12-16+at+12.44.52+PM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
It was Fermat who devised ways to find the slope of the tangent. </div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
And here is <a href="https://en.wikipedia.org/wiki/Cavalieri%27s_quadrature_formula">Cavalieri's Quadrature Formula</a>:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTa2zbm1psduKrV4vfz0e9C-N1OoCFkOmWG5uUihUiEd1P1hshQ2CuhQZqNMwfhy9vpMlTc2JZZR0-M_sXDEftvGOruWl9B5FtBXqJwHfDxJs_fMm3-eAYa-08FT3rFaqJaSWsf3KXdpat/s1600/Screen+Shot+2017-12-16+at+12.37.47+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="68" data-original-width="305" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTa2zbm1psduKrV4vfz0e9C-N1OoCFkOmWG5uUihUiEd1P1hshQ2CuhQZqNMwfhy9vpMlTc2JZZR0-M_sXDEftvGOruWl9B5FtBXqJwHfDxJs_fMm3-eAYa-08FT3rFaqJaSWsf3KXdpat/s1600/Screen+Shot+2017-12-16+at+12.37.47+PM.png" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
Cavalieri's Quadrature Formula.</div>
.<br />
So was Newton <i>The Father of Calculus</i>? This kid had a lot of daddies. A more sensible question would be what was Newton's contribution to this group effort.<div>
<br />Thony Christie paints a more accurate picture -- <a href="https://thonyc.wordpress.com/2015/01/02/preach-truth-serve-up-myths/">The development of calculus was the collaborative effort of many</a>. And it didn't take two months. Christie elaborates on this in his essay <a href="https://hopsblog-hop.blogspot.com/2021/05/the-wrong-question-who-invented.html" target="_blank">The Wrong Question</a>.</div><div><br /></div><div>"Certainly Neil acknowledges that Newton built his models on the work of others," one his defenders told me, "Newton himself said he could see far because he was standing on the shoulders of giants." Nope. <a href="https://www.youtube.com/watch?v=D6_UVBAfdHA&t=736s" target="_blank">Tyson tells us Newton did it all by himself</a>. And goes on to say "If he could see farther than others it's because he's standing among midgets."</div><div>
<br />
Thony also looks at these claims <a href="https://thonyc.wordpress.com/2017/06/14/why-doesnt-he-just-shut-up/">when he disembowels</a> the Big Think Video <i><a href="https://www.youtube.com/watch?v=danYFxGnFxQ">My Man, Sir Isaac Newton</a>.</i><br />
<i><br /></i>
<br />
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/danYFxGnFxQ/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/danYFxGnFxQ?feature=player_embedded" width="320"></iframe></div>
<i><br /></i>
<br />
<div style="text-align: center;">
My Man, Sir Isaac Newton inspired a popular meme.</div>
<div style="text-align: center;">
<a href="https://thonyc.wordpress.com/2017/06/14/why-doesnt-he-just-shut-up/">It's also bull from start to finish</a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvVUR0F-O4BXDNwY7yan67Fn2K5E0soPw93r5TecK3iDXxPe2zL3WqC3i3LpGIWDbOmyH7Q7cdZsistcNSRyqSSyF3sg2yFDFKPeZ0CygBB931_oaZe6SDtdQD3Q0h-1k_do7yapcUA7Zu/s1600/HeTurned26.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1417" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvVUR0F-O4BXDNwY7yan67Fn2K5E0soPw93r5TecK3iDXxPe2zL3WqC3i3LpGIWDbOmyH7Q7cdZsistcNSRyqSSyF3sg2yFDFKPeZ0CygBB931_oaZe6SDtdQD3Q0h-1k_do7yapcUA7Zu/s400/HeTurned26.jpg" width="377" /></a></div><div><br /></div><div>All this supposedly happened in just two months before Newton turned 26. The "dare" was a friend's question on planetary orbits. Halley asked his famous question on planetary orbits in 1684 when Newton was in his 40s <a href="https://www.mathpages.com/home/kmath658/kmath658.htm" target="_blank">Link</a>. </div><div><br /></div><div>Newton started thinking about gravity and planetary orbits in 1665 and made his break through in the years 1676-77 <a href="https://www.laphamsquarterly.org/revolutions/anni-mirabiles" target="_blank">Link</a>. He was in his mid 30s when he deduced that inverse square gravity implied Kepler's laws. And it took Newton 12 years.</div><div><br /></div>
After thinking he had established Newton’s super powers Tyson flatly asserts Newton could have knocked out perturbation theory in an afternoon. “You know this!” Tyson shouts to his enthusiastic audience. Well, no. I don’t. And neither does Tyson or his credulous audience.<br />
<br />
In fact Newton had tried to build n-body perturbation models. He looked at the sun, earth and moon and attempted to build a model that would accurately predict the moon's moon's motion. Astrophysicist <a href="https://letterstonature.wordpress.com/2015/11/04/neil-degrasse-tyson-on-newton-part-1/">Luke Barnes</a> quotes from <a href="https://www.amazon.com/Isaac-Newtons-Scientific-Method-Cosmology/dp/019957040X">William Harper's book on Isaac Newton</a>:<br />
<br />
<blockquote class="tr_bq">
… Newton developed this method in an effort to deal with the extreme complexity of solar system motions. … The passage continues with the following characterization of the extraordinary complexity of these resulting motions. </blockquote>
<blockquote class="tr_bq">
“By reason of the deviation of the Sun from the center of gravity, the centripetal force does not always tend to that immobile center, and hence the planets neither move exactly in ellipses nor revolve twice in the same orbit. There are as many orbits of a planet as it has revolutions, as in the motion of the Moon, and the orbit of any one planet depends on the combined motion of all the planets, not to mention the action of all these on each other. But to consider simultaneously all these causes of motion and to define these motions by exact laws admitting of easy calculation exceeds, if I am not mistaken, the force of any human mind.” (Wilson 1989b, 253) </blockquote>
<blockquote class="tr_bq">
<b><i>It appears that shortly after articulating this daunting complexity problem, Newton was hard at work developing resources for responding to it with successive approximations.</i></b> The development and applications of perturbation theory, from Newton through Laplace at the turn of the nineteenth century and on through much of the work of Simon Newcomb at the turn of the twentieth, led to successive, increasingly accurate corrections of Keplerian planetary orbital motions. [emphasis added]
</blockquote>
<br />
So Tyson's assertion is demonstrably false from the get go. Newton had invested considerable effort in this problem. See also physicist <a href="http://physics.ucsc.edu/~michael/koll.html">Michael Nauenberg's piece on Newton's efforts to model 3 body systems</a>.<br />
<br />
Besides Newton, Euler took a crack at perturbation theory and n-body mechanics. As did Lagrange. Both these men were giants in their own right but did not make satisfactory models. 100 years after Newton, Laplace built on the work of Euler, Lagrange and Newton. To say Newton could have done it in an afternoon is disrespecting Laplace, Euler and Lagrange. It is also profoundly ignorant.<br />
<br />
In Tyson’s alternate history Newton would have easily done Laplace’s n-body work had he not been stopped by his belief in the “God of The Gaps”. Tyson states this as a flat out fact. But an alternate history is not a testable hypothesis. We can’t rewind history and see what happens with different parameters.<br />
<br />
Here’s another alternate history: An agnostic Newton would have been a normal young man who spent his spare time in taverns chasing women. No splitting of light, no laws of motion, and no contributions to calculus. His accomplishments would have been zip, zero, nada. Like Tyson’s alternate history this is nothing more than idle speculation.<br />
<br />
<div id="Transcendental">
<b><span style="font-size: x-large;">More Transcendentals than Irrationals</span></b></div>
<br />
In <a href="https://www.youtube.com/watch?v=Ds2bMtJla70">an interview with Joe Rogan</a>, Tyson asserts there are more transcendental numbers than irrationals. He also tells Joe there are five cardinalities when it comes to infinite sets.<br />
<br />
Was this a fluke? Maybe Neil just mispoke. But Tyson gives a similarly confused account in <a href="https://www.carolineryder.com/carolineryder/2012/03/neil-degrasse-tyson.html">an interview with Dazed and Confused Magazine</a>:<br />
<blockquote class="tr_bq">
You know how numbers, you can count them forever? Well how about fractions? The infinity of fractions is bigger than the infinity of numbers; and then there are transcendental numbers, like Pi. There are more transcendental numbers than pure irrational numbers, and there are more irrational numbers than counting numbers. And more fractions than all of them. </blockquote>
<div>
It's appropriate the above rambling passage comes from <i>Dazed and Confused Magazine</i>. Tyson's assertions earned him <a href="https://www.reddit.com/r/badmathematics/comments/5vnnym/neil_degrasse_tyson_theres_more_transcendental/">a mention in the badmathematics subreddit</a>. The Rational Skepticism blog <a href="http://www.rationalskepticism.org/general-science/neil-degrasse-tyson-doing-a-disservice-t53874.html">also chastised Tyson</a> for this misinformation.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div id="FiveCenturies">
<b><span style="font-size: x-large;">Five Centuries Regressed</span></b></div>
<br />
Is the earth flat or round? This silly argument between Tyson and rapper B.o.B. generated a great deal of publicity for B.o.B., Tyson, and Tyson's nephew.<br />
<br />
<a href="https://mobile.twitter.com/neiltyson/status/691655467978919936">Part of the exchange</a>: "@bobati Duude — to be clear: Being five centuries regressed in your reasoning doesn't mean we all can't still like your music."<br />
<br />
Supposedly folks during the dark ages thought the earth was flat. Sadly Tyson is perpetuating this myth.<br />
<br />
Tyson's misperception of the dark ages is a common error. Well summarized in "The Chart":<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGefczHgOCJnP4XxcLQ2hP4_BreISe9cQYAGIm0ASz8-QMivN_cshkBbR6wlcLtRGIhdYyaauKkufZwEHzGbQyqrRRMBrTkmw3V1nW0G_YRf3mdpPlag2zSlnhU7WisJL1ict-2atU0ZJZ/s1600/Screen+Shot+2017-07-03+at+3.50.29+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="520" data-original-width="563" height="368" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGefczHgOCJnP4XxcLQ2hP4_BreISe9cQYAGIm0ASz8-QMivN_cshkBbR6wlcLtRGIhdYyaauKkufZwEHzGbQyqrRRMBrTkmw3V1nW0G_YRf3mdpPlag2zSlnhU7WisJL1ict-2atU0ZJZ/s400/Screen+Shot+2017-07-03+at+3.50.29+PM.png" width="400" /></a></div>
<div style="text-align: center;">
"The Chart" What Tim O'Neill calls</div>
<div style="text-align: center;">
<a href="http://strangenotions.com/gods-philosophers/">The Most Wrong Thing On The Internet Ever.</a> </div>
<div>
<br /></div>
<br />
In the August 1991 issue of <i>History Today</i> Jeffrey Russel <a href="http://www.historytoday.com/jeffrey-russel/inventing-flat-earth">effectively argues</a> people knew the earth was round during and before the time of Columbus. In his comment reply (below Russel's article) Tyson perpetuates the myth that knowledge of a spherical earth was lost in the "Dark Ages". <a href="http://historyforatheists.blogspot.it/2016/05/the-new-atheist-bad-history-great-myths.html">Historian Tim O'Neill explains where this myth comes from</a>. O'Neill also documents prominent scholars from that period that knew the earth was spherical.<br />
<br />
The above links as well as more interesting reading can be found in this <a href="https://www.reddit.com/r/badhistory/comments/44rs9z/neil_degrasse_tyson_or_how_to_fight_the_flatearth/">reddit badhistory thread</a> on Tyson's battle with B.o.B.<br />
<br />
<div :="" class="separator" id="Eiffel" style="clear: both; text-align: left;"><span style="font-size: x-large;"><b>The Eiffel Tower Was The First Structure Taller Than The Pyramids</b></span></div>
<br />
<div class="separator" style="clear: both; text-align: left;">Tyson <a href="https://www.youtube.com/watch?v=GCIOcqAulLI">tells Joe Rogan</a> that the Eiffel Tower was the first structure taller than the pyramids.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><a href="https://en.wikipedia.org/wiki/List_of_tallest_structures_built_before_the_20th_century" target="_blank">Here</a> is Wikipedia's list of tallest buildings built before the 20th century. There are numerous counter examples to Tyson's claim. A few here: The Washington Monument and Cologne Cathedral.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div id="BlindBat">
<b><span style="font-size: x-large;">Blind As A Bat</span></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIww1jV8F3bLy1uUiWElVx5Yi-siKYEMjRdyxDxSDsqs7r47Ze1d4p-V1Niso-X0LKNikBwuu4SxnMfEJQ97VZcfUEIPRvoHcNXckXead4JTT5B6l_SL4LGbWPsLzYkcsitua6HnROsq2d/s1600/Screen+Shot+2016-03-25+at+4.01.51+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="242" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIww1jV8F3bLy1uUiWElVx5Yi-siKYEMjRdyxDxSDsqs7r47Ze1d4p-V1Niso-X0LKNikBwuu4SxnMfEJQ97VZcfUEIPRvoHcNXckXead4JTT5B6l_SL4LGbWPsLzYkcsitua6HnROsq2d/s640/Screen+Shot+2016-03-25+at+4.01.51+PM.png" width="640" /></a></div>
<br />
This common misconception is addressed in Christie Wilcox's Discover article <a href="http://blogs.discovermagazine.com/science-sushi/2016/03/25/actually-bats-see-just-fine-neil/#.VvXEWevFypM">Actually, Bats See Just Fine, Neil</a>.<br />
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div :="" class="separator" id="TheMartian" style="clear: both; text-align: left;">
<b><span style="font-size: x-large;">Tyson's trailer for The Martian</span></b></div>
<div class="separator" style="clear: both; text-align: left;">
<b><br /></b></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Hermes' impossible trajectory</b></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/lvs0zyDlrT4" width="320" youtube-src-id="lvs0zyDlrT4"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div>
<br />
Above is a link to Neil deGrasse Tyson's trailer for The Martian. At <a href="https://www.youtube.com/watch?v=lvs0zyDlrT4&t=76s">1:15 of the vid</a>, Tyson has the space ship Hermes departing from Low Earth Orbit (LEO). 124 days later he has Hermes arriving at Mars orbit (<a href="https://www.youtube.com/watch?v=lvs0zyDlrT4&t=137s" target="_blank">2:17 of the video</a>).<br />
<br />
Hermes is propelled with low thrust ion engines. In the book when Hermes is about to rendezvous with Watney's Mars Ascent Vehicle (MAV), Lewis says Hermes can do up to 2 mm/s<sup>2</sup>. This acceleration is also given online:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/khIHZp_GTEI/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/khIHZp_GTEI?feature=player_embedded" width="320"></iframe></div>
<br />
<br />
Two millimeters per second squared would require an extremely good <a href="http://hopsblog-hop.blogspot.com/2015/05/the-need-for-better-alpha.html">alpha</a>. But it's possible future power sources will deliver more watts per kilogram. So 2 mm/s<sup>2</sup> is only medium implausible. I'll let this slide.<br />
<br />
Problem is, low thrust ion engines <a href="http://space.stackexchange.com/questions/8420/general-guidelines-for-modeling-a-low-thrust-ion-spiral">really suck at climbing in and out of planetary gravity wells</a>. From low earth orbit, it would take Hermes about 40 days to spiral out of earth's gravity well and about 20 days to spiral from the edge of Mars' gravity well to low Mars orbit. Two months spent climbing in and out of gravity wells destroys Andy Weirs' 124 day trajectory.<br />
<br />
Given 2 mm/s<sup>2</sup>, the trajectory Tyson describes is flat out impossible.<br />
<br />
<b>A slow ride through the Van Allen belts.</b><br />
<br />
At 1:50 of Tyson's video he talks about the danger of solar flares and how astronauts are vulnerable to radiation. Well, departing from LEO means a month long spiral through the Van Allen Belts. Not only does the long spiral wreck Weir's 124 day trajectory, it also cooks the astronauts.<br />
