Saturday, May 29, 2021

The wrong question. Who invented calculus, Newton or Leibniz?

Science historian Thony Christie (also known as @rmathematicus) had a number of essays on the Scientopia website. Scientopia bit the dust and I thought the essays were lost. But Bryan Kelly showed me they still exist on the Wayback Machine.

This essay by Christie is one I often refer to. I copied and pasted it from the Wayback machine with Tony Christie's permission.

Ich bin ein Gastblogger II: The wrong question.

I’m an alien

I’m a legal alien

I’m an Englishman in Nürnberg1

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.

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 2nd century CE and it was first in the High Middle Ages that integration returned to European mathematics.

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 17th 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 14th 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 17th 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.

In the 14th 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 16th 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 17th 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 17th 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!

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 18th 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 19th century.

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.

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 18th 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 19th century. Einstein famous discussion of synchronicity of clocks is foreshadowed by a similar discussion in the 19th century by the operators of railway networks.  Moving from special to general relativity we have the contributions of Minkowski, Hilbert and others.

To close I have made much use of the concept of evolution in this post and anybody who regularly reads John Wilkins at Evolving Thoughts will know that the biological theory of evolution has a long history before Darwin published that book 150 plus years ago and readers of Larry Moran or the fearsome P Z Myers 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?

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 MacTutor is recommended.

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”.

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”.

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”.

“The Leibniz-Clarke Correspondence” has been edited and annotated by H.G. Alexander and anybody interested in the connections between 19th century train time tables and Einsteins Theory of Relativity should read Peter Galison’s excellent “Einstein’s Clocks and Poincare’s Maps”

If you actually read and digest all of the above then you can start writing your own blog posts on the history of calculus.

1) With apologies to Sting!

Sunday, August 25, 2019

Wish list for space video games.

Kerbal Space Program

The Kerbal Space Program has demonstrated video games can be a very effective teaching tool.

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.

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.

I'm hoping for more scientifically accurate games to make their way into pop culture.

Wish Number 1: Shotgun N-body simulations

Readers of this blog may know I'm a little obsessed with EML2 (Earth Moon Lagrange 2).

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.

The Farquhar Route

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.

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. 

Years ago Tom Powell helped me build a shotgun Java n-body sim 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.


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.

By successively narrowing buck shot from earth to EML2 I found this route 3.1 km/s route from LEO to EML2:


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.

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.

Also JAVA seems obsolete. It's very difficult for me to use my own pages any more.

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.

I would use such a tool to learn how to move between different loosely bound lunar orbits.

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?

Supposedly there are heteroclinic paths between halo orbits EML1 and EML2. A shotgun sim might help a player find these paths.

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.

Wish Number 2: Tunneling on small bodies

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.

But the entire volume is accessible for a small body.

If we could exploit the entire volume of Ceres, the dwarf planet could make Trantor look like Dogpatch.

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.

Wish Number 3: Tensile towers on small bodies

Also known as space elevators.

I'd be so happy to see a world building game use something like Wolfe's spreadsheet 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.

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 Clarke Tower from earth or Mars would need.

Besides elevators from synchronous orbits it would also be good to enable users to build from planet-moon L1 and L2 points. 

The Mars Phobos and Mars Deimos are the moon elevators I like most. But elevators from L2 or L2 are usable in any family of tide locked moons.

Various tethers enabling ZRVTOs between Saturn's moons.

A gas giant's family of moons with tethers could be a rich setting for dramatic stories.

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.

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.

Wish Number 4: Compressive towers on small bodies.

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.

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.

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.

Wish Number 5: Thermal management.

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.

Limits to population growth

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?

A good world building sim would take thermal management into account as a barrier to population growth.

Stealth

Infra red signature could make military craft visible. A topic Chung talks about in his Atomic Rockets page.

Rocket propulsion.

Nuclear power electricity generation for ion propelled rockets would generate considerable waste heat. Dumping waste heat requires big radiators which make for a poorer power source alpha. There are other heat sources that need radiators to dump waste heat. These should be counted when calculating mass requirements for a space ship.


Any other ideas?

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.






Saturday, April 6, 2019

Bridenstine's Why The Moon Matters

Back in December 29, 2016 Bridenstine made a blog post "Why The Moon Matters". Bridenstine was representative of Oklahoma at the time.

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 Wayback Machine.

Bridenstine's reasons were pretty the same arguments made by lunar scientist Paul Spudis (RIP).

I post it here for historical reference. Copying and pasting:

Jim's Blog

Why the Moon Matters

by Rep. Jim Bridenstine

f t # e
Washington, December 29, 2016 0 comments
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.”

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.



Wednesday, March 13, 2019

Orbital Mechanics Coloring Book 2nd edition



Now Available at our online store

Hopefully it will soon be available on Amazon as a Kindle book.

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.

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.

New in the second edition

Given 24 more pages I can add a lot of extra stuff. I've kept most of the original 40 pages and added:

Page 18


In the section on Kepler's 2nd Law I've added a visualization that helps show r X v 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.

