Friday, July 22, 2016

Hildas As Cyclers

Hilda Asteroids - Red,   Sun Jupiter Trojans - Blue,   Main Belt - Green

The above image was made from screen captures of Scott Manley's beautiful animation Asteroids In Resonance With Jupiter.

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 asteroids populations so we can tell them apart.

The Sun Jupiter Trojans 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.

The Hildas 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 years periods.

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.

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.

The would be a series of regular fly bys for a Hilda Cycler

1) Main Belt to trailing Trojans — 4 years.
2) Trailing Trojans to Main Belt — 4 years.
3) Main Belt to leading Trojans — 4 years
4) Leading Trojans to Main Belt — 4 years
5) Main Belt to Sun Jupiter L3 — 4 years. But there is no asteroid population at SJL3.
6) From SJL3 to Main Belt 4 years

Then back to step 1). The cycle repeats itself.

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.

As can be seen from Manley's animation, there is a steady stream of Hildas traveling the circuit. 

Delta V

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.).

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.

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.

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.

Ways to mitigate delta V expense

Many asteroids spin about pretty fast. This plus their shallow gravity wells make them amenable to bean stalks, also known as space elevators. 

"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.

Speed of a body on an elevator is ωr where 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.

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.

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 General Guidelines for Modeling a Low Thrust Ion Spiral. In the outer Main Belt, the sun's gravity is about 1 millimeter/sec2. Sun's gravity at the Trojans is about .2 millimeters/sec2.

Jupiter's Trojans

Not much is known about Jupiter's Trojans. Japan hopes to launch a mission in the early 2020's. Another proposed mission is Lucy which would also launch in the early 2020's. 

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.

Their numbers are speculation. According to Wikipedia:

Estimates of the total number of Jupiter trojans are based on deep surveys of limited areas of the sky.[1] The L4 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 L5 swarm contains a comparable number of objects, there are more than 1 million Jupiter trojans 1 km in size or larger. For the objects brighter than absolute magnitude 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.
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 albedo of about 0.04, whereas small bodies may actually have an average albedo as high as 0.12;[16] (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 6.3 ± 1.0×104 and 3.4 ± 0.5×104 in the L4 and L5swarms, respectively. These numbers would be reduced by a factor of 2 if small Jupiter trojans are more reflective than large ones.[16]
The number of Jupiter trojans observed in the L4 swarm is slightly larger than that observed in L5. 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 L4 swarm may be slightly more stable than the L5 swarm. 
The largest Jupiter trojan is 624 Hektor, 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 albedo 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.

I'd love to see science fiction stores set on 624 Hektor.

Thursday, May 26, 2016

Rotovator help with re-entry

There are proposals for rotovators to catch payloads in low earth orbit and then throw them to higher orbits.

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.

1) Rotovator catches upper stage and payload in LEO.
2) Rotovator throws payload to higher orbit.
3) Rotovator drops upper stage into a suborbital orbit.

Step 3) accomplishes two things:

a) It restores some of the orbital momentum the tether lost in catching and tossing the payload.
b) It reduces re-entry velocity of the upper stage. Slower re-entry velocities make recovery and reuse of the upper stage less difficult.

Is this a good idea? Or another hare brained scheme? I'm tossing this out in several venues hoping knowledgeable folks will review it.

Saturday, April 16, 2016

Liftport Lunar Tether

This is the fifth in a series of posts using Chris Wolfe's spreadsheet to look at various elevators.

274,000 km Lunar Tether

This is based on the Ladder PDF written by Liftport  founder Michael Laine and Marshall Eubanks.

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.

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.

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.

Ratios earthside of EML1

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.

In addition to foot station mass of 2250 kg, I got a maximum foot payload mass of 1640 kg.

Zylon taper ratio: 1.61. Tether mass to payload mass ratio: 8.05

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.

Ratios moonside of EML1

But what sort of payload can this elevator support moonside of EML1?

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.

Tether to payload mass ratio: 161.

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.


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.

Thus lunar materials could be delivered to Low Earth Orbit (LEO) without using reaction mass.

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.

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.

Some drawbacks

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.

So in addition to carrying gripping wheels and a motor, the elevator car must carry it's own power source. Photovoltaic arrays? There are solar powered golf carts. These aren't famous for their speed. There are Tesla 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 regenerative braking. Downhill would be moonward or earthward from EML1. Movement towards EML1 would be uphill.