<br />
Tyson enjoys some notoriety for fact checking fantasies like <i>Star Wars</i> or <i>The Good Dinosaur</i>. This leaves me scratching my head. Many of the shows he fact checks make no pretense at being scientifically accurate. However <i>The Martian</i> was an effort at scientifically plausible hard science fiction and thus is fair game. Same goes for Tyson's trailer.<br />
<br />
A physically impossible trajectory along with cooking the astronauts? Tyson's effort at hard science fiction isn't any better than <i>Gravity</i> or <i>Interstellar</i>.<br />
<br />
<br />
<b><span style="font-size: x-large;">Neil's Five Points of Lagrange Essay</span></b><br />
<br />
The <i><a href="http://www.haydenplanetarium.org/tyson/read/2002/04/01/the-five-points-of-lagrange">Five Points of Lagrange</a></i> was a Neil deGrasse Tyson article published in the April, 2002 issue of <i>Natural History Magazine</i>. A few excerpts:<br />
<br />
<div id="GravityExponential">
<b>Gravity falls exponentially with distance</b></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl09MZnmKw13HEB3cRIvVTpe4iRIQ45Ccs-UTuz9pNhiVv1QaAAPtEuc0jP-jT7pxeFMbjbYHZYngsCMqxMYyEqKc3aPhXeqEjRHe-x-FMwbTXKjkmxShCP5xjqb_XM4idZNp2HnHLebvB/s1600/Screen+Shot+2016-01-16+at+12.50.10+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="108" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl09MZnmKw13HEB3cRIvVTpe4iRIQ45Ccs-UTuz9pNhiVv1QaAAPtEuc0jP-jT7pxeFMbjbYHZYngsCMqxMYyEqKc3aPhXeqEjRHe-x-FMwbTXKjkmxShCP5xjqb_XM4idZNp2HnHLebvB/s640/Screen+Shot+2016-01-16+at+12.50.10+PM.png" width="640" /></a></div>
<br />
Popular usage has made "exponential" a general term for dramatic change. But a physicist should know the more specific mathematical meaning of the this word. Gravity falls with inverse square of distance, not exponentially.<br />
<br />
<div id="Clarke">
<b>Arthur C. Clarke was first to calculate altitude of geosynchronous orbits</b><br />
<b><br /></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiACC_KQtIQh7SUkpoI5BuPcG8ncfiay7Vr8hnGW64nm6tsUoCH7FIscbVkyoiIbsy8PPwWP0xmVgK4o3eZ0R16Jh9Zn3wzsBKZ3EcNYMWvUtEwPeMEhOBsaxq0KlkQP4Xerm50Cj53ncgN/s1600/Screen+Shot+2016-01-16+at+1.00.26+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiACC_KQtIQh7SUkpoI5BuPcG8ncfiay7Vr8hnGW64nm6tsUoCH7FIscbVkyoiIbsy8PPwWP0xmVgK4o3eZ0R16Jh9Zn3wzsBKZ3EcNYMWvUtEwPeMEhOBsaxq0KlkQP4Xerm50Cj53ncgN/s640/Screen+Shot+2016-01-16+at+1.00.26+PM.png" width="640" /></a></div>
<br />
Wrong. Clarke's contribution was suggesting communication satellites be placed in geosynchronous orbit (GSO). A fantastic idea with tremendous impact. But Clarke wasn't the first to calculate the altitude of GSOs.<br />
<br />
<a href="https://celestrak.com/columns/v04n07/">Herman Potočnik</a> calculated the altitude of GSO in 1928. It's possible this altitude was calculated even earlier. Newton might have done it.<br />
<br />
<div id="Unhackable">
<b><span style="font-size: x-large;">Unhackable Systems</span></b><br />
<b><span style="font-size: x-large;"><br /></span></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNEoS4oRdpImAn0b_SWAQ-fxB8_l5zuHBFxqtpt0sW9CKkOBegiyfsmX4a1cGmuOo9hAP5leidRXo_B5QceZKWtG2DlSjQkSgJUiKv-fMr0ON_jo7tkn34SDIaZ5C5n9kOmwyfMQF0NTOe/s1600/Screen+Shot+2016-05-19+at+12.04.57+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNEoS4oRdpImAn0b_SWAQ-fxB8_l5zuHBFxqtpt0sW9CKkOBegiyfsmX4a1cGmuOo9hAP5leidRXo_B5QceZKWtG2DlSjQkSgJUiKv-fMr0ON_jo7tkn34SDIaZ5C5n9kOmwyfMQF0NTOe/s640/Screen+Shot+2016-05-19+at+12.04.57+PM.png" width="640" /></a></div>
<br />
The solution is so simple, just make unhackable systems. Oh my gosh, why didn't the cyber security folks ever think of that?<br />
<br />
Twitchy published <a href="http://twitchy.com/dougp-3137/2015/01/03/neil-degrasse-tyson-blows-more-minds-with-idea-to-prevent-computer-hacking/">some good responses</a>.<br />
<br />
<div id="IdiotDoctors">
<br /></div>
<br />
<div id="CoriolisNaval">
<b><span style="font-size: x-large;">The Coriolis Force in Naval Battles</span></b></div>
<br />
<a href="http://www.haydenplanetarium.org/tyson/read/1995/03/01/the-coriolis-force">The Coriolis Force</a> was a Tyson article published in the March 1995 issue of Natural History. In the article Neil has this to say about the 1914 Falklands battle:<br />
<blockquote class="tr_bq">
But in 1914, from the annals of embarrassing military moments, there was
a World War I naval battle between the English and the Germans near the
Falklands Islands off Argentina (52 degrees south latitude). The
English battle cruisers <i>Invincible</i> and <i>Inflexible</i> engaged the German war ships <i>Gneisenau</i> and <i>Scharnhorst</i>
at a range of nearly ten miles. Among other gunnery problems
encountered, the English forgot to reverse the direction of their
Coriolis correction. Their tables had been calculated for northern
hemisphere projectiles, so they missed their targets by even more than
if no correction had been applied. They ultimately won the battle
against the Germans with about sixty direct hits, but it was not before
over a thousand missile shells had fallen in the ocean.</blockquote>
However the role of Coriolis correction in this battle is a <a href="http://dreadnoughtproject.org/tfs/index.php/Battle_of_the_Falkland_Islands#Coriolis_Effect">an urban legend</a>.<br />
<br />
<div id="CoriolisFootball">
<b><span style="font-size: x-large;">Coriolis Force in Football</span></b><br />
<b><span style="font-size: large;"><br /></span></b></div>
Tyson likes to say the <a href="https://twitter.com/neiltyson/status/430158228224507904">Coriolis force would deflect a 50 yard field goal</a> half an inch to the right.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvBsKV07Sc5tZ0UXF5GwTSsP6wuw0b7iJjlFErnHZy2PvyYjWPS5rb0NQUuA8QuI2lBhQlj43yQs2_wqy1l0hXgK5mFQXdDdsXXv4aa05JtbUqU3f5yRATnbi_16WqWOyjOKEQbY9wZOkY/s1600/Screen+Shot+2016-09-29+at+8.31.30+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="330" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvBsKV07Sc5tZ0UXF5GwTSsP6wuw0b7iJjlFErnHZy2PvyYjWPS5rb0NQUuA8QuI2lBhQlj43yQs2_wqy1l0hXgK5mFQXdDdsXXv4aa05JtbUqU3f5yRATnbi_16WqWOyjOKEQbY9wZOkY/s640/Screen+Shot+2016-09-29+at+8.31.30+PM.png" width="640" /></a></div>
<br />
He repeats this fairly often. <a href="https://twitter.com/neiltyson/status/828407205733003271">More recently for the Houston stadium</a>. He seems unaware different latitudes feel different Coriolis accelerations.<br />
<br />
Coriolis force felt by a football would depend on the velocity and direction of the football as well as the latitude of stadium.<br />
<br />
Coriolis acceleration = -2 <span style="background-color: white;"><b>Ω</b> X <b>v</b></span><br />
<br />
Metlife is about at latitude 40.8 degrees. Metlife tilts about 11º from the north. I will go with the horizontal speed of the ball of 23 meters/second.<br />
<br />
We can choose our coordinates so the x axis runs west to east, the y axis runs south to north and the z axis is the local vertical going up...<br />
<br />
<b style="background-color: white;">Ω</b><span style="background-color: white;"> = (0, 5.52e-5, 4.76e-5) 1/sec</span><br />
<span style="background-color: white;"><b>v</b> = (4.39, 22.58, 0) meters/sec</span><br />
<span style="background-color: white;"><b>a</b> = -2 </span><b style="background-color: white;">Ω </b><span style="background-color: white;">X </span><b style="background-color: white;">v</b><span style="background-color: white;"> = (.0021, -0004, .0005) meters/</span>sec<sup>2</sup>,<br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Deflection from uniform acceleration is 1/2 <b>a</b> </span>t<sup>2</sup>,<br />
where t is time of flight. For a ball with a 23 meter/sec horizontal speed, it takes a little less than 2 seconds to traverse 50 yards.<br />
<br />
<span style="background-color: white;">1/2 <b>a</b> </span>t<sup>2</sup> = (.0043, =.0008, .00096) meters = (.167, -.032, .037) inches.<br />
<br />
Of that displacement, the component displacement to the right is .17 inches. Tyson's half inch is off by a factor of three.<br />
<br />
Field goal kickers don't have the level of precision where 1/6 of an inch vs 1/2 an inch makes much difference. However I wouldn't want Dr. Tyson to be calculating Coriolis in situations where it's important, like naval battles.<br />
<br />
<div id="2001">
<span style="font-size: x-large;"><b>2001 Space Odyssey station rotates too fast</b></span><br />
<span style="font-size: x-large;"><b><br /></b></span></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/q3oHmVhviO8/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/q3oHmVhviO8?feature=player_embedded" width="320"></iframe></div>
<br />
19:56 into an <a href="https://www.youtube.com/watch?v=szk8bM2aguY&t=1237s">interview with Dan Le Batard</a>, Tyson tells Batard:<br />
<br />
<blockquote class="tr_bq">
… by the way I calculated the rotation rate of their space station which gives you artificial gravity on the outer rim. And it turns out it's rotating three times too fast. So if you weigh 150 pounds you'd weight 450 pounds on that space station (hee hee).</blockquote>
Tyson also <a href="https://www.youtube.com/watch?v=PhHtBqsGAoA&feature=youtu.be&t=5910">tells Joe Rogan the same thing</a>.<br />
<br />
Tyson is wrong on several counts.<br />
<br />
2001 A Space Odyssey's <a href="http://2001.wikia.com/wiki/Space_Station_V">Space Station V</a> has a radius of about 150 meters and a spin rate of about 1 revolution each 61seconds. That gives an angular velocity <span style="background-color: white;">ω of 2 </span><span style="background-color: white;">π radians per 61 seconds.</span><br />
<span style="background-color: white;"><br /></span>
<a href="https://en.wikipedia.org/wiki/Circular_motion#Formulas"><span style="background-color: white;">Spin grav = </span><span style="background-color: white;">ω</span><sup>2 </sup><span style="background-color: white;">r</span></a><br />
<span style="background-color: white;">Spin grav = (2</span><span style="background-color: white;">π/(61 seconds))</span><sup>2 </sup><span style="background-color: white;">*150 meters</span><br />
<span style="background-color: white;">Spin grav = .106 * 150 meters/second</span><sup>2 </sup><br />
Spin grav = 1.59 meters/<span style="background-color: white;">second</span><sup>2 </sup><br />
<br />
The spin gravity comes out to about one sixth of earth's gravity. A 150 pound man would weigh about 25 pounds on this station. This is close to the gravity on the moon's surface. Which is what Clarke and Kubrick had intended since the station was a stop on the way to the moon.<br />
<br />
Also weight scales with the <b><i>square</i></b> of spin rate. So tripling spin rate would increase weight by a factor of nine.<br />
<br />
<div id="BrickHelicopters">
<b><span style="font-size: x-large;">Brick Helicopters</span></b></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJsxdx5waMp3nQjGmmGM6R3V5Lz6olnF2BqQmq5SMSwDwlj3NLXwfi_7bd_dmsgZI-HCwjuTOguu6mtXnc2R-56YqQrVyyNFYnvUderc91KP1h_aN-eTGulfcdaDKn8zPMuJSb1Li9K9nr/s1600/Screen+Shot+2016-04-28+at+11.54.26+AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="332" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJsxdx5waMp3nQjGmmGM6R3V5Lz6olnF2BqQmq5SMSwDwlj3NLXwfi_7bd_dmsgZI-HCwjuTOguu6mtXnc2R-56YqQrVyyNFYnvUderc91KP1h_aN-eTGulfcdaDKn8zPMuJSb1Li9K9nr/s640/Screen+Shot+2016-04-28+at+11.54.26+AM.png" width="640" /></a></div>
<br />
Helicopter blades will continue rotating after engine failure. Descending through the air at an angle can spin up the blades. Leveling off just before reaching the ground makes for a soft landing.<br />
<br />
The process is described and demonstrated at this<a href="https://www.youtube.com/watch?v=BTqu9iMiPIU"> Getting Smarter Every Day Video</a>.<br />
<br />
<div id="SpacePen">
<b><span style="font-size: x-large;">NASA's million dollar space pen</span></b><br />
<br />
In <a href="http://www.haydenplanetarium.org/tyson/read/1998/09/01/space-travel-troubles">Tyson's column for Natural History Magazine</a> as well as in his <a href="https://www.goodreads.com/work/quotes/16946049-space-chronicles-facing-the-ultimate-frontier">Space Chronicles</a> Tyson wrote:<br />
<blockquote class="tr_bq">
During the heat of the space race in the 1960s, the US National Aeronautics and Space Administration decided it needed a ballpoint pen to write in the zero gravity confines of its space capsules. After considerable research and development, the Astronaut Pen was developed at a cost of approximately $1 million US. The pen worked and also enjoyed some modest success as a novelty item back here on earth. The Soviet Union, faced with the same problem, used a pencil.</blockquote>
Ummmmm..... No.<br />
<br />
This urban legend was debunked in a <a href="https://www.scientificamerican.com/article/fact-or-fiction-nasa-spen/">Scientific American article</a>.<br />
<br />
At one time both NASA and the Russian space program were using pencils. But the tips flaked and broke resulting in potentially harmful particles floating around in the weightless environment. Pencils are also flammable, something to be avoided in a spacecraft.<br />
<br />
Pens were needed. But it wasn't NASA who financed the R&D. It was Paul C. Fisher of the Fisher Pen Company. He invested $1 million to create what we now call the space pen. According to Scientific American, none of that million dollars came from NASA.<br />
<br />
Both NASA and the Russians bought the pens from the Fisher Pen company at $2.39 per pen.<br />
<br />
<br />
<div id="GMOs">
<b><span style="font-size: x-large;">GMO = artificial selection</span></b><br />
<br />
In <a href="https://www.youtube.com/watch?v=1ecT2CaL7NA">this video </a>Tyson defends genetic modification by claiming it's not different from the artificial selection humans have been practicing for millennia.</div>
<br />
Which is wrong. Genetic modification as practiced by Monsanto is splicing DNA from one species onto the DNA of another species. Artificial selection encourages traits that already exist in a population's gene pool. Here is a primer: <a href="http://www.sciencemediacentre.co.nz/2008/09/19/genetic-modification-explained/">Genetic Modification Explained</a>.<br />
<br />
Are GMOs beneficial? Or are they harmful? I don't know. I'm not taking a position pro or con. I'm pointing out Tyson's argument conflates two different techniques.<br />
<br />
<div id="Miniaturization">
<b><span style="font-size: x-large;">Before NASA nobody thought about miniaturizing electronics</span></b></div>
<br />
In <a href="http://transcripts.cnn.com/TRANSCRIPTS/1303/24/fzgps.01.html">an interview with Fareed Zakaria,</a> Tyson said:<br />
<blockquote class="tr_bq">
The urge to miniaturize electronics did not exist before the space program. I mean our grandparents had radios that was furniture in the living room. Nobody at the time was saying Gee, I want to carry that in my pocket. Which is a non-thought. </blockquote>
Well, the <a href="https://en.wikipedia.org/wiki/Transistor_radio#Regency_TR-1.C2.A0.E2.80.94_the_first_transistor_radio">TR-1</a> hit the market in November of 1954 and <a href="https://en.wikipedia.org/wiki/NASA#Creation">NASA was formed in 1958</a><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRzcPGWfxzBwxzsFIQ8eyB0NBMxBCD7SmOEVUaQUeKwxGB7XQFUXjs4I6bqaP7dCBrQzlznTHXT8TurSP5QfB-23MJ4rFfF8PlXqkChEXSTbgBDGeG2jvA0AQgwNFC-ra_MZczkufoq38S/s1600/Screen+Shot+2015-08-24+at+7.48.17+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRzcPGWfxzBwxzsFIQ8eyB0NBMxBCD7SmOEVUaQUeKwxGB7XQFUXjs4I6bqaP7dCBrQzlznTHXT8TurSP5QfB-23MJ4rFfF8PlXqkChEXSTbgBDGeG2jvA0AQgwNFC-ra_MZczkufoq38S/s320/Screen+Shot+2015-08-24+at+7.48.17+PM.png" width="209" /></a></div>
<div style="text-align: center;">