Page 22


Page 22 attempts to portray my visualization that helps me remember centrifugal acceleration is ω2r.

Pages 28 and 29



Attempts to explain radians and to show circular motion is ωr where ω is angular velocity in radians.

Pages 30 to 35

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.

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:



Pages 49 - 51

Are about the Oberth Benefit and EML2



Pages 51 - 52

Are about the rocket equation and mass fractions.




Pages 53 to 63

Looks at thrust vs exhaust velocity, dynamic pressure and the need to make a rapid ascent from a planetary surface to avoid gravity loss.

Page 64

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.

Inside back cover

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.

Here is the coloring book as of  March 2020 (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.

My email is hopd at cunews dot info.






Saturday, June 30, 2018

Asteroid Day

On June 30 in 1908 the Tunguska object took out a good chunk of forest in Siberia.

In February of 2016 the United Nations approved a resolution stating

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

A good time to talk about a project on my wish list. An orbital telescope devoted to finding  asteroids.

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.

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.

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.

I was surprised and pleased to learn such a telescope had already been proposed. NEOCam. Principal Investigator Amy Mainzer.

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.

Another potential NEOCam benefit: It could inventory potential asteroids for mining companies like Planetary Resources or Deep Space Industries.

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.

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.

A few days ago Marshall Eubanks commented:

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.

I hope this changes. We need a telescope devoted to asteroid discovery.

Space Meow Boys


Sections of this long post:

1) Space Cadets
2) Space Meow Boys
3) Tom Murphy
4) James Nicoll
5) Charlie Stross
6) Opening A New Frontier Is Doable


Space Cadets


We are confined to a small, fragile planet. Being limited to a finite body of resources mean logistic growth. And we're rapidly approaching the ceiling to our logistic growth.

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.

But can we open the solar system to settlement and economic use? This is an open question in my opinion.

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.

Civil, rational arguments are worth listening to. But some discussions are long on vitriol and short on math and physics.

Tarring With A Wide Brush

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.

Physics professor Tom Murphy does this. He holds up his clueless students as examples of space enthusiasts and tars us all with the label space cadets. Judging by the stories he tells, his students are some of the stupidest people on the planet. I suspect he teaches Astronomy 101 for Liberal Arts Majors.

Science fiction writer Charles Stross and book reviewer James Nicoll also like to use the label space cadet. 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.

Wrestling With A Pig

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!



I don't mind their dirty tricks. I'll do the same.

First I'll find nay sayers clueless in math and science. My label will be Space Meow Boys.


Space Meow Boys


Tom Murphy, James Nicoll and Charlie Stross are my examples of space meow boys.




Tom Murphy


Let's look at Murphy’s blog post Stranded Resources.

Murphy correctly puts a big emphasis on delta V and Tsiolkovsky’s rocket equation. But he sucks at calculating delta V. From his blog:

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.



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. 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, . . .

I bolded Murphy’s discussion of the Earth to Mars trip. Let’s look at his delta V.

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

A first year aerospace student would cringe at Murphy’s bungled math. You don’t simply add Vescape and Vinfinity.

To get velocity of the hyperbolic orbit needed for TMI (Trans Mars Injection):

Vhyperbola = sqrt(Vescape2 + Vinfinity2)



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.

Correctly patching conics get us 17 km/s from Earth surface to Mars surface

What About The Atmosphere?

Murphy points to a penalty imposed by Earth’s atmosphere:

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).

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.

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.

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.

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.

Grab That Asteroid!

Asteroid retrieval is a notion entertained by John S. Lewis, Planetary Resources, Deep Space Industries and others. If not retrieval of an entire asteroid, then retrieval of commodities from an asteroid.

Murphy argues against this using a ridiculous straw man scenario:

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. 
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.

Four things wrong this picture.

1) Murphy hasn't heard of NEAs? There are NEAs (Near Earth Asteroids) much closer to the Earth-Moon system. The Keck Report talks about NEAs that could be parked in a loose lunar orbit for as little as .17 km/s. 2006 RH120 was temporarily captured to the earth moon system with no delta V.

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.

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 their report. They look at retrieving a 5 meter rock. Should a 5 meter rock fall earthward, it'd burn up harmlessly in the upper atmosphere.

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.

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.

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.



The fellow on the left is Tom Murphy. To the right is a self portrait.

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.


Only 3 orders of magnitude off.

Refuel In Space?

The lunar cold traps are thought to have rich deposits of water ice as well as other volatile ices. These potential propellant sources are about 2.5 km/s from EML1 and EML2.

Here's some delta V maps focusing on EML1 and EML2:



There are also asteroid folks who hope to mine water from NEAs. See this Planetary Resources video or this Deep Space Industries video. 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.

What is Murphy's argument against refueling in space?

He tells us it'd take a lot of delta V to get propellant from Jupiter or Titan.

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? 
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.

No shit, Sherlock. Knock yourself out beating up this straw man.


Tom Murphy's argument is perhaps the stupidest straw man ever.

