Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction

by Adler, Charles L.

  The total kinetic energy of the fuel burned is

  Using a mass ratio of 20, we get a net kinetic energy supplied by the fuel of 7 × 1012 J, or about 2.5 times the initial estimate. Viewed this way, the cost of gasoline holding the equivalent energy is about $200,000. Since the low Earth orbit payload mass of the shuttle is about 24,000 lb, this in principle is a cost of $8 per pound, or (since the shuttle holds seven crew members) roughly $30,000 per person. The shuttle doesn’t use gasoline, of course, but the true fuel costs are only about ten times higher, or roughly $2 million per launch. This would still only be a ticket cost of roughly $300,000 per traveler. Unfortunately, the real picture isn’t this rosy.

  6.3.3 The Current Cost of Space Travel

  According to the NASA website, a shuttle mission has a cost of about $450 million [8]. That is, the true cost of putting a payload into orbit is about 200 times higher than the cost of the fuel. This is a cost of about $19,000 per pound for the payload. I think that this is because of the enormous infrastructure which the shuttle required: support staff, maintenance and repair to the shuttle, processing costs for the fuel, and so on. Typical single-use rockets have similar costs per payload pound, although they tend to be somewhat cheaper. The Falcon-1e rocket designed by SpaceX Corporation supposedly has the current lowest cost per payload of about $9,000 per pound [13]. However, this rocket can only launch satellites; it isn’t capable of putting a person into orbit.

  If we were to use it for space tourism, the Space Shuttle held a crew of seven. This means a cost of $64 million per person simply to break even. Of course, a lot of the space on board the shuttle was taken up by experiments. If we made a true “luxury” vehicle, maybe we could increase the number of people it would holdup to fifteen. (This is a pretty liberal estimate.) This would lower the ticket cost of a shuttle flight to $30 million.

  How realistic is our estimate? Since 2001, Space Adventures has sent about seven very rich private citizens into orbit. They were launched using Soyuz rockets and stayed at the International Space Station for several days apiece. The cost was approximately U.S. $20 million, with another $15 million if participants wanted to do a space walk outside the shuttle. These numbers match pretty well our estimate of the cost per traveler using the Space Shuttle as the vehicle. When one reads about these ventures, a reason for the high infrastructure costs becomes very clear: all of the people going into space have to undergo hundreds of hours of expensive training at high-tech facilities in Russia and the United States. The personnel costs for such facilities are also high, as there are several dozen support personnel who stay on the ground for every one person going into orbit. In 2010 Space Adventures advertised a new mission: a trip around the Moon. The cost is a mere $100 million per traveler.

  There’s another potential cost for these vacations. Since 1986, fourteen Shuttle crewmembers died in two disasters that resulted in the destruction of the shuttle involved: the Challenger blew up shortly after launch on January 28, 1986, and the Columbia disintegrated on reentry into Earth’s atmosphere on February 1, 2003. This represents two fatal disasters in 135 total flights, or a roughly one in 60 chance of being killed on any given shuttle flight. The late Richard Feynman, the Nobel laureate physicist who was on the team investigating the first shuttle disaster, harshly criticized the NASA administration for grossly underestimating the dangers of such flights:

  For a successful technology, reality must take precedence over public relations, for Nature cannot be fooled. [83]

  This death rate would be absolutely unacceptable for any commercial form of transportation; the per-flight probability of being killed in an airline crash is something like one in 10 million [30]. This estimate is from a 1989 paper, but the situation hasn’t changed much in the last two decades; if anything, airplane flight has become safer. For a car crash, the death rate as of 2009 was roughly one person killed per 100 million miles driven. If we assume that the “average person” drives about 15,000 miles per year, over a 20-year period this turns into a probability of about one in 166 of being killed in a car crash [16]. This means that the danger of being killed on one flight of the shuttle was about two or three times higher than the danger of being killed in 20 years of driving. Few people are going to regularly travel into space if those are the odds, even if there were a cheap way of getting there. It remains to be seen if commercial ventures such as Space Adventures are as dangerous.