The <a href="https://en.wikipedia.org/wiki/Transistor_radio#Regency_TR-1.C2.A0.E2.80.94_the_first_transistor_radio">TR-1</a> hit the market 4 years before NASA was formed
</div>
<br />
<a href="https://en.wikipedia.org/wiki/History_of_the_transistor">Here</a> is the Wikipedia article on the history of transistors.<br />
<br />
<b><span style="font-size: x-large;"></span></b><br />
<div id="Deflategate">
<b><span style="font-size: x-large;">Deflategate</span></b></div>
<br />
<br />
<a href="https://en.wikipedia.org/wiki/Deflategate">Deflategate</a> was a controversy over the American Football Conference championship game January, 2015. The New England Patriots were accused of cheating when their footballs were found to be about 2 pounds under inflated.<br />
<br />
Tyson <a href="https://twitter.com/neiltyson/status/559814692936237057?ref_src=twsrc%5Etfw&ref_url=https%3A%2F%2Fnews.avclub.com%2Fajax%2Finset%2Fiframe%3Fid%3Dtwitter-559814692936237057%26autosize%3D1">tweeted</a>:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXeJJKoJteNfGaWUrvYw20Kdaq6zQesySBpvzo_8tHMRARr88eqV5c_xZQzl5RUMsQzua7RwsoNCu0ouCSbAk8Kcr_IqqNOVN6IaP3h1-i0II5Gx-7gupyIBkDjHXzYxGrHjqrCqk84gyh/s1600/Screen+Shot+2018-01-22+at+8.26.11+AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="230" data-original-width="508" height="288" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXeJJKoJteNfGaWUrvYw20Kdaq6zQesySBpvzo_8tHMRARr88eqV5c_xZQzl5RUMsQzua7RwsoNCu0ouCSbAk8Kcr_IqqNOVN6IaP3h1-i0II5Gx-7gupyIBkDjHXzYxGrHjqrCqk84gyh/s640/Screen+Shot+2018-01-22+at+8.26.11+AM.png" width="640" /></a></div>
<br />
A 2 PSI drop from 13 PSI gauge pressure is about 15%, right? Well, no, not really. The 13 PSI gauge pressure is the pressure above the surrounding air pressure. Atmospheric pressure at sea level is about 15 PSI. Absolute pressure would be 13+15 PSI. So the drop in absolute pressure is 2/28 or about 7%.<br />
<br />
Confusing gauge pressure for absolute pressure would be understandable if coming from a freshman engineering student doing a pop quiz. But this is a supposedly world renowned astrophysicist accusing the Patriots coaching staff of cheating.<br />
<br />
More on Tyson's Deflategate errors can be found at <a href="https://news.avclub.com/neil-degrasse-tyson-bungles-science-of-deflate-gate-sca-1798276120">Neil deGrasse Tyson bungles science of Deflategate scandal</a>.<br />
<br />
<div id="RocketEquation"><b><span style="font-size: x-large;">Tyson's rocket equation: propellant mass scales exponentially with payload mass</span></b></div><br />In his "explanation" of the rocket equation Tyson tells us <a href="https://www.youtube.com/watch?v=-73MZsj8bVI&t=340s">"the amount of fuel you need okay to deliver a certain payload grows exponentially ... for every extra pound of payload"</a> .</div><div id="SpacePen"><br /></div><div id="SpacePen">This is wrong. Rocket propellant mass grows exponentially with increasing delta v, not payload mass. </div><div id="SpacePen"><br /></div><div id="SpacePen">In fact, amount of propellant mass per kilogram of payload tends to go <i>down</i> with increasing payload mass. This is partly due to the square cube law, amount of surface area per volume goes down with increasing volume. Also the avionics of a large rocket can be the same mass as the avionics for a small rocket. See <a href="https://forum.nasaspaceflight.com/index.php?topic=31023.0">this thread from the NasaSpaceFlight Forum</a>. </div>This is particularly annoying to me. Many of my blog entries are devoted to the rocket equation and therefore focus on delta V. <br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/-73MZsj8bVI" width="320" youtube-src-id="-73MZsj8bVI"></iframe></div><br /><div id="SpacePen"><br /></div><div id="Copernicus"><b><span style="font-size: x-large;">Copernicus kept his theory secret for fear of the church</span></b></div>From the Mental Floss Article <a href="https://www.mentalfloss.com/article/93783/10-things-we-learned-neil-degrasse-tysons-inexplicable-universe-course" target="_blank">10 Things We Learned From Neil deGrasse Tyson's "The Inexplicable Universe" Course:</a><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs2O74S5jfjmZl5Yez3IdcPKdczzvXEd019mS6YQspapiOEjTKE2KjR6P5SpJCc3N-bPrbcqFhapz1AxUpBXtYiQZsOSDyHMDgUZqrht8F8JhpSV-qjlY6_Mlp3JeNkeeZkq5wvDzlMicJ/s1532/TysonCopernicusMentalFloss.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="990" data-original-width="1532" height="414" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs2O74S5jfjmZl5Yez3IdcPKdczzvXEd019mS6YQspapiOEjTKE2KjR6P5SpJCc3N-bPrbcqFhapz1AxUpBXtYiQZsOSDyHMDgUZqrht8F8JhpSV-qjlY6_Mlp3JeNkeeZkq5wvDzlMicJ/w640-h414/TysonCopernicusMentalFloss.png" width="640" /></a></div><br /><br />Evidently Neil hasn't heard of Copernicus' <a href="https://en.wikipedia.org/wiki/Commentariolus" target="_blank">Commentariolus</a>. Copernicus wrote this in 1514, almost thirty years before <a href="https://en.wikipedia.org/wiki/De_revolutionibus_orbium_coelestium" target="_blank">De revolutionibus orbium coelestium</a> which was published in 1543 when Copernicus was on his deathbed.<br />In 1533<a href="https://en.wikipedia.org/wiki/Johann_Albrecht_Widmannstetter" target="_blank"> Johann Albrecht Widmannstetter</a> delivered a series of lectures in Rome on Copernicus ideas. Widmannstetter was secretary to Pope Clement VII, Pope Paul III and Cardinal Nikolaus von Schönberg. His lectures were heard by Pope Clement VII and the cardinals. <br /><a href="https://en.wikipedia.org/wiki/Nikolaus_von_Schönberg" target="_blank">Cardinal Nikolaus von Schönberg</a> was impressed with Widmannstetter's lectures and wrote a letter to Copernicus in 1536 urging him to publish.<br />Copernicus finally published De revolutionibus with the help of his friend <a href="https://en.wikipedia.org/wiki/Tiedemann_Giese" target="_blank">Bishop Tiedemann Giese</a>. <br />De revolutionibus was placed on the Catholic Church's Index of Forbidden Books in 1616. But this was more than 70 years after publication. The book was not formally banned but merely withdrawn from circulation.<br />So it is not true that Copernicus kept these ideas secret from the Catholic Church. Widmanstetter had shared his ideas with a pope and a number of bishops and cardinals. It was a cardinal who urged him to publish and a bishop who helped him publish.</div><div><br /><div id="PainfulSex"><b><span style="font-size: x-large;">Painful sex would make a species go extinct</span></b><br /><br />Tyson received some ridicule when <a href="https://twitter.com/neiltyson/status/708427052433678336?lang=en" target="_blank">he tweeted</a></div><div id="GMOs"><br /></div><div id="GMOs"><span style="font-size: medium;"></span><blockquote><span style="font-size: medium;">If there were ever a species for whom sex hurt, it surely went extinct long ago.</span></blockquote></div><br />Emily Willingham called him out with her Forbes article <a href="https://www.forbes.com/sites/emilywillingham/2016/03/12/what-neil-degrasse-tyson-doesnt-know-about-sex-fills-many-books/?sh=6a29ad3929b6" target="_blank">What Neil deGrasse Tyson doesn't know about sex fills many books</a>. She gives a number of counter examples. Tyson defended himself saying in all her examples it is just a single partner that experiences pain. And that reproduction might occur if one partner finds it pleasurable while the other finds it painful.</div><div id="SpacePen"><br />Biologist P Z Myers weighed in with <a href="https://freethoughtblogs.com/pharyngula/2016/03/17/some-days-its-very-hard-to-defend-neil-degrasse-tyson/" target="_blank">Some days, it's very hard to defend Neil deGrasse Tyson</a>. He opined that Tyson's reply was making the goal posts dance. And that in biological systems it often isn't pleasure and pain that drives behavior.<br />And Myers went on to note that Willingham did provide a counter example where both partners experience pain to reproduce: salmon. He writes:<br /><blockquote>"And Willingham addressed his excuse with her very first example:semelparous fish, like salmon. Neither sex gets a lot of joy aout of reproduction. They batter themselves half to death trying to get upstream; they exert themselves to such a degree that their flesh is like an exhausted disintegrating bruise by the time they get to the spawning grounds, and then they die."</blockquote><br /><br />
<span style="font-size: x-large;"><b><div id="JWST">The James Webb Space Telescope is parked in Earth's shadow</div></b></span></div><br />In this <a href="https://www.youtube.com/watch?v=E_eTO3ujD4w&t=622s">Lagrange point explainer</a> Neil tells us that the James Webb Space Telescope is parked at the Sun-Earth L2 where earth blocks the Sun. This is to keep the Sun's rays off of the sensitive infra-red telescope.<div><br /></div><div>Earth does mostly eclipse the sun at the L2. However the JWST isn't parked at SEL2. It is in <a href="https://en.wikipedia.org/wiki/James_Webb_Space_Telescope#Location_and_orbit" target="_blank">a large halo orbit around SEL2 and never comes near Earth's shadow</a>. The telescope relies on a <a href="https://en.wikipedia.org/wiki/James_Webb_Space_Telescope#Sunshield_protection" target="_blank">sun shade</a> to keep sunlight off of the scope. </div><div><br /></div><br /><br /><span style="font-size: x-large;"><b><div id="SmoothEarth">
Earth is smoother than a cue ball</div></b></span><br />In this <a href="https://www.youtube.com/watch?v=0ub7Yt9WZJs">Joe Rogan interview</a> Neil tells us that that Earth scaled down to the size of a cue ball would be smoother than any cue ball ever machined.<div><br /><div>Scaled down to a 57 mm diameter cue ball Earth's biggest mountains and valleys would be around .04 mm. Which is about 10 times the size of the biggest bumps and pits on a cue ball.</div><div><br /></div><div>Neil seems to confuse tolerance for sphericity with texture. VSauce takes a look at this fifteen minutes into his video <a href="https://www.youtube.com/watch?v=mxhxL1LzKww&t=902s">How much of the Earth can you see at once</a>?</div>
<div><br /></div><div><span style="font-size: x-large;"><b><div id="Curvature">Curvature not visible from Branson's flight</div></b></span><br />Tyson claims he has done the calculations and tells us that the curvature of the earth is not visible from the altitude of Richard Branson's suborbital fight with Virgin Galactic. </div><div><br /></div><div>Six minutes into his <a href="https://www.facebook.com/StarTalk/videos/232721992631315" target="_blank">Facebook video Why Do Billionaires Love Space</a> Neil says "So, now high up are they relative to the earth? Are they gonna see the curvature? I did a calculation, the answer is NO." He makes the same claim <a href="https://youtu.be/ulTQcLFNiTs" target="_blank">here</a>.</div><div><br /></div><div><a href="https://www.youtube.com/watch?v=rE3QOj6t48c&t=43s" target="_blank">Here</a> Neil claims you would not see curvature from the altitude of Felix Baumgartner's jump.</div><div><br /></div><div>And <a href="https://www.youtube.com/watch?v=4qYkio86uHY">Neil tells Joe Rogan the same thing</a>.</div><div><br /></div><div>Scott Manley did an excellent video <a href="https://www.youtube.com/watch?v=xpUcZXiKtfU" target="_blank">How High Do You Have To Be Before You See The Curvature Of the Earth 360/VR</a>.</div><div><br /></div><div>Felix Baumgartner made his jump at about a 39 kilometer altitude. A <a href="https://www.youtube.com/watch?v=xpUcZXiKtfU&t=201s" target="_blank">little more than 3 minutes</a> in Scott shows curvature at at 30 kilometer altitude. Curvature is visible. A <a href="https://www.youtube.com/watch?v=xpUcZXiKtfU&t=260s" target="_blank">little more than 4 minutes in</a> he shows the view from a 100 kilometer up.</div><div><br /></div><div>Either Neil hasn't done the calculation he claims or he is incompetent. This gaffe is especially annoying since Flat Earthers have been citing these claims and appealing to Neil's authority.</div>
<div><br /></div><div><span style="font-size: x-large;"><b><div id="Cordless">NASA invented cordless power tools</div></b></span><br />Tyson <a href="https://www.youtube.com/watch?v=_otJ63cy-UY" target="_blank">tells Joe Rogan that NASA invented cordless power tools</a> because there are no power outlets in outer space.</div><div><br /></div><div><br /></div><div>However Black and Decker Developed the first cordless power tool in 1961 before the company had any contracts with NASA. From a <a href="https://www.nasa.gov/offices/ipp/home/myth_tools.html">NASA page</a>: </div><div><br /></div><div></div><blockquote><div>Did NASA invent cordless power tools?</div><div>No. The first cordless power tool was unveiled by Black & Decker in 1961. In the mid-1960s, Martin Marietta Corporation contracted with Black & Decker to design tools for NASA. The tool company developed a zero-impact wrench for the Gemini project that spun bolts in zero gravity without spinning the astronaut. Black & Decker also designed a cordless rotary hammer drill for the Apollo moon program. The drill was used to extract rock samples from the surface of the moon and could operate at extreme temperatures and in zero-atmosphere conditions. Before the zero-impact wrench and rotary hammer drill could go into space, they needed to be tested in anti-gravity conditions. Black & Decker and NASA tested the tools either under water or in transport planes that would climb to the highest possible altitude and then nosedive to simulate anti-gravity conditions. As a result of this work, Black & Decker created several spinoffs, including cordless lightweight battery powered precision medical instruments and a cordless miniature vacuum cleaner called the Dustbuster, but cordless power tools predate the Space Agency's involvement with the company.</div></blockquote>
<b><span style="font-size: x-large;"><div id="NoFallout"></div></span></b></div></div><p> </p><b><span style="font-size: x-large;"><div id="NoFallout">Modern nuclear weapons would have no fall out</div></span></b><div></div><p> </p>
<div>From <a href="https://youtu.be/XqJ1T6r-2WQ?t=28" target="_blank">an interview with Bill Maher</a>:</div>
<div><b><br /></b></div><div><b></b></div><blockquote><div><b>Tyson</b>: Modern nukes don't have the radiation problem -- just to be clear</div><div><b>Maher</b>: Really?</div><div><b>Tyson</b>: you're still blown to Smithereens but yeah it's a different kind of weapon than the Hiroshima and Nagasaki</div><div><b>Maher</b>: Nuclear weapons -- If they're exploded don't have a radiation problem?</div><div><b>Tyson</b>: Not if it's a hydrogen bomb. No, not in the way that you we used to have to worry about it with fallout and all the rest of that.</div></blockquote><div><br /></div>Neil would be somewhat correct if modern hydrogen bombs were pure fusion bombs. But they are not.<div><br /></div><div>Modern hydrogen bombs use a fission trigger. And many hydrogen bombs use a fission reaction during the fusion reaction to increase destructive power. There is a potential for much more fall out than Hiroshima or Nagasaki.</div><div><br /></div><div>Alex Wellerstein, a historian specializing in nuclear weapons, <a href="https://twitter.com/wellerstein/status/1581725339218497536" target="_blank">gave a break down on Twitter</a>.</div><div><br /></div><div><a href="https://en.wikipedia.org/wiki/Thermonuclear_weapon" target="_blank">Here</a> is the Wikipedia article on hydrogen bombs.</div>
<div><b><span style="font-size: x-large;"><br /></span></b></div><div><b><span style="font-size: x-large;"><div id="OtherComplaints">Other complaints against Tyson</div></span></b></div><div><br /></div><div>The above is a list of Neil's questionable claims. What follows is other Tyson related information.</div>
<div><br /></div>
<div><a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Allegations">Allegations of Sexual Misconduct</a></div>