Momentum Exchange Tethers

In the comments section for Stranded Resources, Monte Davis writes:

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.

Murphy replies to Davis:

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.

Momentum isn't thrown away. It's exchanged.

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.

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.

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.

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.

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.

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.


James Nicoll


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 More Words Deeper Hole.

Apparently the subject line I was going to use is offensive so I will go with "halfway to anywhere" 
james_nicoll
april 1st, 2012 
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. 
Further, suppose
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.


How would you go about adapting a vehicle designed to do the LEO-LLO trip to a LLO-Mars trip? 
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. 
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.

Delta V

Let's start with James' delta V budget.

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.

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.

4.1 + .7 = 4.8, not 8.



A direct route from LEO to LLO would be more like 4 km/s.

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.

Aerobraking

James stipulates

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.

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?

Maybe he's heard Mars folks say LEO to Mars is less delta V than LEO to the moon. Which is true enough if aerobraking is used. 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.

Hohmann Launch windows

Here's the biggest howler:

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.

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.

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.

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.

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.


Charlie Stross


Charlie Stross was one of the participants in the Nicoll post I just fisked. In that forum he goes by the handle autopope.  Nicoll’s lack of math and science savvy was not noticed by Stross or most of those commenting.

Stross was also crowing that physics professor Tom Murphy shared his opinions, as if that validates his views.

But we shouldn’t condemn Stross because of the company he keeps. Instead, let’s look at his High Frontier Redux.

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.

To show the Kuiper Belt is forever beyond reach, Stross needs to demonstrate intermediate destinations aren’t within reach.

Later he does argue against colonizing neighboring bodies. But starting off with the most difficult, furthest destinations is wasting the reader’s time.

Let’s look at Stross’ argument against developing the moon:

What about our own solar system? 
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. 
But when we start examining the prospects for interplanetary colonization things turn gloomy again. 
Bluntly, we're not going to get there by rocket ship. 
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. 
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 ... 
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.

In Situ Resources

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 in situ resources. 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.

Stross acknowledges that robots could establish infrastructure on the lunar surface. And in fact this is what Spudis and Lavoie advocate.

In Situ Resources and Delta V

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.

Mass propellant / mass payload = e(delta V/Vexhaust) - 1.

Exhaust velocity of hydrogen/oxygen bipropellant is about 4.4 km/s. Now 3/4.4 is very close to ln(2).

That means when using oxygen/hydrogen, every 3 km/s added to the delta V budget doubles over all mass.

Starting with 1 tonne rocket dry mass plus payload,
For 3 km/s you’d need 1 tonne propellant.
For 6 km/s you’d need 3 tonnes propellant.
For 9 km/s you’d need 7 tonnes propellant.
And so on.

Overall mass grows exponentially with increasing delta V. The legend of Paal Paysam 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:



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:


We can start back to 1 grain of rice at each propellant depot.
Mount Everest is visible in this version, no longer covered with rice.


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.

If the ship could refuel in LEO, that would cut GLOW (Gross Lift Off Weight) four fold.

Here’s a delta V map focusing on EML2 and LEO. Moon to LEO is about 3 km/s using aerobraking.




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.

Also with delta V budgets on the order of 4 km/s, inter orbital vehicles can devote a higher mass fraction 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.


A racing bike vs a mountain bike.
With a racing bike we want to minimize mass.
But a racing bike is fragile while a mountain bike is durable and rugged.
When an upper stage has a 4% dry mass fraction, durability is not an option.

Elon Musk and Jeff Bezos seem well on their way to developing economical, reusable booster stages. Bezos wants to help establish lunar propellant mines. 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.

Space Elevators

Stross mentions the possibility of Space Elevators.

Arthur C. Clarke popularized the notion with his novel Fountains of Paradise. 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.

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.

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:



See this Space Stack Exchange discussion on orbital debris.

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.

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.

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 Trans Cislunar Railroad. 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.

Orbital tethers could also be anchored on Phobos and Deimos.

Given tethers of modest mass, payloads can be exchanged between Phobos and Deimos via a Zero Relative Velocity Transfer Orbit (ZRVTO).



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).

An upper Phobos tether capable of launching payloads to various regions of our solar system needn't be that massive.



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.

Summary of Stross' Errors

Stross gives us numbers assuming all propellant and hab mass comes from earth's surface.

Using in situ resources most of the hab mass can be made from materials at hand.

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.

Momentum exchange tethers are doable. This would further reduce energy and propellant needed to travel between space destinations.


Opening A New Frontier Is Doable


It is possible to establish infrastructure that would greatly reduce the cost of traveling about in space.

Yes, it would be expensive but it is doable. Dennis Wingo's book Moonrush documents several examples of government/private enterprise partnerships establishing massive transportation and communication infrastructure. The trans continental railroad was such a collaboration.

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.

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.

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.

Once robots have established infrastructure to extract propellant and keep humans alive, the cost of human presence plummets.

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.  Bill Maher makes the same argument.

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.

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.

Musk and Bezos are doing more for a sustainable future than a million space meow boys.