Saturday, November 5, 2022

You Won't Get To Mars That Way

Making predictions is hard - especially about the future.
- Ancient Internet Saying

Elon Musk has been much in the news lately.  Elon is purported to be the richest man on earth, and his corps of public-relations spin doctors present him as a man whose wealth is largely self-made.  Like Stephen Wolfram, Musk talks much about his supposed "genius."  Not only does Musk appear to be a "cerebral narcissist," but he also appears to be a "somatic narcissist" as well, based on the fact that he posted pictures of himself fighting a sumo wrestler and that he challenged Vladimir Putin to a fight.  When people make such grandiose claims as his, it's only natural for objective observers to want to put such claims to the test.  I'd like to consider myself such an objective observer (although some may disagree).  Today's post will examine the claims of Musk through my particular lens, and will try to show Musk as a typical case of a certain symptom of late capitalism.  Note: I am not interested in Musk's claim to be a bad sumo-wrestling dude.  Maybe he can sort that out with other contestants on some American "reality TV" show.

First, let's consider Musk the late-capitalism phenomenon.  To me he seems to represent the kind of "hero" who would have been quite at home in an Ayn Rand novel such as Atlas Shrugged.  That is to say, he is a poster child for the assertion by many of the wealthiest members of the Right that transcendent projects of human endeavor are best handled by heroes who have enormous wealth and not by governments or the collective efforts of societies.  Such assertions are the basis for claims that privatizing of government services leads to better service for the citizens who depend on those services.  Of course, the actual track record of privatization is horrible, and includes people whose houses have burned down because they could not afford the services of privatized fire departments.  Other notable side effects of privatization include the monstrous expansion of the private prison industry as well as the creation of professional mercenary corporations like Blackwater.  

Those who promote the benefits of privatization claim that it saves public funds.  Yet these are often the recipients of massive corporate welfare payments to rich people, also known as government subsidies.  In this, Elon Musk is no exception.  Musk started life with massive advantages already in place, as he is the wealthy son of a white South African family which built its wealth by means of the apartheid regime during its existence in South Africa.  And the companies which Musk has founded since he came to the United States have all been the recipients of corporate welfare, as documented in the following articles:
It is an open question whether most of Musk's business ventures would have survived without subsidies and other corporate welfare.  This is particularly true of Tesla.

Now among the claims which Musk has made, one of his most spectacular is that he will boldly take mankind where no man has gone before.  This claim also includes the claim that he, a private individual with enormous wealth, will manage this feat even though the space agencies of various governments have not managed to do this.  Therefore his claim goes beyond merely putting people into space.  It also transcends merely going to the moon.  Nay, it reaches even to the planet Mars.  It is this particular claim which I'd like to examine in more detail.

First, a bit of background about space travel.  To send a spacecraft from Earth to anywhere else, one must provide that spacecraft with a certain amount of kinetic energy.  That kinetic energy is given by the equation 

Kinetic Energy = 0.5 x (spacecraft mass) x (spacecraft velocity squared)

At a minimum, this amount of kinetic energy must be greater than the potential energy represented by the distance from your target to the surface of the Earth (and to a much lesser extent, the surface of the Sun since the sun is much farther away).  Potential energy represents the energy you must supply to an object to raise it a certain distance above the surface of a body that produces a gravitational field.  If Mars was stationary with respect to the Earth, then in order to reach Mars you would need to supply only the minimum kinetic energy required to equal the difference in potential energy of the gravitational field of the Earth and Sun at the position of Mars relative to the Earth's surface.  But it would take you a really long time to get to Mars!  

However, Mars is not stationary, but moving in its own orbit around the sun.  So your spacecraft must have additional velocity in order to catch up with Mars and enter into orbit around it.  Supplying the energy to move from a moving Earth to a moving Mars is an expensive proposition.  If we therefore wanted to supply only the minimum energy required for such a trip, we'd need to inject our spacecraft into what is known as a Hohmann transfer orbit.  A trip from Earth to Mars using a Hohmann orbit would take 259 days, according to the NASA source in the preceding link.  So a manned mission to Mars would require a spacecraft capable of keeping at least four people alive for nearly ten months - unless you wanted to bring those people alive and safe back to Earth again after their mission to Mars was completed, in which case your mission would require another 259 days, plus the time required for the Earth and Mars to align in such a way that a Hohmann transfer from Mars to Earth would be successful.  We're talking about a mission that could last over three and a half years.