<div><a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#NewYorker">Neil trashing an admiring writer from the New Yorker</a><a></a></div>
<div><a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#BusinessPartner">Neil's former business partner alleges Neil misled him.</a></div>
<div><a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#KickStarter">Investors sink $734,287 into Neil's vapor ware video game.</a></div>
<div><a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Students">Students pay big bucks for a nothing burger appearance.</a></div>
<div><a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Astrophysicist?">Is Tyson an astrophysicist?</a></div>
<div><a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Vegans">Vegans lack the cosmic perspective</a></div>
<div><a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Misinformation">Failing to correct misinformation</a></div>
<div><br /></div><div><div><b><span style="font-size: x-large;"><div id="Allegations">Allegations of sexual misconduct</div></span></b></div><div><br /></div><div>Tchiya Amet alleges that Tyson drugged and raped her in 1984. There are many articles on her allegations. <a href="https://www.vox.com/identities/2018/12/6/18125457/neil-degrasse-tyson-tchiya-amet-cosmos-natgeo">Here is an article from Vox</a> is one. Is Tyson guilty? I can't tell. It Tyson's word against Amet's on an event that happened decades ago. </div></div><div><br /></div><div><a href="https://www.youtube.com/watch?v=SfItg7qLqTI" target="_blank">Here</a> Tchiya talks about her experience in a YouTube interview with David McAffee.</div><div><br /></div><div>The Vox story also talks about Katelyn Allers' complaint that Neil lifted her blouse to look at a tattoo. Creepy but not really a serious transgression, in my opinion.</div><div><br /></div><div>However Ashley Watson's story is very credible. Neil has corroborated most of Watson's account.</div><div><br /></div><div>Watson was Neil's production assistant for the Cosmos TV show. One evening Neil invited her to his apartment at 10:30 pm. Watson thought they were going to discuss the show and a possible promotion.</div><div><br /></div><div>According to Watson Neil was partially dressed. She said he was playing one of Nina Simone's songs and kept repeating the lyric "Do I make you quiver." He gave her a "Native American Handshake" where he felt her pulse as he looked into her eyes.</div><div><br /></div><div>Ashley didn't put out and within days she resigned/was let go. </div><div><br /></div><div>Watson complained and National Geographic says they conducted an investigation. However Watson says she gave the investigators contact information of people who could corroborate their complaints. She says none of them were contacted. See t<a href="https://www.thedailybeast.com/neil-degrasse-tysons-accuser-disgusted-by-cosmos-return-says-she-was-a-sexual-object-to-him" target="_blank">his story from the Daily Beast</a>.</div><div><br /></div><div>An older married man hitting on a younger engaged woman is creepy but not a career destroying offense. However holding someone's career hostage is an abuse of power. If Tyson is guilty of this he should be fired from any administrative position. Personally, I believe Ashley Watson.</div><div><br /></div><div>See also <a href="https://www.facebook.com/notes/10158921227506613/" target="_blank">Tyson's Facebook post</a> on the allegations.</div><div><br /></div><div><br /></div>
<div><b><span style="font-size: x-large;"><div id="NewYorker">Neil trashing a writer from the New Yorker magazine</div></span></b><br />
<br />Karen Heller did <a href="https://www.washingtonpost.com/lifestyle/style/star-talker-neil-degrasse-tyson-on-fame-education-and-tweets/2015/02/24/5ec101fa-b854-11e4-a200-c008a01a6692_story.html" target="_blank">an interview with Tyson</a> for The Washington Post. In that interview Neil expressed his anger at Rebecca Mead, a writer for the New Yorker.</div><div><br /></div><div>Meade's <a href="https://www.newyorker.com/magazine/2014/02/17/starman" target="_blank">profile of Tyson</a> was dripping with admiration for Tyson. However she made the mistake of correctly noting "Tyson attended public schools, and was not a distinguished student. He was social, and teachers criticized him for being inattentive." </div><div><br /></div><div>Tyson responded by commenting on Meade's article:</div><div><br /></div><div><blockquote>No, no, no, no, no. As far as I can judge, I was anything but a mediocre child. I was active in all these activities that were intellectually stimulating. What’s interesting is I have two or three times as many Twitter followers as the New Yorker has circulation. So I haven’t done it yet, but I’m going to post the article and say, ‘This is verbally accurate and impressionistically false.’ It will be an exercise in journalism.</blockquote></div><div><br /></div><div>In my opinion Neil deserved his bad grades. He has repeatedly displayed incompetence in math and physics and horrendously sloppy scholarship in his attempts to recount history. Rebecca Meade could have mentioned that <a href="https://alcalde.texasexes.org/2012/02/star-power/" target="_blank">Neil flunked out at the University of Texas</a> with his advisors suggesting he pursue a different career (scroll to trouble in Texas). </div><div><br /></div><div>Neil was treated more than fairly by Rebecca Meade, in my opinion.</div><div><br /></div><div><br /></div>
<div><div><b><span style="font-size: x-large;"><div id="BusinessPartner">Neil's business partner complains he was misled.</div></span></b><br /><br />David Gamble was one of Tyson's former business partners. He claimed Tyson misled him when his partners bought out their share of StarTalk. From <a href="https://nypost.com/2017/08/31/neil-degrasse-tyson-left-co-creator-in-the-star-dust-suit/" target="_blank">an article in The New York Post</a>:</div><div></div><blockquote><div>Celebrity astrophysicist Neil deGrasse Tyson defrauded one of the creators of his popular “StarTalk” show while the producer was suffering physically and financially from a rare liver disorder, according to a new lawsuit. </div></blockquote><blockquote><div>David Gamble says he and NASA employee Helen Matsos brought the idea for the “StarTalk” radio show to Tyson in 2006. </div></blockquote><blockquote><div>Their partnership began to fray in 2011, however, when Gamble was diagnosed with polycystic kidney disease, according to Gamble’s Manhattan federal suit. Tyson and Matsos cut Gamble out of “StarTalk’s” operations, Gamble claims. </div></blockquote><blockquote><div>Gamble — who was undergoing dialysis for three to fours hours each day — agreed to sell his stake in “StarTalk” to Tyson and Matsos, the lawsuit claims. But Tyson and Matsos defaulted on their payments and only agreed to pay after convincing Gamble to take a lesser deal, he said. </div></blockquote><blockquote><div>Tyson personally convinced Gamble to take the new deal by telling Gamble “that Tyson would likely be leaving StarTalk and that he did not believe the show had any future,” the lawsuit said.</div></blockquote><div></div></div><div><br /></div><div>I can understand excluding a partner if his health were failing. But did Tyson tell Gamble StarTalk had no future? If so, there's no question Gamble was misled.</div><div><br /></div><div><br /></div>
<div><div><div><b><span style="font-size: x-large;"><div id="KickStarter">Kickstarter and Indiegogo supporters put $734,287 into Neil's vapor ware video game.</div></span></b><br /><br />Neil deGrasse Tyson's Space Odyssey was a crowd funded video game. 7207 backers invested $356,866. The goal was $314,159, the first 6 digits of pi. Estimated delivery of the game was July 2018. The game has still not been delivered. <a href="https://www.kickstarter.com/projects/2000580152/neil-degrasse-tyson-presents-space-odyssey-the-vid" target="_blank">Here</a> is the Kickstarter page.</div></div><div><br /></div><div>And 7,568 backers pitched in $377,421 on <a href="https://www.indiegogo.com/projects/space-odyssey-the-video-game#/">Indiegogo</a>.</div><div><br /></div><div><a href="https://www.kickstarter.com/projects/2000580152/neil-degrasse-tyson-presents-space-odyssey-the-vid/comments" target="_blank">Here</a> is the KickStarter comment page. And <a href="https://www.indiegogo.com/projects/space-odyssey-the-video-game#/comments" target="_blank">here</a> is the Indiegogo comment page. Needless to say those who invested are disappointed and angry.</div><div><br /></div><div>MinnMax did a video on this: <a href="https://www.youtube.com/watch?v=vc5sNWT91VE" target="_blank">What Happened to Neil deGrasse Tyson's Video Game</a>? And there is also Coffeezilla's <a href="https://www.youtube.com/watch?v=xmUFKkTaH5w" target="_blank">Go Fund Me Ep 2 Neil deGrasse Tyson's Video Game</a>.</div><div><br /></div>
<div><span style="font-size: x-large;"><b><div id="Students">Students sink $50,000 to hear Neil B.S.</div></b></span></div><div><br /></div><div><a href="https://np.reddit.com/r/OutOfTheLoop/comments/4bwshx/why_are_people_so_mean_to_neil_degrasse_tyson_on/d1daa05/?context=4" target="_blank">Here</a> is a college student's account of Neil's disappointing presentation. It had a net 10.3 k upvotes. <a href="https://np.reddit.com/r/AskReddit/comments/2sqd3h/have_you_ever_met_a_celebrity_who_turned_out_to/cnrzdiu/" target="_blank">Here</a> is another student describing the same event.</div><div><br /></div><div><br /></div>
<div><span style="font-size: x-large;"><b><div id="Astrophysicist?">Is Tyson an</div> <div id="Astrophysicist">astrophysicist?</div></b></span></div><div><br /></div><div>On <a href="https://en.wikipedia.org/wiki/Talk:Neil_deGrasse_Tyson/Archive_1#Career">a talk page</a> of Wikipedia's Tyson article someone asks if Neil is a practicing astrophysicist. </div><div><br /></div><div>Don Barry, an actual astrophysicist from Cornell, replies:</div><div><br /></div><div></div><blockquote><div>Not since graduate school (he did not successfully progress towards a degree at UT/Austin, and convinced Columbia to give him a second try). Aside from the obligatory papers describing his dissertation, he's got a paper on how to take dome flats, a bizarre paper speculating about an asteroid hitting Uranus, and courtesy mentions *very* late in the author lists of a few big projects in which it is unclear what, if anything, of substance he contributed. No first author papers of any real significance whatsoever. Nor is the there any evidence that he has been awarded any telescope time on significant instruments as PI since grad school, despite the incredibly inflated claims in his published CVs. He cozied up to Bush and pushed Bush's version of man to the Moon, Mars, and Beyond, and now gets appointed to just about every high level political advisory board. To an actual astronomer, this is almost beyond inconceivable. It's just bizarre. To answer Delon's question, no: he is not a practicing astrophysicist - Don Barry, Ph.D. Dept of Astronomy, Cornell University</div><div></div></blockquote><div><br /></div><div>Barry's assessment was written December 3, 2008. <a href="https://neildegrassetyson.com/cv/#papers" target="_blank">This</a> is from Neil's C.V. which I retrieved on June 12, 2023. I count 5 peer reviewed papers where Neil is the lead author, published from 1988 to 1993. He is listed as co-author is the COSMOS papers in 2007 and 2008. I believe these are the few big projects Barry mentions. Barry is correct -- Neil's name appears late in long lists of authors. Barry's assessment remains correct to this day.</div><div><br /></div><div>Even as a student Tyson's performance was sub mediocre. <a href="https://www.youtube.com/watch?v=F-_bpXLD2Qw" target="_blank">Harvard turned him down</a> for their post graduate program. </div><div><br /></div><div>And he flunked out of his doctoral program at the University of Texas. From <a href="https://alcalde.texasexes.org/2012/02/star-power/" target="_blank">The Alcalde</a>, a University of Texas publication:</div><div><br /></div><div></div><blockquote><div>Back in the lab, though, things weren't going as well. Tyson wasn't making progress on his dissertation, and professors encouraged him to consider alternate careers. He took the criticism hard, and he also faced racial discrimination on campus.</div><div><br /></div><div>"I was stopped and questioned seven times by University police on my way into the physics building," he says. "Seven times. Zero times was I stopped going into the gym — and I went to the gym a lot. That says all you need to know about how welcome I felt at Texas."</div><div><br /></div><div>At the same time, Tyson says that racism, while an everyday reality, didn't play a major role in his leaving the University. "Getting stopped by the police—I don't count that as significant racism. That's just 'same shit, different day' racism. I was stopped by campus police at other schools too—though not with the same frequency as in Texas. And I still get followed by security guards in department stores."</div><div><br /></div><div>After Tyson finished his master's thesis, his advisors dissolved his dissertation committee—essentially flunking him. "I still don't talk about it much," he says, "because it was a failed experiment, and I've moved on from that chapter of my life."</div><div><br /></div><div>"With or Without skin color, I wasn't the model student," he adds. "There was simply no room for me to be the full person that I was. If race was at play in all this, it was only at the edges of the experience"</div></blockquote><div><br /></div><div>Kudos to Neil's U.T. doctoral committee for having the backbone to flunk him. Given the numerous errors in his pop science I am wondering how he got a bachelor's degree, much less a doctorate.</div><div><br /></div><div>R. Michael Rich was Tyson's doctoral advisor at Columbia. It's my belief Rich noticed the popularity of Neil's lectures and gave Neil his credentials thanking that science and astronomy needed a charismatic advocate.</div><div><br /></div><div>It says in <a href="https://en.wikipedia.org/wiki/Neil_deGrasse_Tyson#Early_life_and_education" target="_blank">Tyson's Wikipedia</a> article that Rich hired students to help Neil with the data reduction on his thesis. So I am wondering how much of his doctoral dissertation Neil wrote.</div><div><br /></div><div>In my opinion Tyson demonstrates that charisma and political skills suffice to get an Ivey League degree -- competence in physics is not required.</div><div><br /></div>