  Space travel needs to become much cheaper and much safer for it to become a common part of everyday life. Unfortunately, the two requirements are opposed: an increase in safety usually means an increase in cost, all other things being equal. Even something as simple as delaying a launch because of bad weather or a fuel leak can cost hundreds of thousands of dollars [14].

  6.4 FINANCING SPACE TRAVEL

  I’d like to summarize a few points:

  • There is an irreducible minimum energy cost in putting a rocket into orbit, namely, the kinetic energy needed to get it to orbital speed.

  • More energy than the minimum is required because you take the rocket fuel along with you, at least part of the way. This consideration leads to the rocket equation.

  • However, the total energy costs of launching people into space seem to be small compared to the net overall launch costs, probably due to infrastructure costs.

  • Over the past decade, fewer than ten people have taken self-funded orbital flights, at a cost of roughly $20 million per person.

  • Finally, the danger of traveling to orbit may be unacceptably high for any sort of commercial venture. (This last item is conjectured based on the high number of people killed in the two shuttle disasters.)

  The last three points are extremely important. In particular, when writing this chapter I found the point about costs very surprising. I had always assumed that the energy costs of spaceflight were the reason it wasn’t more common, and that if cheap enough energy were available, space travel could become cheap. At first glance, this doesn’t seem to be true. Space travel enthusiasts often allege that government bureaucracy and inefficiency kept the costs of shuttle flights high and if more commercial development of space were allowed, the costs would drop astronomically. This is an interesting point, but I am inclined to disbelieve it. Richard Feynman’s book, cited above, gives a rather detailed look at the infrastructure devoted to putting the shuttle into orbit. In particular, one section stands out: he discusses the procedures the computer programmers went through to develop codes for each launch. I quote from his appendix to the official report on the Challenger disaster:

  The software is checked very carefully in a bottom-up fashion. First, each new line of code is checked, then sections of code or modules with special functions are verified. The scope is increased step by step until the new changes are incorporated into a complete system and checked. This complete output is considered the final product, newly released. But completely independently there is an independent verification group, that takes an adversary attitude to the software development group, and tests and verifies the software as if it were a customer of the delivered product. There is additional verification in using the new programs in simulators, etc. A discovery of an error during verification testing is considered very serious, and its origin studied very carefully to avoid such mistakes in the future [83].

  This is clearly a complicated and time-consuming process: you are paying for the services of perhaps twenty highly educated professionals for several months of work for each launch. And this represents a tiny fraction of the total infrastructure needed to put the shuttle into orbit. Feynman cited this as the best aspect of the shuttle program. To bring the rest of the program to its level, presumably the infrastructure costs would need to be made even greater.

  In 2006, NASA started the Commercial Orbital Transportation Services program, which is meant to fund vendors to develop and provide “commercial delivery of crew and cargo” to the International Space Station. The program is funded at a level of $500,000,000
, or roughly the cost of one shuttle flight. Awards were made to Orbital Sciences and SpaceX Corporation to develop cargo delivery vehicles; the SpaceX Dragon could also potentially carry personnel to the station [12]. NASA awarded a $1.6 billion cargo delivery contract to SpaceX for deliveries of up to 20,000 kg each for twelve flights. This would represent a cost of about $6,700 per kg. Alternately, since the Dragon could be designed to carry up to seven passengers, meaning a cost of about $19 million per person carried. Unfortunately, this is not significantly different from the $20 million Dennis Tito paid for his jaunt.