Batteries, solar arrays and/or regenerative brakes would boost elevator car mass and thus subtract from cargo mass.

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.

And what justifies this investment? What are the benefits of a facility at Sinus Medii?

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.

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.

Charles Radley has suggested mining He3.  I'm not holding my breath but what if we achieved fusion power? Here is John Schilling's take on fusion and lunar He3:
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.
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.
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.
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.
And no, that analysis doesn’t change significantly if we include accessible reserves or environmental impact.
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.

Other than fuel for fusion it is hard to imagine He3 markets that would justify the expense of a lunar tether and mine.

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.

But there are other possible elevators in the moon's neighborhood.

Thursday, February 11, 2016

Limits to growth, logistic vs exponential

Malthusian growth model

The Malthusian growth model sees population growth as exponential.

P(t) = Poert
P=  P(0) is the initial population size,
r = population growth rate
t = time

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.

Day 1: 1 amoeba
Day 2: 2 amoeba
Day 3: 4 amoeba
Day 4: 8 amoeba

And so on. Population doubles each day. Exponential growth is famous for starting out slow and then zooming through the roof.

On the left is exponential growth in cartesian coordinates. On the right in polar coordinates, radius doubles every circuit.

Malthus imagined a rapidly growing population consuming all their available food supply and then starving to death.

Logistic growth

Sometimes populations have suffered Malthusian disaster. More often rate of growth slows as the population approaches the limit that resources can support. This is logistic growth.

P(t) = Le-rt / (L +( e-rt - 1))

Where L is the maximum population local resources can support.

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.

What slows growth?

In Heinlein's science fiction, war limits growth. This was also the foundation idea of Niven and Pournelle's The Mote In God's Eye -- War is the inevitable result of burgeoning populations.

The Four Horsemen of Apocalypse -- plague, war, famine and death are seen as natural outcomes of uncontrolled population growth.

A declining fertility rate 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.

Bad vs worse

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.

Whether it levels off via the 4 horsemen or moderation and voluntary birth control, either option sucks.  It's disaster vs stagnation.


Above is a Johnny Robinson cartoon from the National Space Society's publication.

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.

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.

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.

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.

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.

Sunday, January 17, 2016

Fact checking Neil deGrasse Tyson

Tyson is well known for fact checking movies, comics and other pop culture stuff. Here's giving Tyson a taste of his own medicine.

A Rainbow Forms Only Broadside
To Your Line Of Sight

Neil seems to be saying the rainbow lies in a plane perpendicular with your line of sight. We'll go with that. But what does Tyson mean by "line of sight"?

A Tyson defender who goes by the name of Peef_Rimgar wrote
"... if you look it up it is defined as the straight, uninterrupted line between your eyes and something you can see. "That building is in my line of sight" doesn't mean it has to be directly right in front of me."

We'll look at Peef's definition. It includes the multitude of lines passing through the viewer's pupil and striking the retina.

Lines of sight from the edge of the rainbow to the viewers eye intersect the rainbow plane at 48º. Not perpendicular.

There is one line through the viewer's pupil that is perpendicular to the plane. The line that passes through the sun as well as the viewer's head. Also lying on this line is the shadow of the viewer's head. The shadow of the head occupies the rainbow's center. I'll call this line the center line.

Now the viewer turns his head to the right. The rainbow remains perpendicular to the center line. However now the center line lies outside of the viewer's cone of vision. In this case there are zero lines of sight perpendicular to the plane.

The rainbow does remain perpendicular to the line passing through the sun, the viewer's head and the shadow of the viewer's head. To reach the Pot of Gold, the viewer would have to detach himself from his shadow and walk to the rainbow's end. Clearly impossible. But calling this line "line of sight" is a sloppy, inaccurate label.

Blind As A Bat

This common misconception is addressed in  Christie Wilcox's Discover article Actually, Bats See Just Fine, Neil.

Tyson's trailer for The Martian

Hermes' impossible trajectory

Above is a link to Neil deGrasse Tyson's trailer for The Martian. At 1:15 of the vid, Tyson has the space ship Hermes departing from Low Earth Orbit (LEO). 124 days later he has Hermes arriving at Mars orbit (2:17 of the video).

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/s2. This acceleration is also given online:

Two millimeters per second squared would require an extremely good alpha. But it's possible future power sources will deliver more watts per kilogram. So 2 mm/s2 is only medium implausible. I'll let this slide.