<div><b><span style="font-size: large;"><div id="Vegans">Meatatarians vs Vegetarians</div></span></b></div><div><br /></div><div>There are a number of reasons to eat less meat. Vegans express concern for the suffering of animals we grow and kill to eat meat. The meat industry has a large carbon footprint and a greater impact on the environment. I am not a vegan or a vegetarian. But I have tried to reduce my meat intake. My daughter is vegetarian.</div><div><br /></div><div>In his book <i>Starry Messenger</i> Neil has a chapter ridiculing vegans and vegetarians. He regurgitates much of this chapter when promoting his book on TV or podcasts. From <a href="https://www.youtube.com/watch?v=z9HrMdNEKPA&t=91s">an interview with Steven Colbert</a>:</div><div><br /></div><div></div><blockquote><div>"People say 'I don't want to kill animals.' I don't have a problem with that. They probably have a humane mouse trap in their basement. They don't want to snap the neck of the mouse. So they capture the mouse -- you've got to check on it every couple of days because they dry out real quick. </div><div><br /></div><div>"So there it is and they set it loose into the wild where they have guaranteed it will be swallowed whole by, and picked apart by woodland predators. The average life of a mouse in the wild is nine to 18 months. Best thing you can do for a mouse is leave it in your basement where it will live up to six years."</div></blockquote><div></div><div><br /></div><div>This is a ridiculous straw man. Is it practical to share our home with a fire and health hazard? No. Is it practical to reduce animal suffering by eating less meat? Yes.</div><div><br /></div><div>Personally I use traps that snap the rodent's neck. I believe this is quickest most painless death I can give them. I am not going to let them dwell in my wall where they can chew the insulation off my electrical wiring.</div><div><br /></div><div>Neil goes on to describe a bizarre scenario where <a href="https://www.youtube.com/watch?v=z9HrMdNEKPA&t=228s" target="_blank">sentient plant aliens would be appalled at vegans eating baby plants</a>:</div><div><br /></div><div></div><blockquote><div>"Imagine photosynthesizing sentient aliens. They're in a spaceship and saw earth, has a good biodiversity of plants and it's on their tour book. They come to visit.</div><div><br /></div><div>"Then they meet vegetarians who expressly eat plants. And they'll freak out. And it's not just plants. They notice that vegetarians target the reproductive organs of plants -- its flowers the berries, the nut, all of the things -- the plant's just trying to make another version of itself.</div><div><br /></div><div>"Nope, let's eat it!</div><div><br /></div><div>...</div><div><br /></div><div>"Imagine the aliens check in on Whole Foods and they see people shopping in the produce aisle. And they notice these same vegetarians are into infanticide because they're selecting baby carrots, baby spinach, baby arugula, baby everything. And these aliens say 'What the hell is going on here on earth?' and they attack us!"</div></blockquote><div></div><div>Maybe the aliens would notice the plants we eat aren't sentient. Mushrooms are more closely related to us than to photosynthesizing plants. But there's no evidence they feel pain or fear. Nor have I seen evidence plants suffer.</div><div><br /></div><div>Do Neil and his plant aliens equate slicing up a carrot to slicing up a living puppy?</div><div><br /></div><div>But let's say for the sake of argument that plants do suffer.</div><div><br /></div><div>By <a href="https://stanfordmag.org/contents/can-vegetarianism-save-the-world-nitty-gritty" target="_blank">some estimates</a> it takes 8 pounds of grain to grow a pound of beef. So to get a pound of food the meat eater has to slaughter eight times as much plant life as the vegan getting his food directly from plants. The aliens would be eight times as pissed at Neil. Maybe more as it has taken many pounds of meat for Neil to grow his enormous buttocks.</div><div><br /></div><div>Neil lets rip one of his dramatic sound bites: "If you cut a tree, does it not bleed?" I am thinking of torrents of tree blood being splattered as Neil takes a chainsaw to trees in the Amazon rain forest so he can eat more beef. </div><div><br /></div>
<div><b><span style="font-size: large;"><div id="Misinformation">Failure to correct misinformation.</div></span></b></div><div><br /></div><div>It's June 21, 2023 as I write this. I started this page in 2016. For nearly nine years I've been asking Neil to correct the misinformation he has spread. At first I tried to be courteous and respectful. But it seems like Tyson has no desire to combat the misinformation he has spread over the years. I have to conclude he has no regard for the truth.</div><div><br /></div><div><b>Reluctance to admit error for his Bush and Star Names story.</b></div><div><br /></div><div>In 2014 Sean Davis sent a series of questions to Tyson. Neil responded to them<a href="https://www.facebook.com/notes/10224657946615626/" target="_blank"> here</a>. One of the questions:</div><div><br /></div><div><blockquote>3) Tyson regularly tells his his audiences about the time time that President Bush said, in the week after 9/11, "Our God is the God who named the stars" as a way of dividing people based on religion. Can you please provide me with the original sources of this exact quote from President George W. Bush, including the date on which he said it, the venue, and the full remarks in which the quote appeared?</blockquote></div><div><br /></div><div>Tyson responded:</div><div><br /></div><div></div><blockquote><div>2001 affected me deeply, as was true with most people. ...</div><div><br /></div><div>I have explicit memory of those words being spoken by the President. I reacted on the spot, making note for possible later reference in my public discourse. Odd that nobody seems to be able to find the quote anywhere -- surely every word publicly uttered by a President gets logged. </div><div><br /></div><div>FYI: There are two kinds of failures of memory. Ones remembering that which has never happened and the other is forgetting that which did. In my case, from life experience, I'm vastly more likely to forget an incident than to remember an incident that never happened. So I assure you, the quote is there somewhere. When you find it, tell me. Then I can offer it to others who've taken as much time as you to explore these things.</div><div><br /></div><div>One of our mantras in science is that the absence of evidence is not the same as evidence of absence.</div></blockquote><div></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNfbFxYXJF7Ohxo_5AT9laGDvNfPXjBuyXBMURlbNuzKQsjXJLqAE9yYp5Wm_JLGtACU3WjIKLZrm2zX8EHRjq5nXk5P-tlKbN6fcrg7XmHnnJf73jtVqCSSQpnU7aw7AXB68ebRXRnH-xZaoFKvei1Vlb9k0pN2FYKyENdCB6Gfef-ngkMGZ5wVxSYA98/s1234/Screenshot%202023-06-21%20at%205.31.55%20PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="158" data-original-width="1234" height="82" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNfbFxYXJF7Ohxo_5AT9laGDvNfPXjBuyXBMURlbNuzKQsjXJLqAE9yYp5Wm_JLGtACU3WjIKLZrm2zX8EHRjq5nXk5P-tlKbN6fcrg7XmHnnJf73jtVqCSSQpnU7aw7AXB68ebRXRnH-xZaoFKvei1Vlb9k0pN2FYKyENdCB6Gfef-ngkMGZ5wVxSYA98/w640-h82/Screenshot%202023-06-21%20at%205.31.55%20PM.png" width="640" /></a></div><div><br /></div><div><br /></div><div>That last sentence is galling. Neil is always going on about backing up claims with evidence. But when he makes a serious accusation against the President, he doesn't need evidence. And he is using his eyewitness testimony to back up his story? The unreliability of eye witness testimony is a staple for his shows. He should use this as an example.</div><div><br /></div><div>Tyson would not admit error.</div><div><br /></div><div>And then the story started trending. Even appearing in outlets like The Washington Post (<a href="https://www.washingtonpost.com/news/volokh-conspiracy/wp/2014/09/22/does-neil-degrasse-tyson-make-up-stories/" target="_blank">Link</a>). </div><div><br /></div><div>Tyson was <a href="https://www.washingtonpost.com/news/volokh-conspiracy/wp/2014/09/27/neil-degrasse-tyson-admits-he-botched-bush-quote/" target="_blank">eventually forced to admit error</a>. But it took a great deal of arm twisting.</div><div><br /></div><div><b>Kinda Sorta admitting error in regarding Ghazali and the Islamic Golden Age</b></div><div><br /></div><div>Neil sort of admitted error in his comments on this blog (<a href="http://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html?showComment=1458056847836#c5302117705517347439" target="_blank">Link</a>).</div><div><br /></div><div>But my blog is a very obscure corner of the internet. Neil has been loudly and publicly repeating this story for years, maybe decades. And his fans are still reposting this misinformation. Neil needs to make more of an effort to correct this chunk of false history.</div><div><br /></div><div><b>No admission whatsoever regarding his Newton falsehoods</b></div><div><br /></div><div>Regarding Newton Thony Christie has been trying to give Neil a heads up since at least 2014. Maybe earlier. See <a href="https://twitter.com/rmathematicus/status/548736354436546561" target="_blank">this tweet</a>.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_mzaeHgW4r2yy6-EH7HKhYSy_VSvUACBRR7sWunCCu7deanl1xSbzgGVewPYigcsW7Sj1nU6xCMb4dZM2oOAu5BnCiwhUrJRpyF5KKqULupb3DUgoziJTUOJaxmbBcARedTZndM-upSPoxVvrrXsWwq2koTiY4jngW7DgpWYTF6RQBX_kVp-MTr2mYupg/s1178/Screenshot%202023-06-21%20at%206.00.10%20PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="776" data-original-width="1178" height="422" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_mzaeHgW4r2yy6-EH7HKhYSy_VSvUACBRR7sWunCCu7deanl1xSbzgGVewPYigcsW7Sj1nU6xCMb4dZM2oOAu5BnCiwhUrJRpyF5KKqULupb3DUgoziJTUOJaxmbBcARedTZndM-upSPoxVvrrXsWwq2koTiY4jngW7DgpWYTF6RQBX_kVp-MTr2mYupg/w640-h422/Screenshot%202023-06-21%20at%206.00.10%20PM.png" width="640" /></a></div><br /><div>And I have been hounding Neil for years. On occasion he has responded to me. Here is a screen capture I made in 2019:</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh72uaevGyhpE2ZZ3kXe4WigraHjrFrgy_nrdntIlpSKp5l_E1ZW7qjSLbG_Pkv5cGZWp7rk4dwBhsdwCTduXgt8kGzQgZb-7n1L3sAHWiTvdOQC5k_Jj1xNHvhI1iDj1qSrQI5vEtkYrXEhhKgH2FlpfN8WooD7p-UM-Mn-5_aSr8sCBmreUjui-M5d7PI/s1724/Tyson'sNonAdmission.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="754" data-original-width="1724" height="280" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh72uaevGyhpE2ZZ3kXe4WigraHjrFrgy_nrdntIlpSKp5l_E1ZW7qjSLbG_Pkv5cGZWp7rk4dwBhsdwCTduXgt8kGzQgZb-7n1L3sAHWiTvdOQC5k_Jj1xNHvhI1iDj1qSrQI5vEtkYrXEhhKgH2FlpfN8WooD7p-UM-Mn-5_aSr8sCBmreUjui-M5d7PI/w640-h280/Tyson'sNonAdmission.png" width="640" /></a></div><br /><div><br /></div><div>I think it finally got through, though. I've noticed his Newton stories seem to have dropped from his routine around 2019. </div><div><br /></div><div>On this page I have a long section on Neil's misinformation regarding Newton (<a href="https://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html#Newton" target="_blank">Link</a>). To summarize Neil has Newton doing Principia and inventing calculus in just two months on a lark. But then Tyson has Newton turning into a drooling idiot when he started basking in the majesty of God. </div><div><br /></div><div><b>Systemic dishonesty</b></div><div><br /></div><div>It's not just Neil pointedly ignoring the falsehoods he's spread.</div><div><br /></div><div>Jonathan Adler wrote an article on how Neil's Bush and Star Names debacle was censored from Tyson's Wikipedia article (<a href="https://www.washingtonpost.com/news/volokh-conspiracy/wp/2014/09/24/what-makes-an-accusation-wiki-worthy/" target="_blank">Link</a>).</div><div><br /></div><div>And, indeed, it's all there in <a href="https://en.wikipedia.org/wiki/Talk:Neil_deGrasse_Tyson" target="_blank">Wikipedia's talk pages</a>. I will give Wikipedia credit that their process if much more transparent than in most information outlets.</div><div><br /></div><div>Discussion of Bush and Star Names starts on <a href="https://en.wikipedia.org/wiki/Talk:Neil_deGrasse_Tyson/Archive_2" target="_blank">Archive 2</a> of the talk pages for Neil's article. At first the censors argue that Sean Davis and the Federalist aren't reliable sources. </div><div><br /></div><div><a href="https://en.wikipedia.org/wiki/Talk:Neil_deGrasse_Tyson/Archive_3" target="_blank">Archive 3</a> starts with references to Neil's admission his Bush and Star Names story was wrong. Yet numerous editors continue to make the reliable sources argument even up to Archive 12. Major coverage was another argument against inclusion in the article even though the story appeared in many major news outlets.</div><div><br /></div><div>Starting in <a href="https://en.wikipedia.org/wiki/Talk:Neil_deGrasse_Tyson/Archive_13" target="_blank">Archive 13</a> Tyson's defenders try censor allegations of sexual misconduct. I was surprised that mention of the allegations eventually made it into the article</div><div><br /></div><div>In my opinion if a pundit is busted disseminating false information it should be included in his Wikipedia article. I doubt Wikipedia's article will ever note any of the falsehoods Tyson has spread.</div><div><br /></div><div>The Wikipedia process is transparent. I would guess similar conversations have gone on behind the scenes at other information outlets.</div><div><br /></div><div>Tyson is seen as the voice of rationality and objective truth. He must be protected even if it means suppressing data. </div><div><br /></div><div><br /></div><div><br /></div><div> </div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div></div><div><br /></div><div><br /></div></div>Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com52tag:blogger.com,1999:blog-3596550435682943926.post-80345776833517436962016-01-07T14:57:00.000-08:002020-04-13T12:49:22.908-07:00Deimos Tether<div class="separator" style="clear: both;">
This is a fourth in a series of blog posts looking at various tethers using <a href="http://hopsblog-hop.blogspot.com/2015/12/how-wolfes-tether-spreadsheet-works.html">Chris Wolfe's model</a>.</div>
<br />
<b><span style="font-size: large;">50 kilometer Deimos tether</span> - minimum length to remain aloft.</b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_p0Q-FB2pCk8Uzt5sqgK7JdhbaO4b_7LU-wbcaXL_EoUQ79RoL91M6FFXYPQ7-guJ4mclLCM_mGrI41P4wvtyE8UP1MObnDogL0O8YBMsRo74hA9MP4smt0z3m5cHzM5LqIO_I-Xmr4qS/s1600/Deimos.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="144" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_p0Q-FB2pCk8Uzt5sqgK7JdhbaO4b_7LU-wbcaXL_EoUQ79RoL91M6FFXYPQ7-guJ4mclLCM_mGrI41P4wvtyE8UP1MObnDogL0O8YBMsRo74hA9MP4smt0z3m5cHzM5LqIO_I-Xmr4qS/s640/Deimos.jpg" width="640" /></a></div>
Mars-Deimos L1 and L2 are about 14 kilometers from Deimos' surface. Another 26.5 kilometer length extended past these points would balance. Extending the tether 50 kilometers either way along with a counterweight would provide enough tension for the elevators to stay aloft.<br />
<br />
<table><tbody>
<tr><td><div style="text-align: center;">
<b>Safety</b></div>
<div style="text-align: center;">
<b> Factor </b></div>
</td><td><div style="text-align: center;">
<b>Zylon</b></div>
<div style="text-align: center;">
<b>Taper</b></div>
<div style="text-align: center;">
<b>Ratio</b></div>
</td><td><div style="text-align: center;">
<b>Tether to</b></div>
<div style="text-align: center;">
<b>Payload</b></div>
<div style="text-align: center;">
<b> Mass Ratio </b></div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
1</div>
</div>
</td><td><div style="text-align: right;">
1.000003</div>
</td><td><div style="text-align: right;">
.000007</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
2</div>
</div>
</td><td><div style="text-align: right;">
1.000006</div>
</td><td><div style="text-align: right;">
.000015</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
3</div>
</div>
</td><td><div style="text-align: right;">
1.000009</div>
</td><td><div style="text-align: right;">
.000022</div>
</td></tr>
</tbody></table>
<br />
Even with a safety factor of three, needed Zylon mass is tiny. Less than a quarter kilogram of tether could handle a 10 tonne payload.<br />
<br />
<b>Benefits</b><br />
<br />
There is no net acceleration at L1 and L2, so docking at ports at these locations would be like docking with the I.S.S.<br />
<br />
This first step could serve as a scaffolding additional tether infrastructure could be added onto.<br />
<br />
<b><span style="font-size: large;"></span></b><br />
<div id="ZRVTO">
<b><span style="font-size: large;">2942 kilometer lower Deimos tether</span></b>
<b> - ZRVTO to Phobos tether</b></div>
<br />
<br />