  From these examples, the current cost of developing a manned vehicle for near Earth orbit appears to be somewhere around $500,000,000. This sort of funding is not readily available from any other source than the federal government. Let’s assume that somehow a company could develop a new reusable manned spacecraft for a cost of $100,000,000, one-fifth of our estimate; let’s also assume that it had a projected life span of ten years, with ten missions per year and ten passengers per mission. Assuming fuel costs of $1,000,000 per mission and the same for infrastructure costs (which is a liberal assumption, given the discussion above), this represents a total cost of $300,000,000 over the lifetime of the spacecraft. I used a mortgage calculator on the web to calculate that if this money were borrowed from a bank at a 5% interest rate over a ten-year loan period, the developers would have to pay back $380,000,000 ultimately. Because the craft would carry 1,000 passengers over this period, each would have to pay at least $380,000 for their trip for the developers to break even.

  It is possible that the reasoning used above is too pessimistic: the ultimate irreducible cost is that of fuel. As mentioned earlier, the total fuel costs were about $2,000,000 for a shuttle launch, or about $130,000 per person, assuming we could pack fifteen people into our redesigned-for-tourism shuttle. If we could bring these costs down by an order-of-magnitude (to where they are about the same as today’s cost of gasoline), the fuel costs would still be about $13,000 per person (call it $10,000 if we want to round off). Let’s assume that we can limit the infrastructure costs to an order of magnitude more than this value. We would then have a cost of about $130,000 for an orbital vacation (per person), at least for the ride to their “orbital hotel.” This isn’t within the price range of most people, but there are a few very expensive Earth-bound tourist vacations that cost about this much.

  But what of this orbital hotel? Is this likely to be built also? Will we ever see structures in space capable of holding large numbers of people for settlement or visitation?

  NOTES

  1. Freeman Dyson showed in a very interesting paper that if one can somehow change the ejection velocity as a function of mass ratio, we can do better than the rocket equation. This is mostly of interest at high values of the mass ratio. I recommend the paper for any readers interested in the subject [72, p. 42, boxed text]

  CHAPTER SEVEN

  SPACE COLONIES

  7.1 HABITATS IN SPACE

  In the 1930s the science fiction writer George O. Smith penned a series of stories that were subsequently collected into a book titled The Complete Venus Equilateral [222]. The stories take place on a large space station placed in the orbit of Venus. That is, it circles the Sun in the same orbit Venus follows, but located 60 degrees ahead of Venus in orbit; it is not circling Venus. The space station serves as a radio relay, shuttling messages between Earth, Venus, and Mars, and is crewed by a few hundred engineers and support staff. The stories featured the adventures of Donald Channing, the chief engineer, and his attempts to keep the station running despite interference from mad scientists, evil bureaucrats, and space pirates. They are pure space opera and a lot of fun; additionally, the Venus Equilateral station has all the features of later proposals for real structures built in space. It has a large crew, its own ecology, and artificial “gravity,” provided by rotating the structure; it is also placed in one of the Lagrange points of Venus’s orbit around the Sun.

  Communications satellites have taken away the need for a manned station, even if we establish colonies on other planets. However, there is still serious discussion of large manned space stations. The rationale for them can be summarized in a few points:

  • They can be used as platforms in orbit for assembling deep space probes, which can be launched from there at a fraction of the cost as from Earth.

  • They can be used to generate power for Earth from solar power (undiluted by Earth’s atmosphere and weather, and available 24 hours a day, 365 days a year).

  • They can be used for industries that benefit from a zero-G environment, such as the growth of large industrial crystals.

  • They can be used for industries that require extremely high-vacuum environments.

  • They could potentially be used to move heavily polluting industries off Earth and into space.

  • They could be used for space tourism, as large orbital hotels.

  • They represent the next step in humankind’s move from Earth to inhabit the cosmos.

  As in previous chapters, I’ll take a hard-nosed look at these reasons. First, however, we need to look into the science behind the station.

  7.2 O’NEILL COLONIES

  I will first describe a community of what I like to call “moderate” size; it is larger than the first model habitat, but far below the dimensions that might be built. “Island Three” is efficient enough in the use of materials that it might be built in the early years of the next century…. Within the limits of present technology, “Island Three” could have a diameter of four miles, a length of twenty miles, and a total land area of five hundred square miles, supporting a population of several million people.