Problem is, low thrust ion engines really suck at climbing in and out of planetary gravity wells. 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.

Given 2 mm/s2, the trajectory Tyson describes is flat out impossible.

A slow ride through the Van Allen belts.

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.

Tyson enjoys some notoriety for fact checking fantasies like Star Wars or The Good Dinosaur. This leaves me scratching my head. Many of the shows he fact checks make no pretense at being scientifically accurate. However The Martian was an effort at scientifically plausible hard science fiction and thus is fair game. Same goes for Tyson's trailer.

A physically impossible trajectory along with cooking the astronauts? Tyson's effort at hard science fiction isn't any better than Gravity or Interstellar.

Neil's Five Points of Lagrange Essay

The Five Points of Lagrange was a Neil deGrasse Tyson article published in the April, 2002 issue of Natural History Magazine.

A few excerpts:

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.

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.

Herman Potočnik calculated the altitude of GSO in 1928.  It's possible this altitude was calculated even earlier. Newton might have done it.

Unhackable Systems

The solution is so simple, just make unhackable systems. Oh my gosh, why didn't the cyber security folks ever think of that?

Twitchy published some good responses.

Tyson on "idiot doctors"

The first half of the video Tyson argues it's foolish to believe surviving cancer demonstrates divine intervention. I'm fine with that.

But the second half of the video is a clueless rant against idiot doctors, the American Medical Association and Pre-Med students.

So a patient lives longer than predicted. Does this make the doctor an idiot? No. Typically a doctor will give his patient statistics for people in a similar condition. If someone lives longer than the norm, 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.

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!

A more thorough fisking of this vid can be found at the Tracinski Letter. Robert Tracinski is an atheist, by the way.

The Coriolis Force

The Coriolis Force 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:
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 Invincible and Inflexible engaged the German war ships Gneisenau and Scharnhorst 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.
However the role of Coriolis correction in this battle is a an urban legend.

Arabic Star Names

In a number of vids Tyson mentions that most common star names in use are Arabic. George Bush and Star Names and Naming Rights are a couple.

George Bush

The videos start with Tyson describing a speech Bush gave shortly after the 9-11 attack. According to Tyson, Bush quotes the bible saying God named the stars in order to "distinguish we from they." "They" being Muslims.

Except that Bush never gave this post 9-11 speech. His actual 9-11 speech called Islam the religion of peace. Bush was calling for inclusion and tolerance. Exactly the opposite of the xenophobic demagogue Tyson falsely portrays.

Bush did quote scripture in his eulogy for the Space Shuttle Columbia astronauts. In no way was this eulogy a xenophobic slam against Arabs.

Hamid Al-Ghazali

In the naming rights videos Tyson likes to blame Hamid Al-Ghazali for the end of the "Islamic Golden Age". From 800 to 1100, Islamic civilization made great strides in mathematics and science. Much of the star names we use today are Arabic due to the work of Arabic astronomers in that era. According to Tyson Al-Ghazali thought mathematics was the work of the devil.

Did Al-Ghazali demonize mathematics? So far as I know, Tyson hasn't given any cites supporting this notion. But numerous historians dispute this claim. Here's a Reddit AskHistorian Thread, a blog post by Yusuf Chaudhary, and a Reddit BadHistory thread.

Tyson's name turns up often in the badhistory subreddit group.

Elaboration on Hamid al Ghazali

In the comments below Tyson back pedals from Ghazali demonizing mathematics. He writes
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.
I've been reading Ghazali's writings to get some of his statements in context. I've come to the conclusion that Ghazali does indeed discourage his followers from pursuing the discipline of mathematics. Tyson has a point. But it is wrong to say Ghazali characterized math as the work of the devil.

Five Centuries Regressed

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.

Part of the exchange: "@bobati Duude — to be clear: Being five centuries regressed in your reasoning doesn't mean we all can't still like your music."

Supposedly folks during the dark ages thought the earth was flat. Sadly Tyson is perpetuating this myth.

In the August 1991 issue of History Today Jeffrey Russel effectively argues people knew the earth was round during and before the time of Columbus.

In his comment reply (below) Tyson perpetuates the myth that knowledge of a spherical earth was lost in the "Dark Ages". Historian Tim O'Neill explains where this myth comes from. O'Neill also documents prominent scholars from that period that knew the earth was spherical.