Given an ~1000 upper Phobos tether and a ~3000 lower Deimos tether, it is possible to move payloads between the two moons with almost no reaction mass. The tether points connected by the ellipse match the transfer ellipse's velocities. See my <a href="http://hopsblog-hop.blogspot.com/2016/01/upper-phobos-tether.html">Upper Phobos Tether</a> post.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqcRrC-MG5OniWTcz6tPHmORp0q0FwLL9uWT6B03AsnRhnfDlel9efaR-ayWTB5JwSJzg7tlUPhmbbdsI6_b2rHuCwAVo6vn_i8wOUlqxgjYAomCn5GXLeROZzW69A08ekLUjFxGxSa_7B/s1600/PhobosToDeimos.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqcRrC-MG5OniWTcz6tPHmORp0q0FwLL9uWT6B03AsnRhnfDlel9efaR-ayWTB5JwSJzg7tlUPhmbbdsI6_b2rHuCwAVo6vn_i8wOUlqxgjYAomCn5GXLeROZzW69A08ekLUjFxGxSa_7B/s400/PhobosToDeimos.jpg" width="325" /></a></div>
<br />
<br />
<br />
<table><tbody>
<tr><td><div style="text-align: center;">
<b>Safety</b></div>
<div style="text-align: center;">
<b> Factor </b></div>
</td><td><div style="text-align: center;">
<b>Zylon</b></div>
<div style="text-align: center;">
<b>Taper</b></div>
<div style="text-align: center;">
<b>Ratio</b></div>
</td><td><div style="text-align: center;">
<b>Tether to</b></div>
<div style="text-align: center;">
<b>Payload</b></div>
<div style="text-align: center;">
<b> Mass Ratio </b></div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
1</div>
</div>
</td><td><div style="text-align: right;">
1.01</div>
</td><td><div style="text-align: right;">
.04</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
2</div>
</div>
</td><td><div style="text-align: right;">
1.03</div>
</td><td><div style="text-align: right;">
.06</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
3</div>
</div>
</td><td><div style="text-align: right;">
1.04</div>
</td><td><div style="text-align: right;">
.09</div>
</td></tr>
</tbody></table>
<br />
So even with a safety factor of 3, the elevator's Zylon mass is modest. 1 tonne of Zylon can handle 11 tonnes of payload.<br />
<br />
The red transfer orbit pictured above is called a ZRVTO - Zero Relative Velocity Transfer Orbit. At either end of the transfer orbit, relative velocity with the tether at rendezvous point is zero. ZRVTO is a term coined by Marshall Eubanks.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiri2KtLhJP_3OnLiei0PEYylsGKdurXudfMvIprgqNWw6kIyYLD3HB-o2dIo0pPtrm8lvSOPQaCIe1P68Xwl6kOydfSYt0ZMOn47fcSjQRVAKq4Mo2tCdHKMqOb5LyNVki8Bz5DPt-4foc/s1600/Screen+Shot+2017-07-31+at+9.35.54+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="187" data-original-width="605" height="196" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiri2KtLhJP_3OnLiei0PEYylsGKdurXudfMvIprgqNWw6kIyYLD3HB-o2dIo0pPtrm8lvSOPQaCIe1P68Xwl6kOydfSYt0ZMOn47fcSjQRVAKq4Mo2tCdHKMqOb5LyNVki8Bz5DPt-4foc/s640/Screen+Shot+2017-07-31+at+9.35.54+AM.png" width="640" /></a></div>
The notion of a ZRVTO between Deimos and Phobos tethers is not new. Above is a diagram from an article by JPL engineer Paul Penzo. Page 70 of the 1997 publication <a href="http://www.tethers.com/papers/TethersInSpace.pdf">Tethers In Space Handbook</a>. I believe Penzo came up with this idea in 1984.<br />
<br />
Penzo's 940 and 2960 km lengths aren't that far from my 937 and 2942 numbers. It is reassuring that an aerospace engineer's numbers are close to my own.<br />
<br />
<b>Benefits</b><br />
<br />
The idea of ion driven interplanetary vehicles excites me. The <a href="https://en.wikipedia.org/wiki/Dawn_(spacecraft)">Dawn probe</a> has demonstrated ion rockets are long lived and amenable to re-use. An ion rocket's fantastic ISP means a lot more mass fraction can be devoted to the dry mass structure and payload.<br />
<br />
However ion rockets have pathetic thrust. They suck at climbing in and out of planetary gravity wells.<br />
<br />
<a href="http://space.stackexchange.com/questions/8420/general-guidelines-for-modeling-a-low-thrust-ion-spiral/8421#8421">Here</a> Mark Adler talks about ion rocket trajectories:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3vKoJrhfApGSp-2oPBF9RZRiuWzhWsVtV4hBy7m1JCpfwbQY3GeEHcb_XHz2wdDw7jcN6xLbtL3I26V_J-TSorODvRlRPP4rZYv7TuCBMsgkFBgCeSjxAm9shaBYgJxGKu0zBnQzEFeRY/s1600/Screen+Shot+2016-01-02+at+1.13.37+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3vKoJrhfApGSp-2oPBF9RZRiuWzhWsVtV4hBy7m1JCpfwbQY3GeEHcb_XHz2wdDw7jcN6xLbtL3I26V_J-TSorODvRlRPP4rZYv7TuCBMsgkFBgCeSjxAm9shaBYgJxGKu0zBnQzEFeRY/s640/Screen+Shot+2016-01-02+at+1.13.37+PM.png" width="558" /></a></div>
The fictitious Hermes from Andy Weir's <i>The Martian</i> can do 2 mm/sec<sup>2</sup> acceleration. That would take an implausibly high <a href="http://hopsblog-hop.blogspot.com/2015/05/the-need-for-better-alpha.html">alpha</a>, But perhaps possible so I will go with that number.<br />
<br />
At Deimos' distance from Mars, gravitational acceleration is about 80 mm/s^2. The Hermes' acceleration over Mars gravitational acceleration at that orbit is about 1/40. A small fraction but a lot larger than the 10^-3 fraction Adler mentions.<br />
<br />
Deimos moves about 1.35 km/s about Mars. With an impulsive chemical burn, it would take about .56 km/s to achieve escape. But with a 2 mm/s^2 acceleration, it would take about 5 days and and .8 km/s to achieve escape.<br />
<br />
To spiral down to low Mars Orbit, it'd take Hermes more than 17 days and 3 km/s. So the Deimos rendezvous saves about two weeks and more than 2 km/s delta V.<br />
<br />
Once in heliocentric orbit, it is the sun's gravitational acceleration that we put in the denominator. Here is a chart of gravitational acceleration at various distances from the sun:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXh1J6xokS3tUt8-t9Pdqgvc7G9DvLDtDIsnXbwOBFdPMLIkkkq_106tSJP2N_Ls2w2zT6rogrL2xSx01KXpuIZGV9mYRnRKr4auOy5JRrkvneeRkaGqVz4TY-g0Tr1e5ajkNrz8Mykd66/s1600/sun+acceleration.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXh1J6xokS3tUt8-t9Pdqgvc7G9DvLDtDIsnXbwOBFdPMLIkkkq_106tSJP2N_Ls2w2zT6rogrL2xSx01KXpuIZGV9mYRnRKr4auOy5JRrkvneeRkaGqVz4TY-g0Tr1e5ajkNrz8Mykd66/s640/sun+acceleration.jpg" width="598" /></a></div>
<br />
If the rocket's acceleration is a significant fraction of central body's acceleration, we can model burns as impulsive. The trajectory would be more like an ellipse than a spiral. At earth's distance from the sun., Hermes 2 mm/s^2 acceleration would be about a third the sun's gravity. At Mars, it's about four fifths. In the asteroid belt, Hermes acceleration exceeds acceleration from sun's gravity.<br />
<br />
Ion rockets may not be great for climbing in and out of planetary gravity wells. But they're fine for changing heliocentric orbits, especially in the asteroid belt and beyond.<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com0tag:blogger.com,1999:blog-3596550435682943926.post-32078570861998535932016-01-02T13:21:00.001-08:002020-04-13T12:49:45.727-07:00Upper Phobos Tether<div class="separator" style="clear: both;">
This is third in a series of posts that rely on <a href="http://hopsblog-hop.blogspot.com/2015/12/how-wolfes-tether-spreadsheet-works.html">Wolfe's model of tethers from tide locked moons</a>. As with the <a href="http://hopsblog-hop.blogspot.com/2015/12/lower-phobos-tether.html">Lower Phobos Tether post</a>, I will look at possible stages of this tether examining tether to payload mass as well as benefits each stage confers.</div>
<div>
<br /></div>
<div>
<b><span style="font-size: large;">7 kilometer upper Phobos tether</span> - tether doesn't collapse but remains extended</b></div>
<div>
<br /></div>
<div>
I used Wolfe's spreadsheet to find location of tether top where tether length Phobos side of L2 balances the length extending beyond L2. This occurs 6.6 kilometers from the tether anchor. Having the tether extend 7 kilometers is sufficient to maintain tension.</div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieKyXnpOv2F8eZ_IN5j6ebCO2eGqCZ1yt0gUVQHJ1vdrz_WCiqIbTbPpjHZhHyuUQp5prwq0Kdd2_0q8JLGxgT44plASsneMZ5CsPk3H7hzP3GXIsMzU8WIWdG-tFqBRNfiCPDasR07Hu_/s1600/Upper+Phobos+7+kilometer+tether.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="286" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieKyXnpOv2F8eZ_IN5j6ebCO2eGqCZ1yt0gUVQHJ1vdrz_WCiqIbTbPpjHZhHyuUQp5prwq0Kdd2_0q8JLGxgT44plASsneMZ5CsPk3H7hzP3GXIsMzU8WIWdG-tFqBRNfiCPDasR07Hu_/s640/Upper+Phobos+7+kilometer+tether.jpg" width="640" /></a></div>
<div>
<br />
<div>
<br />
<br />
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: Times; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
</div>
<br />
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: Times; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<div>
<table><tbody>
<tr><td><div style="text-align: center;">
<div style="margin: 0px;">
<b>Safety</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b> Factor </b></div>
</div>
</td><td><div style="text-align: center;">
<div style="margin: 0px;">
<b>Zylon</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b>Taper</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b>Ratio</b></div>
</div>
</td><td><div style="text-align: center;">
<div style="margin: 0px;">
<b>Tether to</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b>Payload</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b> Mass Ratio </b></div>
</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
<div style="margin: 0px;">
1</div>
</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
1.01</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
.04</div>
</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
<div style="margin: 0px;">
2</div>
</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
1.03</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
.06</div>
</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
<div style="margin: 0px;">
3</div>
</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
1.04</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
.09</div>
</div>
</td></tr>
</tbody></table>
<div style="margin: 0px;">
<br /></div>
</div>
</div>
<br />
<b>Benefits</b><br />
Docking with a facility at the L1 or L2 regions is easier than landing on Phobos. In the words of Paul451: "Instead of a tricky rocket landing at miniscule gravity on a loosely consolidated dusty surface, you just dock with the L1-hub of the ribbon (same as docking with ISS), transfer the payload to the elevator car and gently lower it to the surface. Reverse trip to bring fuel from Phobos to your ship (Assuming ISRU fuel is available on Phobos.)"<br />
<br />
Also this small tether can serve as scaffolding on which to add longer tether lengths.<br />
<br /></div>
</div>
<div>
<b><span style="font-size: large;">937 kilometer upper Phobos tether</span> - transfer to Deimos tether</b></div>
<div>
<br /></div>
<div>
Given tethers from two coplanar moons tidelocked to the same central body, it is possible to travel between the two moons using nearly zero reaction mass.</div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsyoIFGE6JTcT2ub5t1a-Qr-swfN_lKX76FWAY_96q2AofaJ-3yuQjLMnklpM6rR_sJS-6QgsM0YBeU52wdeEdLPkt7oepuz-fh52uHaQPfZGIyvQYSafsLOQaJWT-3phV6zqvYxBVZPu5/s1600/Screen+Shot+2016-01-02+at+12.24.22+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsyoIFGE6JTcT2ub5t1a-Qr-swfN_lKX76FWAY_96q2AofaJ-3yuQjLMnklpM6rR_sJS-6QgsM0YBeU52wdeEdLPkt7oepuz-fh52uHaQPfZGIyvQYSafsLOQaJWT-3phV6zqvYxBVZPu5/s400/Screen+Shot+2016-01-02+at+12.24.22+PM.png" width="375" /></a></div>
<div>
Above I attempt to show how peri-aerion and apo-aerion of elliptical transfer orbit matches velocity of the tether points this ellipse connects. Tether Vs are red, transfer ellipse'sVs are blue.</div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOvYsbb6ZYsgkPtgGQb9opPehWEbGwh2koJpXExwla3hWmHiZhCylFlXvAwcKxcZ8tlwzv2rff5w04qcg3opqKgYuzIAlgs-tvpRCK90ADrf2I9GlzRnGyeWZt3XByHVib1VXkj9N4EJo-/s1600/PhobosDeimos.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="424" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOvYsbb6ZYsgkPtgGQb9opPehWEbGwh2koJpXExwla3hWmHiZhCylFlXvAwcKxcZ8tlwzv2rff5w04qcg3opqKgYuzIAlgs-tvpRCK90ADrf2I9GlzRnGyeWZt3XByHVib1VXkj9N4EJo-/s640/PhobosDeimos.jpg" width="640" /></a></div>
<div>
<br /></div>
<div>
Above I try to explain the math for finding the tether lengths from Deimos and Phobos.</div>
<div>
<br /></div>
<div>
Trip time between the two tethers is about 8 hours.</div>
<div>
<br /></div>
<div>
<br />
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: Times; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
</div>
<br />
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: Times; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<table><tbody>
<tr><td><div style="text-align: center;">
<div style="margin: 0px;">
<b>Safety</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b> Factor </b></div>
</div>
</td><td><div style="text-align: center;">
<div style="margin: 0px;">
<b>Zylon</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b>Taper</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b>Ratio</b></div>
</div>
</td><td><div style="text-align: center;">
<div style="margin: 0px;">
<b>Tether to</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b>Payload</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b> Mass Ratio </b></div>
</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
<div style="margin: 0px;">
1</div>
</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
1.02</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
.035</div>
</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
<div style="margin: 0px;">
2</div>
</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
1.04</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
.070</div>
</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
<div style="margin: 0px;">
3</div>
</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
1.05</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
.107</div>
</div>
</td></tr>
</tbody></table>
<div style="margin: 0px;">
<br /></div>
</div>
</div>
<div>
With a safety factor of three, one tonne of Zylon could accommodate about 9 tonnes of payload.<br />
<br />
I look at the Deimos tether <a href="http://hopsblog-hop.blogspot.com/2016/01/deimos-tether.html">here</a>.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiri2KtLhJP_3OnLiei0PEYylsGKdurXudfMvIprgqNWw6kIyYLD3HB-o2dIo0pPtrm8lvSOPQaCIe1P68Xwl6kOydfSYt0ZMOn47fcSjQRVAKq4Mo2tCdHKMqOb5LyNVki8Bz5DPt-4foc/s1600/Screen+Shot+2017-07-31+at+9.35.54+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="187" data-original-width="605" height="196" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiri2KtLhJP_3OnLiei0PEYylsGKdurXudfMvIprgqNWw6kIyYLD3HB-o2dIo0pPtrm8lvSOPQaCIe1P68Xwl6kOydfSYt0ZMOn47fcSjQRVAKq4Mo2tCdHKMqOb5LyNVki8Bz5DPt-4foc/s640/Screen+Shot+2017-07-31+at+9.35.54+AM.png" width="640" /></a></div>
The notion of a ZRVTO between Deimos and Phobos tethers is not new. Above is a diagram from an article by JPL engineer Paul Penzo. Page 70 of the 1997 publication <a href="http://www.tethers.com/papers/TethersInSpace.pdf">Tethers In Space Handbook</a>. Penzo came up with this idea in 1984 (I believe).<br />
<br />
Penzo's 940 and 2960 km lengths aren't that far from my 937 and 2942 numbers. It is reassuring that an aerospace engineer's numbers are close to my own.</div>
<div>
<br /></div>
<div>
<b>Benefits</b></div>
<div>
<br /></div>
<div>
Easy travel between Deimos and Phobos is a benefit in itself. </div>
<div>
<br /></div>
<div>
But this would be a huge help to ion driven Mars Transfer Vehicles.</div>
<div>
<br /></div>
<div>
I like the notion of reusable ion driven MTVs. Ion engines have have great ISP thus allowing a more substantial payload mass ratio. However they have pathetic thrust. <a href="https://www.youtube.com/watch?v=khIHZp_GTEI">Andy Weir's fictional Hermes spacecraft can accelerate at 2 millimeters/sec^2</a>. Which actually is very robust ion thrust. However ithis is only medium implausible. Low thrust means little or no planetary Oberth benefit. Plus a lo-o-o-ng time to climb in and out of planetary gravity wells.</div>
<div>
<br /></div>
<div>