  —GERARD K. O’NEILL, THE HIGH FRONTIER

  In 1977 Gerard K. O’Neill, a physicist at Princeton University, suggested that with then current technology it was possible to build permanent habitats in space with all of the comforts of life on Earth [189]. He proposed building large space stations capable of permanent habitation for thousands or even millions of people. These structures were typically spherical or cylindrical in shape and spun on their axes to provide artificial gravity for the people living inside them.

  The idea for such a structure predates him. O’Neill cites a number of predecessors, including Konstantin Tsiolkovsky and J. D. Bernal, who had similar ideas before him. The science fiction writer Arthur C. Clarke also considered Bernal an intellectual precursor, saying that Bernal’s book The World, the Flesh and the Devil was one of the most important he had ever read. However, it was O’Neill’s book that brought these ideas to the wider community, particularly as it was published shortly after the first Moon landings, when the wider human exploration of space seemed to be just around the corner.

  O’Neill’s motivations for building these space colonies are noble: on reading his book, one gets the sense of a liberal-minded man concerned for the future of the human race. He envisioned a time when the bulk of Earth’s population would live off-planet in these habitats, when heavy industry would be moved into space to prevent it polluting the Earth, when the asteroid field and the Moon were mined for raw materials. In an article in the journal Physics Today he estimated that by 2008, more than 20 million people could be living off-Earth, and that by 2060 more people could be living off-Earth than on it [188]. He calculated the sticker cost of such stations to be about $30 billion for a colony housing 10,000 people (about $100 billion in 2013 money), and that such stations could pay for themselves in 20 years’ time. His work led to several incredibly detailed NASA studies of large space colonies involving multiple designs. The first of them is the impressive Space Settlements: A Design Study, a 185-page investigation of topics as diverse as launch systems, radiation shielding, and how to plan a space-based community to avoid the psychological stresses of living in a completely artificial environment [10]. The full text of this report is available on the web, along with other studies up through 1992, the same year in which Gerard O’Neill died.

  7.
3 MATTERS OF GRAVITY

  The great realization was that a man falling off a roof would not feel his own weight.

  —ALBERT EINSTEIN

  One of the many features of life in a space station, in both science fiction and real life, is that there are essentially two realistic options: either the station is essentially gravity-free or the station is spun to provide a simulation of gravity. The third option presented in science fiction stories is some form of artificial “gravity,” a la Star Trek, but as far as anyone knows, this is impossible.

  The first option, as in real life aboard the International Space Station (ISS), is that the people in the station float around in a seemingly gravity-free way. However, why they do this is subtle, as a calculation of the acceleration of gravity on the space station shows. For a spherical planet, the acceleration of gravity at any distance r away from the center of the planet is given by the formula

  The ISS’s orbit is about 400 km (4×105 m) above the ground. Therefore, the distance from the center of the Earth is the radius of the Earth (6,400 km) plus the height of the orbit (400 km), for a grand total of r = 6, 800 km = 6.8 × 106 m. The weight of an object is equal to the acceleration of gravity multiplied by its mass (W = mg). Because the acceleration of gravity decreases with distance from the center of the planet, we expect that someone’s weight decreases as well. This is why a lot of people think that people are “weightless” on the space station: they must be far enough away from the center of the Earth that their weight drops off to nearly nothing. This is untrue. Let’s take the example of an adult male with a mass of 80 kg. On the surface of the Earth, the acceleration of gravity is 9.8 m/s2. Therefore, his weight is 80 kg × 9.8 m/s2 = 784 N. (The Newton, N, is the unit of force in the metric system; it has units of kgm/s2). If we repeat the calculation for the space station, the acceleration of gravity on board the station, using the numbers given above, is 8.7 m/s2, meaning that the 80 kg man’s weight on the station is W′ = 8.7 m/s2 × 80 kg = 694 N, or about 88% of his weight on Earth. The terms “zero-G” or “microgravity” environment to describe the station are misnomers; the correct idea is that the astronauts aboard the Space Station are in free fall.