The above links as well as more interesting reading can be found in this reddit badhistory thread on Tyson's battle with B.o.B.

No Northern Penguins
To which Sean Davis replies noting there are Galapagos Penguins.

Brick Helicopters

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.

The process is described and demonstrated at this Getting Smarter Every Day Video.

GMO = artificial selection

In this video Tyson defends genetic modification by claiming it's not different from the artificial selection humans have been practicing for millennia.

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: Genetic Modification Explained.

Are GMOs beneficial? Or are they harmful? I don't know. Here I'm not taking a position pro or con GMOs. I'm pointing out Tyson's argument conflates two different techniques.

Are there more Tyson bloopers?

I've only seen a fraction of Tyson's prolific output so I suspect I'm just scratching the surface. If readers know of more Tyson bloopers, drop me a line. The folks at The Federalist are also enthusiastic Tyson fact checkers.

Thursday, January 7, 2016

Deimos Tether

This is a fourth in a series of blog posts looking at various tethers using Chris Wolfe's model.

50 kilometer Deimos tether - minimum length to remain aloft.

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.

Zylon taper ratio is 1. Tether to payload mass ratio: about .01. A ten kilogram tether could accommodate a thousand kilogram payload.


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.

This first step could serve as a scaffolding additional tether infrastructure could be added onto.

2942 kilometer lower Deimos tether - transfer to Phobos tether

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 Upper Phobos Tether post.

Zylon taper ratio: 1.01. Tether to payload mass ratio: .04. A one tonne tether could accommodate a twenty-five tonne payload.


The idea of ion driven interplanetary vehicles excite me. The Dawn probe 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 payload.

However ion rockets have pathetic thrust. They suck at climbing in and out of planetary gravity wells.

Here Mark Adler talks about ion rocket trajectories:

The fictitious Hermes from Andy Weir's The Martian can do 2 mm/sec^2 acceleration. Due to the need for a high alpha, I regard the Hermes as medium implausible but I will go with that number.

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.

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.

To spiral down to low Mars Orbit, it'd take Hermes more than 17 days and 3 km/s. So the Deimos rendezvous says about two weeks and more than 2 km/s delta V.

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:

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.

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.

Saturday, January 2, 2016

Upper Phobos Tether

This is third in a series of posts that rely on Wolfe's model of tethers from tide locked moons. As with the Lower Phobos Tether post, I will look at possible stages of this tether examining tether to payload mass as well as benefits each stage confers.

7 kilometer upper Phobos tether - tether doesn't collapse but remains extended

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.

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.)"

937 kilometer upper Phobos tether - transfer to Deimos tether

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.

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.

Above I try to explain the math for finding the tether lengths from Deimos and Phobos.

Trip time between the two tethers is about 8 hours.

Zylon taper ratio for a 937 kilometer tether length is 1.02. Tether to payload mass ratio is .0448. Or the tether is about 1/20 the mass of the payload.

I'll look at the Deimos tether in a later post.


Easy travel between Deimos and Phobos is a benefit in itself. 

But this would be a huge help to ion driven Mars Transfer Vehicles.

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. Andy Weir's fictional Hermes spacecraft can accelerate at 2 millimeters/sec^2. 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.

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 less 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.

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.

I was very disappointed when Neil deGrasse Tyson's trailer had Hermes departing from low earth orbit and arriving in Mars' orbit 124 days later.

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.

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 EML2 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.

2345 kilometer upper Phobos tether - Mars escape

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 here. Phobos is in a nearly circular orbit. To achieve escape, the tether would need to be 2435 kilometers long.

Zylon taper ratio: 1.11. Tether to payload mass ratio: .23. A little more than 1/5 of the payload mass.


Achieve mars escape.

6155 km kilometer upper Phobos tether - To a 1 A.U. heliocentric orbit

A tether this long can fling payloads to a 1 A.U. heliocentric orbit, in other words an earth transfer orbit.

Taper ratio: 1.8. Tether to payload mass ratio 1.6. The tether mass is nearly double payload mass.


Catch/throw payload to/from earth.

7980 kilometer upper Phobos tether - to a 2.77 A.U. heliocentric orbit.

Zylon aper ratio: 2.53. Tether to payload mass ratio 3.21. A little more than triple payload mass.


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.

Even with plane change expense, this tether could be very helpful for traveling to and from The Main Belt.