That's a lot of time, and thus a manned spacecraft would require extensive life-support systems on the same order of magnitude as the systems on the International Space Station.  But there are two further wrinkles: first, the effects of prolonged weightlessness on human bodies, and second, the fact that astronauts would need to be shielded from lethal radiation from both cosmic rays and solar storms.  It is well-known by now that prolonged weightlessness produces harmful changes in human bodies (see this, this, and this, for instance), so missions that use Hohmann transfers might need some means of exposing humans to near-Earth gravity on a daily basis.  This would require centrifuges, which would add mass to the spacecraft.  Radiation shielding would also add mass.

So let's talk about mass.  The International Space Station has a mass of 450 tons and can support seven astronauts.  But the ISS is also regularly resupplied from Earth.  Let's optimistically assume that a crew of four astronauts would need a spacecraft with a mass of 200 tons for a Mars mission.  How much fuel would it take to get them to Mars?  The answer to that question is found in the rocket equation, namely

Wet mass (that is, rocket + fuel) = rocket mass x exp((change in velocity)/(exhaust velocity))

So for a rocket that had a 200-ton payload and that needed to change its velocity by an amount needed for a Hohmann orbit, we could calculate the fuel required.  I leave that exercise to you, although I will give you the escape velocity of the earth: 11.2 kilometers (or 7 miles) per second.  I'll also give you another hint: Elon Musk has focused on rockets which burn a mixture of liquid methane and liquid oxygen.  An optimistic exhaust velocity for such a mix is 3,780 meters per second according to one source.  If you do the math (which I don't have time to do now, but which I may get around to in the next week), you will see what a sizable amount of chemical propellant is required to get your spacecraft to Mars.  And we haven't begun to discuss how to get it back to Earth again!  To get a glimpse of how someone else solved the rocket equation, consider Expedition Mars by Martin J.L. Turner.  He calculated that a spacecraft with a mass of 145 tons would need a total fuel mass of 5,000 tons.  That's 10 million pounds of fuel.  And that's just to get to Mars.  It would take another 400 tons of fuel to return to Earth.

Now you can travel faster than the minimum required velocity for a Hohmann transfer, but that will require more fuel, and the fuel requirement increases exponentially the faster you want to go.  If you switch from chemical rockets to rockets powered by nuclear fission, it is possible to save a significant amount of reaction mass.  But worldwide rates of extraction of naturally occurring fission fuel have already peaked, according to the German Energy Watch Group.  Making artificial fission fuel in breeder reactors has never yet been commercially viable, although the process has been used to create small amounts of plutonium.  But breeder reactors don't last long, as they suffer from neutron embrittlement.  Building a fleet of fission-powered manned spacecraft might therefore not have much of a future.  So Musk might barely be able to send a few people to Mars (although he might bankrupt himself in the process), but it appears that neither he nor anyone else has the ability to establish a colony there.  Speaking of colonies, the colonists would likely need to carry soil or expensive chemical processing apparatus from Earth to Mars if they wanted to live there long-term.  The ground on Mars is toxic to Earth-based plants.  So forget about becoming a Martian farmer.  And Mars has no free oxygen or natural shielding from cosmic rays or radiation from solar flares.  It would be a really hard place to try to colonize.

And Musk's boast has been that he will establish a colony there.  Musk's boast about Mars thus appears to be a boast without much basis in fact.  It may be that during the last ten years we have developed the ability to send a 150-ton or 200-ton spacecraft to Mars - but the journey would have been prohibitively expensive even for governments, let alone individuals, which is why no government has done it.  I think putting humans in such a craft and bringing them back again alive is still beyond our capability.  Making such a mission pay benefits that are worth the expense is even farther beyond our capability.  The challenges of such a journey appear to place a limit on the modern myth of the uber-wealthy hyper-capitalist self-made hero.  These challenges demonstrate once again that there are challenges beyond the powers of any individual, challenges which can only be met by the collective response of societies.  Such a conclusion may cause some of Elon's flying monkeys to choke a bit - but such is life.  As for me, I don't think he, much less "we", will be going to Mars anytime soon.  Maybe Musk would be better off wrestling Putin.

P.S. For more information on the life-support challenges of a manned mission to Mars, please see "Red risks for a journey to the red planet: The highest priority human health risks for a mission to Mars," Nature, November 2020.

P.P.S Today's post is an example of the kind of post that I can currently write with only a modest amount of pain and suffering, since I already have a fairly large background knowledge of the subject and therefore I don't need to do as much research.  I still owe readers some posts which I promised over a year ago, but those posts will involve high levels of pain and suffering, due to the large amount of research and analysis involved.  Just saying that I haven't forgotten...  Also, I'm really irked by the way so many websites that present technical information have dumbed down their content over the last several years.  (See this for instance.)  Their coverage of many topics has collapsed into mere titillating "soundbytes" full of cute pictures and sometimes baseless hype, and their web pages are now full of paid ads, which reduces one's ability to take them seriously.  This is a crying shame.
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