From <a href="http://space.stackexchange.com/questions/8420/general-guidelines-for-modeling-a-low-thrust-ion-spiral/8421#8421">Mark Adler's explanation on how to model ion rocket trajectories</a>: </div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDwJ0AEScXP840JVULJEOqRZGKgjjG9ivBQ-aHGSR54tXWlGVpoc3k99mfBzivt1FpvK0789eAhTNtPpHQ8v3nds8hx6dfAmIs72b4JQWXtx5eNITVvV9f7ypbOXAlEg9xRyEjkWV_qXk1/s1600/Screen+Shot+2016-01-02+at+1.13.37+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDwJ0AEScXP840JVULJEOqRZGKgjjG9ivBQ-aHGSR54tXWlGVpoc3k99mfBzivt1FpvK0789eAhTNtPpHQ8v3nds8hx6dfAmIs72b4JQWXtx5eNITVvV9f7ypbOXAlEg9xRyEjkWV_qXk1/s640/Screen+Shot+2016-01-02+at+1.13.37+PM.png" width="558" /></a></div>
<div>
<br /></div>
<div>
300 km above Mars surface in low Mars orbit, gravitational acceleration is about 3 meters/sec^2. For a 300 km altitude low earth orbit, gravitational acceleration is about 9 meters/sec^2. 2 mm/s^2 acceleration is <i><b>less</b></i> than 10^-3 of the gravitational acceleration at initial orbit velocity in both these case. However I will be kind and go with Adler's .856 * initial orbit velocity.</div>
<div>
<br /></div>
<div>
At 2 millimeters/s^2 it would take Hermes 38 days to spiral out of earth's gravity well from low earth orbit and 17 days to spiral out of Mars gravity well. Most of the slow spiral out of earth's gravity would be through the intense radiation of the Van Allen belts.</div>
<div>
<br /></div>
<div>
I was very disappointed when <a href="https://www.youtube.com/watch?v=-fdKyszL1Zo">Neil deGrasse Tyson's trailer</a> had Hermes departing from low earth orbit and arriving in Mars' orbit 124 days later.</div>
<div>
<br /></div>
<div>
Besides adding 10 km/s to the delta V budget, climbing in and out of gravity wells would add about two months to Hermes' trip time. Tyson's video describes an impossible trajectory. I wish he'd fact check himself with the same enthusiasm he applies to others.</div>
<div>
<br /></div>
<div>
It would be much better for Hermes to travel between the edges of each gravity well. At least as close as practical to the edge. In earth's neighborhood, Hermes could park at <a href="http://hopsblog-hop.blogspot.com/2015/05/eml2.html">EML2</a> between trips. In Mars' neighborhood, parking at Deimos would save a lot of time and delta V. From Deimos, astronauts and payloads can transfer to Phobos and then to Mars surface. In this scenario, Hermes' 124 day trip from earth to Mars is plausible.</div>
<div>
<br /></div>
<div>
<b><span style="font-size: large;">2345 kilometer upper Phobos tether</span> - Mars escape</b></div>
<div>
<br /></div>
<div>
If anchor in a circular orbit, escape velocity can be achieved if tether top is at a distance 2^(1/3) anchor's orbital radius. I try to demonstrate that <a href="http://space.stackexchange.com/questions/5253/whats-the-path-of-something-dropped-from-a-space-elevator">here</a>. Phobos is in a nearly circular orbit. To achieve escape, the tether would need to be 2435 kilometers long.</div>
<div>
<br /></div>
<div>
<br />
<br />
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: Times; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
</div>
<br />
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: Times; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: Times; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<table><tbody>
<tr><td><div style="text-align: center;">
<div style="margin: 0px;">
<b>Safety</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b> Factor </b></div>
</div>
</td><td><div style="text-align: center;">
<div style="margin: 0px;">
<b>Zylon</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b>Taper</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b>Ratio</b></div>
</div>
</td><td><div style="text-align: center;">
<div style="margin: 0px;">
<b>Tether to</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b>Payload</b></div>
</div>
<div style="text-align: center;">
<div style="margin: 0px;">
<b> Mass Ratio </b></div>
</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
<div style="margin: 0px;">
1</div>
</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
1.11</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
.204</div>
</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
<div style="margin: 0px;">
2</div>
</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
1.22</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
.436</div>
</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
<div style="margin: 0px;">
3</div>
</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
1.35</div>
</div>
</td><td><div style="text-align: right;">
<div style="margin: 0px;">
.700</div>
</div>
</td></tr>
</tbody></table>
<div style="margin: 0px;">
<br /></div>
<div style="margin: 0px;">
A 7 tonne Zylon tether could deal with a 10 tonne payload, even with a safety factor of three.</div>
<div style="margin: 0px;">
<br /></div>
</div>
</div>
</div>
<div>
<b>Benefits:</b></div>
<div>
<br /></div>
<div>
Achieve mars escape.</div>
<div>
<br /></div>
<div>
<b><span style="font-size: large;">6155 km kilometer upper Phobos tether</span> - To a 1 A.U. heliocentric orbit</b></div>
<div>
<br /></div>
<div>
A tether this long can fling payloads to a 1 A.U. heliocentric orbit, in other words an earth transfer orbit.</div>
<div>
<br />
<table><tbody>
<tr><td><div style="text-align: center;">
<b>Safety</b></div>
<div style="text-align: center;">
<b> Factor </b></div>
</td><td><div style="text-align: center;">
<b>Zylon</b></div>
<div style="text-align: center;">
<b>Taper</b></div>
<div style="text-align: center;">
<b>Ratio</b></div>
</td><td><div style="text-align: center;">
<b>Tether to</b></div>
<div style="text-align: center;">
<b>Payload</b></div>
<div style="text-align: center;">
<b> Mass Ratio </b></div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
1</div>
</div>
</td><td><div style="text-align: right;">
1.80</div>
</td><td><div style="text-align: right;">
1.57</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
2</div>
</div>
</td><td><div style="text-align: right;">
3.24</div>
</td><td><div style="text-align: right;">
4.77</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
3</div>
</div>
</td><td><div style="text-align: right;">
5.82</div>
</td><td><div style="text-align: right;">
11.16</div>
</td></tr>
</tbody></table>
<br />
With a safety factor of three, an 11.2 tonne elevator could lift a one tonne payload. Not great, but it'd be worthwhile if we were tossing lots of payloads earthward.<br />
<br /></div>
<div>
<b>Benefits</b></div>
<div>
<br /></div>
<div>
Catch/throw payloads to/from earth. Phobos is about 24º from Mars orbital plane. Mars orbit is about 1.5º from the ecliptic. So there may be some plane change expense.</div>
<div>
<br /></div>
<div>
<b><span style="font-size: large;">7980 kilometer upper Phobos tether</span> - to a 2.77 A.U. heliocentric orbit.</b></div>
<div>
<br /></div>
<div>
<table><tbody>
<tr><td><div style="text-align: center;">
<b>Safety</b></div>
<div style="text-align: center;">
<b> Factor </b></div>
</td><td><div style="text-align: center;">
<b>Zylon</b></div>
<div style="text-align: center;">
<b>Taper</b></div>
<div style="text-align: center;">
<b>Ratio</b></div>
</td><td><div style="text-align: center;">
<b>Tether to</b></div>
<div style="text-align: center;">
<b>Payload</b></div>
<div style="text-align: center;">
<b> Mass Ratio </b></div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
1</div>
</div>
</td><td><div style="text-align: right;">
2.5</div>
</td><td><div style="text-align: right;">
3.1</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
2</div>
</div>
</td><td><div style="text-align: right;">
6.4</div>
</td><td><div style="text-align: right;">
12.5</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
3</div>
</div>
</td><td><div style="text-align: right;">
16.2</div>
</td><td><div style="text-align: right;">
39.5</div>
</td></tr>
</tbody></table>
<br />
With a safety factor of three, it would take a 40 tonne Zylon tether to handle a 1 tonne payload. We would need to be tossing many payloads for this to be worthwhile. <br />
<br /></div>
<div>
<b>Benefits:</b></div>
<div>
<br /></div>
<div>
2.77 A.U. is the semi major axis of Ceres. A tether this long could catch/throw payload to/from Ceres. But this doesn't take into account plane change because of Ceres inclination.</div>
<div>
<br /></div>
<div>
Even with plane change expense, this tether could be very helpful for traveling to and from The Main Belt.<br />
<br />
This could also throw payloads into a faster than Hohmann transfer orbit towards earth.</div>
<div>
<br /></div>
<div>
<br /></div>
<div>
<br /></div>
<div>
<br /></div>
<div>
<br /></div>
<div>
<br /></div>
<div>
<br /></div>
<div>
<br /></div>
Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com3tag:blogger.com,1999:blog-3596550435682943926.post-76495753756657298372015-12-24T10:15:00.000-08:002020-04-13T12:50:12.885-07:00Lower Phobos Tether<div class="separator" style="clear: both;">
A <a href="http://hopsblog-hop.blogspot.com/2015/06/phobos-panama-canal-of-inner-solar.html">Phobos tether</a> can be built in increments, it is useful in the early stages. So there's no pressing need to build a huge structure overnight. I will look at various stages of a Phobos tether, examining mass requirements and benefits each length confers. To model the tether I am using <a href="http://hopsblog-hop.blogspot.com/2015/12/how-wolfes-tether-spreadsheet-works.html">Wolfe's spreadsheet</a>. I will use Zylon with a tensile strength at 5,800 megapascals and density of 1560 kilograms per cubic meter. <a href="http://clowder.net/hop/TMI/LowerPhobosTether.xls">Here</a> is the version of the spreadsheet with Phobos data entered.</div>
<br />
<b><span style="font-size: large;">7 kilometer lower Phobos tether</span> - tether doesn't collapse but remains extended</b><br />
<b><br /></b>
At a minimum, the lower Phobos tether must extend far enough past Mars-Phobos L1 that the Mars-ward newtons exceed the Phobos-ward newtons. This will maintain tension and keep the elevator from falling back to Phobos.<br />
<br />
I used Wolfe's spreadsheet to find location of tether foot where tether length Mars side of L1 balances tether length from Phobos to L1. That occurs when tether foot is about 6.6 kilometers from tether anchor:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGm4_qfZHXOHkbBO9qeY0n1kj7EoC55nTWExRkAAtmWGlGx7zpdBbQwfCYesMuYPiBRbgW5Y5ERvEQDFHyaSrl7CUzNick0YJXGY2D4K5s5TjLDII9CrYDcISYyAVeoMTU0U-eIGftbPfn/s1600/Screen+Shot+2015-12-23+at+8.49.37+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGm4_qfZHXOHkbBO9qeY0n1kj7EoC55nTWExRkAAtmWGlGx7zpdBbQwfCYesMuYPiBRbgW5Y5ERvEQDFHyaSrl7CUzNick0YJXGY2D4K5s5TjLDII9CrYDcISYyAVeoMTU0U-eIGftbPfn/s400/Screen+Shot+2015-12-23+at+8.49.37+AM.png" width="400" /></a></div>
<br />
So going past that a ways will give a net Marsward force.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI6g1HPHxYSmlvjj64Cd9HljLhWG8xz5tYEKbGHZcr2Ckt9Ek6oA4EwYdh2svwFtXMxivcsxo6upTC_cc8OrvSewmOAYDOZTxFMcpWUFWW31cIFGyXVzTWjByRfARcvQKSxQsxvXjGIFpn/s1600/Phobos+7+kilometer+tether.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="280" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI6g1HPHxYSmlvjj64Cd9HljLhWG8xz5tYEKbGHZcr2Ckt9Ek6oA4EwYdh2svwFtXMxivcsxo6upTC_cc8OrvSewmOAYDOZTxFMcpWUFWW31cIFGyXVzTWjByRfARcvQKSxQsxvXjGIFpn/s640/Phobos+7+kilometer+tether.jpg" width="640" /></a></div>
<br />
<br />
<table><tbody>
<tr><td><div style="text-align: center;">
<b>Safety</b></div>
<div style="text-align: center;">
<b> Factor </b></div>
</td><td><div style="text-align: center;">
<b>Zylon</b></div>
<div style="text-align: center;">
<b>Taper</b></div>
<div style="text-align: center;">
<b>Ratio</b></div>
</td><td><div style="text-align: center;">
<b>Tether to</b></div>
<div style="text-align: center;">
<b>Payload</b></div>
<div style="text-align: center;">
<b> Mass Ratio </b></div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
1</div>
</div>
</td><td><div style="text-align: right;">
1</div>
</td><td><div style="text-align: right;">
.000003</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
2</div>
</div>
</td><td><div style="text-align: right;">
1</div>
</td><td><div style="text-align: right;">
.000006</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
3</div>
</div>
</td><td><div style="text-align: right;">
1</div>
</td><td><div style="text-align: right;">
.000009</div>
</td></tr>
</tbody></table>
<br />
<div>
</div>
<br />
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<br /></div>
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
Even with a safety factor of three, a tenth of a kilogram tether (about 3 ounces) can handle a 10 tonne payload.</div>
<br />
<b>Benefits</b><br />
<br />
Escape velocity of Phobos is about 11 meters/sec or about 25 miles per hour. A small rocket burn would be needed for a soft landing. This burn could kick up dust and grains of sand, some of which could achieve orbit. This would create an annoying debris cloud.<br />
<br />
However a spacecraft could dock with a station at Mars Phobos L1 much the same way we dock with the I.S.S. Payloads could then descend the tether and arrive at Phobos without kicking up debris.<br />
<br />
It would also allow low thrust ion engines to rendezvous with Phobos.<br />
<br />
It would also serve as a foundation which can be added to.<br />
<br />
It would take a Mars Ascent Vehicle about 5 km/s to leave mars and rendezvous with this tether. Trip time would be about two hours, so the MAV could be small.<br />
<br />
From this Phobos tether, a .55 km/s burn can send drop a lander to an atmosphere grazing periapsis. Aerobraking can circularize to a low Mars orbit moving about 3.4 km/s. If Phobos is capable of providing propellent, much of that 3.4 km/s could be shed with reaction mass.<br />
<br />
In contrast, a lander coming from earth will enter Mars atmosphere at about 6 km/s. Since it takes about 14 km/s to reach this point, the lander will not have reaction mass to shed the 6 km/s. For more massive payloads like habs or power plants, shedding 6 km/s in Mars atmosphere is a difficult Entry Descent Landing (EDL) problem.<br />
<br />
<b><span style="font-size: large;">87 kilometer lower Phobos tether </span>- copper pulls it's own weight</b><br />
<b><span style="font-size: large;"><br /></span></b>
It would be nice to have power to the elevator cars. However copper only has a tensile strength of 7e7 pascals and density of 8920 kilograms per cubic meter. Have copper wire along the length of the Zylon tether would boost taper ratio. Using the spreadsheet, I set tensile strength and density to that of copper and lowered the tether foot until I got a taper ratio of 1.1. That gives a length of about 87 kilometers.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIggWg1wCvHfpf-TeqWZZMR-wvdRFOBx3X7wDOkiKVWJJp6v-5yOb4PS8OIjVLIGAFUdIlRjduGwmOEOGx58TO80l8wrm-T7kIyp2_P-WJaVva1CHfKC5g3d1VT-keXf13tW_gueqtZo-v/s1600/Phobos+87+kilometer+tether.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="110" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIggWg1wCvHfpf-TeqWZZMR-wvdRFOBx3X7wDOkiKVWJJp6v-5yOb4PS8OIjVLIGAFUdIlRjduGwmOEOGx58TO80l8wrm-T7kIyp2_P-WJaVva1CHfKC5g3d1VT-keXf13tW_gueqtZo-v/s640/Phobos+87+kilometer+tether.jpg" width="640" /></a></div>
<br />
<b>Benefits</b><br />
<br />
Along this length of the tether, copper pulls it's own weight, as well as supports the payload. A massive power source can be placed at L1 -- at L1 there are no newtons either Phobos-ward or Mars-ward. A copper only tether of this length would be about .2 times that of payload mass.<br />
<br />
Elevator cars can ascend this length without having to carry their own solar panels and battery.<br />
<br />
If descending from L1 Mars-ward, Mars' gravity can provide the acceleration and no power source is needed.<br />
<br />
Of course copper wires can be extended further but this would boost taper ratio as well as tether mass to payload mass ratio.<br />
<br />
From this tether foot, it takes .54 km/s to drop to an atmosphere grazing orbit. Trip time is about two hours.<br />
<br />
<b><span style="font-size: large;">1,400 kilometer lower Phobos tether </span>- release to an atmosphere grazing orbit</b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh__Wj5RGcTbplokD-XKAkEyiZH6-WBrvaJQgdl3Nq1TAnesTDifKC8PyWX-WY1_uldClQrSUWcEAV2K6KdPNHUiMqsht_XRM8IaRZLryHXias5XaETSTO3s-f41I2qFdMrLVyjE-YgzI-c/s1600/Phobos+1400+kilometer+tether.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="50" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh__Wj5RGcTbplokD-XKAkEyiZH6-WBrvaJQgdl3Nq1TAnesTDifKC8PyWX-WY1_uldClQrSUWcEAV2K6KdPNHUiMqsht_XRM8IaRZLryHXias5XaETSTO3s-f41I2qFdMrLVyjE-YgzI-c/s640/Phobos+1400+kilometer+tether.jpg" width="640" /></a></div>
<br />
<table><tbody>
<tr><td><div style="text-align: center;">
<b>Safety</b></div>
<div style="text-align: center;">
<b> Factor </b></div>
</td><td><div style="text-align: center;">
<b>Zylon</b></div>
<div style="text-align: center;">
<b>Taper</b></div>
<div style="text-align: center;">
<b>Ratio</b></div>
</td><td><div style="text-align: center;">
<b>Tether to</b></div>
<div style="text-align: center;">
<b>Payload</b></div>
<div style="text-align: center;">
<b> Mass Ratio </b></div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
1</div>
</div>
</td><td><div style="text-align: right;">
1.05</div>
</td><td><div style="text-align: right;">
.1</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
2</div>
</div>
</td><td><div style="text-align: right;">
1.1</div>
</td><td><div style="text-align: right;">
.21</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
3</div>
</div>
</td><td><div style="text-align: right;">
1.15</div>
</td><td><div style="text-align: right;">
.33</div>
</td></tr>
</tbody></table>
<br />
<div>
</div>
<br />
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<br /></div>
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
Even with a safety factor of three, a 1 tonne zylon elevator could handle 3 tonnes of payload.</div>
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<br /></div>
<b>Benefits</b><br />
<br />
Releasing from the foot of this tether will send a payload to within a 100 kilometers of Mars' surface. Skimming through Mars upper atmosphere each periapsis will shed velocity and lower apoapsis.<br />
<br />
Low Mars orbit velocity is about 3.5 km/s. The payload arrives at 4.1 km/s.<br />
<br />
<b><span style="font-size: large;">4,300 kilometer lower Phobos tether</span> - payload enters atmosphere at 3 km/s.</b><br />
<br />
<table><tbody>
<tr><td><div style="text-align: center;">
<b>Safety</b></div>
<div style="text-align: center;">
<b> Factor </b></div>
</td><td><div style="text-align: center;">
<b>Zylon</b></div>
<div style="text-align: center;">
<b>Taper</b></div>
<div style="text-align: center;">
<b>Ratio</b></div>
</td><td><div style="text-align: center;">
<b>Tether to</b></div>
<div style="text-align: center;">
<b>Payload</b></div>
<div style="text-align: center;">
<b> Mass Ratio </b></div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
1</div>
</div>
</td><td><div style="text-align: right;">
1.9</div>
</td><td><div style="text-align: right;">
2.6</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
2</div>
</div>
</td><td><div style="text-align: right;">
3.4</div>
</td><td><div style="text-align: right;">
8.3</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
3</div>
</div>
</td><td><div style="text-align: right;">
6.3</div>
</td><td><div style="text-align: right;">
20.4</div>
</td></tr>
</tbody></table>
<br />
<div>
</div>
<br />
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<br /></div>
<b>Benefits</b><br />
<br />
At 4,300 kilometers from Phobos, dropping a payload will have an atmospheric entry of 3 km/s, about .5 km/s less than low Mars orbit.<br />
<br />
<b><span style="font-size: large;">5800 kilometer lower Phobos tether</span> - maximum length</b><br />
<br />
Phobos orbit has an eccentricity of .0151. It bobs up and down a little. Mars' tallest mountain is about 25 kilometers tall. Given these considerations, tether can't be more than 5800 kilometers. Else the foot might crash into the top of Olympus mons.<br />
<br />
<table><tbody>
<tr><td><div style="text-align: center;">
<b>Safety</b></div>
<div style="text-align: center;">
<b> Factor </b></div>
</td><td><div style="text-align: center;">
<b>Zylon</b></div>
<div style="text-align: center;">
<b>Taper</b></div>
<div style="text-align: center;">
<b>Ratio</b></div>
</td><td><div style="text-align: center;">
<b>Tether to</b></div>
<div style="text-align: center;">
<b>Payload</b></div>
<div style="text-align: center;">
<b> Mass Ratio </b></div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
1</div>
</div>
</td><td><div style="text-align: right;">
4.4</div>
</td><td><div style="text-align: right;">
16.1</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
2</div>
</div>
</td><td><div style="text-align: right;">
19.2</div>
</td><td><div style="text-align: right;">
114</div>
</td></tr>
<tr><td><div style="text-align: right;">
<div style="text-align: center;">
3</div>
</div>
</td><td><div style="text-align: right;">
83.8</div>
</td><td><div style="text-align: right;">
638</div>
</td></tr>
</tbody></table>
<br />
<div>
</div>
<br />
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<br /></div>
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
Given a reasonable safety factor of three, it would take a nearly 640 tonne elevator to lift a one tonne payload. I don't think a Zylon elevator from Phobos to Mars' upper atmosphere is practical.</div>
<div style="-webkit-text-stroke-width: 0px; color: black; font-family: -webkit-standard; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; margin: 0px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px;">
<br /></div>
<b>Benefits</b><br />
<br />
The tether foot will be moving about .57 km/s with regard to Mars. Mars Entry, Descent and Landing (EDL) is far simpler with .57 km/s. If Phobos is a source of propellent, much of that .57 km/s can be taken care of with reaction mass.<br />
<br />
For an ascent vehicle, only a small suborbital hop is needed to rendezvous with the tether foot.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com10tag:blogger.com,1999:blog-3596550435682943926.post-47548269005432169292015-12-16T10:36:00.000-08:002020-04-13T12:50:40.936-07:00How Wolfe's tether spreadsheet works<div class="separator" style="clear: both;">
I plan to do a series of posts examining elevators and tethers. I will link to them as posts are completed:</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
<a href="http://hopsblog-hop.blogspot.com/2015/12/lower-phobos-tether.html">Lower Phobos Tether</a></div>
<div class="separator" style="clear: both;">
<a href="http://hopsblog-hop.blogspot.com/2016/01/upper-phobos-tether.html">Upper Phobos Tether</a></div>
<div class="separator" style="clear: both;">
<a href="http://hopsblog-hop.blogspot.com/2016/01/deimos-tether.html">Deimos Tether</a></div>
<div class="separator" style="clear: both;">
<a href="http://hopsblog-hop.blogspot.com/2017/06/zylon-mars-elevator.html">Mars Elevator</a></div>
<div class="separator" style="clear: both;">
<a href="http://hopsblog-hop.blogspot.com/2016/04/liftport-lunar-tether.html">Liftport Lunar Elevator through EML1</a></div>
<div class="separator" style="clear: both;">
<a href="http://hopsblog-hop.blogspot.com/2016/08/lunar-sky-hook.html">Lunar Sky Hook</a></div>
<div class="separator" style="clear: both;">
<a href="http://hopsblog-hop.blogspot.com/2016/08/tran-cislunar-railroad.html">Trans Cislunar Railroad</a></div>
<div class="separator" style="clear: both;">
LEO Rotovator</div>
<div class="separator" style="clear: both;">
Pluto Charon elevator</div>
<br />
They will be based on <a href="http://phobosorbust.blogspot.com/">Chris Wolfe</a>'s spreadsheet for modeling tethers.<br />
<br />
I'll try to explain how Wolfe's spreadsheet works.<br />
<br />
<b><span style="font-size: large;">Tensile strength</span></b><br />
<br />
Density and tensile strength are important quantities for tether material. Tensile strength is measured in pascals.<br />
<br />
A pascal is a newton per square meter, newton/(meter<sup>2</sup>). A newton is a unit of force, mass times acceleration.<br />
<br />
Zylon has a tensile strength of 580 megapascals or 580 meganewtons per square meter. On earth's surface with it's 9.8 meter/sec<sup>2</sup> acceleration, it would take a 591,836,735 kilogram mass to exert that much force. It would take a zylon cord with a cross section of one square meter to support this force. But that's more than half a million tonnes!<br />
<br />
10 tonnes is more plausible payload for space cargo. A much thinner cord could support this. Cross section of a Zylon cord need only be 1.72e-9 square meters. If a circular cross section, cord would be about 47 micrometers thick. Strands of hair can be anywhere from 17 to 181 micrometers thick.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3KYetvu9DXGlaC_NIX6D_Pab9l6rBqz1p6nXp-RPYmXfAiONwlW6jFxLejYSmodETiGBCUiM2J1seA-b0bWsZHmiQICEXavlxFdmRbfqu5h3CdZhajW3HnSryQEjQch-CtxxPI6n80CaA/s1600/10+tonne+weight.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="322" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3KYetvu9DXGlaC_NIX6D_Pab9l6rBqz1p6nXp-RPYmXfAiONwlW6jFxLejYSmodETiGBCUiM2J1seA-b0bWsZHmiQICEXavlxFdmRbfqu5h3CdZhajW3HnSryQEjQch-CtxxPI6n80CaA/s400/10+tonne+weight.jpg" width="400" /></a></div>
<br />
<br />
<i><b>So number of newtons determines tether cross sectional area</b>.</i><br />
<br />
<b><span style="font-size: large;">How many newtons?</span></b><br />
<br />
How to figure number of newtons at the tether foot? First we set maximum payload mass as well as foot station mass. The default in Wolfe's spreadsheet is a ten tonne payload mass and a foot station massing 100 kilograms. But how many newtons does this 1,100 kilogram mass exert?<br />
<br />
The net acceleration on this foot mass is acceleration from planet's gravity minus centrifugal acceleration minus moon's gravity.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5bQwa2Gvzkz536eLSsLnLQGRyY5ECBXoLI8slMbiI0G2K4bG5wQvvx5hDSfbM-IKRbRsNbjpSWAhzQ_yiecS7fUJ-xZ0lVAWXI6C-q_KrD3ZSJKFHbcNJzefAnJPTAQyD-29v1rO7iGTl/s1600/TetherSpreadsheetIllustration.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="334" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5bQwa2Gvzkz536eLSsLnLQGRyY5ECBXoLI8slMbiI0G2K4bG5wQvvx5hDSfbM-IKRbRsNbjpSWAhzQ_yiecS7fUJ-xZ0lVAWXI6C-q_KrD3ZSJKFHbcNJzefAnJPTAQyD-29v1rO7iGTl/s640/TetherSpreadsheetIllustration.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
(Click on illustration to embiggen)</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
This spreadsheet sets the origin at the planet center.</div>
<div class="separator" style="clear: both; text-align: left;">
Tether foot radius is the foot's distance from planet center.</div>
<div class="separator" style="clear: both; text-align: left;">
Barycenter radius is Orbital Radius * mass planet / (mass moon/(mass planet + mass moon)</div>
<div class="separator" style="clear: both; text-align: left;">
Tether anchor radius is Orbital Radius - Moon Radius. The tether anchor is assumed to be at the near point of a tide locked moon.</div>
<div class="separator" style="clear: both; text-align: left;">
Distance from Barycenter to Tether Foot is Tether Food Radius - Barycenter Radius.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The three force equations:</div>
<div class="separator" style="clear: both; text-align: left;">
<b>Gravity Planet</b> = G * Mplanet / Tether Foot Radius<sup>2</sup></div>
<div class="separator" style="clear: both; text-align: left;">
<b>Centrifugal Acceleration</b> = <span style="background-color: white;">ω<sup>2</sup> * Distance from Barycenter to Tether Foot. </span><span style="background-color: white;">ω is constant, it is the angular velocity of the orbit.</span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;"><b>Gravity Moon</b> = G * Mmoon / (Orbital Radius - Tether Foot Radius)<sup>2</sup></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;">Net acceleration is the sum of these three.</span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSr3zBaUEwSGMxVKq5WHRmjY5VYfvhG6FUNrIanFa9LV8_m1WDVKahU7PuPGWq5Zc65pc653lRZQ0yCXjrT9PQ-C9WH12sPRrZ1_1eNR1DTw9QfT6II3oXe25BYbtqCcYVGgCzhskE4uxB/s1600/TetherSpreadsheetIllustration2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="376" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSr3zBaUEwSGMxVKq5WHRmjY5VYfvhG6FUNrIanFa9LV8_m1WDVKahU7PuPGWq5Zc65pc653lRZQ0yCXjrT9PQ-C9WH12sPRrZ1_1eNR1DTw9QfT6II3oXe25BYbtqCcYVGgCzhskE4uxB/s640/TetherSpreadsheetIllustration2.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="background-color: white;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
An illustration of the accelerations with net acceleration in red. Moon gravity is negative because it is pulling away from the planet. Centrifugal acceleration is also pulling away from the planet except left of the barycenter it is towards the planet. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
When a curve crosses the axis the value is zero. Centrifugal crosses the axis at the barycenter. In most cases barycenter will be beneath planet surface. The illustration above has an exceptionally large moon. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Net acceleration crosses the axis at L1, at this point the three accelerations sum to zero. to the right of L1, net acceleration is towards the moon.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
To approximate the tether we chop it into many small lengths:</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtA1cgctgyEyp93tc8bwBLUg4HBC-_lFAHpIP75U2xhj7gN9E4wI43wf5b0y_uJ1bpDnHT2SCeDhO9U3IoTfCqgwgnJv1ai00y6fsKdqxk69AejBHMsCIKoo8zZexsjJ1JqaYx07QWOd_J/s1600/TetherSpreadsheetIllustration3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="532" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtA1cgctgyEyp93tc8bwBLUg4HBC-_lFAHpIP75U2xhj7gN9E4wI43wf5b0y_uJ1bpDnHT2SCeDhO9U3IoTfCqgwgnJv1ai00y6fsKdqxk69AejBHMsCIKoo8zZexsjJ1JqaYx07QWOd_J/s640/TetherSpreadsheetIllustration3.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
To find tether volume in step 1, we multiply the cross section by length of step 1. (Recall cross sectional area is set by number of newtons coming from tether foot.) Multiplying this volume by tether density gives step 1 tether mass. Multiplying this mass by net acceleration gives us the newtons this length exerts.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Adding the newtons from step 1 to payload newtons means the next step has a thicker cross section. We multiply this new cross section by tether length * tether density * net acceleration to get newtons from the tether length along step two.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
And so on.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Summing all the masses from each step gives us total tether mass.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
This is an approximation. The finer we chop the tether, the closer the approximation. The spread sheets we'll be using cut the tether length into 1,000 parts.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Our sheet can be found <a href="http://clowder.net/hop/TMI/LowerMoonTether.xls">here</a>. It is a 1.7 megabyte file.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
For an upper moon tether, anchor will be on the far side. Moon's gravity will be added instead of subtracted from planet's gravity. I'll label tether end "Tether Top" instead of "Tether Foot". Otherwise, the spread sheet will be the same as the lower moon tether spreadsheet.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<br />
<br />Hop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.com1