CHAPTER SIX

VACATIONS IN SPACE

6.1    THE FUTURE IN SCIENCE FICTION: CHEAP, EASY SPACE TRAVEL?

The last conjectures may seem absurd to those who look still on manned space flight in terms of todays multimillion dollar productions. But … the cost and difficulty of space travel will be reduced by orders of magnitude in the decades to come.

—ARTHUR C. CLARKE, THE PROMISE OF SPACE

In an early scene in the movie 2001: A Space Odyssey, Dr. Heywood Floyd travels via a commercial (Pan Am) shuttle to a space station in orbit around the Earth. The humdrum way in which this is shown in the movie makes it clear that in the future world of 2001, such “flights” are common. This scene is almost unique among science fiction movies for actually getting the dynamics of space flight correct. Clarke’s observations from his popular 1968 book on space exploration reinforced this idea in the movie: in the future, space travel will be as easy and as common as traveling on an airplane.

This is the great theme of science fiction, one that has permeated the genre since it became a separate branch of literature. Essentially every science fiction writer between 1900 and 1980 published stories involving interplanetary travel, even those writers who weren’t primarily known for writing hard science fiction. A sampling of some well-known stories from this time period makes the point clear:

•  From the Earth to the Moon, by Jules Verne. This is not the first story of space travel (Verne was anticipated by Cyrano de Bergerac and Johann Kepler), nor is it scientifically accurate: his astronauts build a cannon to launch the spacecraft, which in reality would smash them to jelly on launch [241].

•  First Men in the Moon, by H. G. Wells. Again, this isn’t scientifically accurate: Prof. Cavour invents a metal that shields anything placed above it from gravity. Even at the time, this was known to be impossible because it violated the first law of thermodynamics: one could use such a metal to build a perpetual motion machine. Regardless, the intrepid heroes build a spacecraft made from Cavourite and travel to the Moon where they meet the insect-like Selenites living in caves beneath the surface [249].

•  Ralph 124C41+, by Hugo Gernsback. This represents the prehistory of American hard science fiction. Space travel isn’t central to the theme, but the eponymous hero travels into space at the end of the novel [91].

•  Rocket Ship Galileo, by Robert Heinlein. Heinlein is one of the best of the golden age space writers, and this book represents a wonderful blend of good writing and good science. In the book three Boy Scouts and an adult build a nuclear-powered spacecraft, anticipating the NERVA program of the 1970s. It’s still worth reading, and is one of the books that drew me into science fiction in the first place. It is also worth looking at because it exemplifies what the science fiction writers paid attention to (the science) and ignored (the enormous infrastructure costs associated with projects like this). But more on this below [109].

•  The Martian Chronicles, by Ray Bradbury. The science is unimportant to the story, but it does, of course, center on the exploration of Mars by humanity [40].

•  Ubik, by Philip K. Dick. This is a very weird novel mostly taking place in an artificially created afterlife, but the first scenes of the novel involve a trip to the Moon. The world in which the story takes place, as in most of Dick’s stories, is a near-future Earth where travel to outer space is as common as airplane travel is today, although such details are seldom important to the story. One should note that the “near future” date of Ubik was sometime in the 1980s, now thirty years past [67].

•  Neuromancer, by William Gibson. Usually thought of as the first cyberpunk novel, Neuromancer is firmly set in a world consistent with earlier science fiction expectations: the main characters travel to inhabited space stations in orbit around the Earth toward the end of the novel. Gibson is an interesting case because his earlier novels are firmly set in this milieu but his later ones essentially abandon these science fiction trappings [95].

I could cite hundreds of other examples. The entire genre was essentially considered the literature of space travel from about 1930 to 1980 and is still strongly linked to it in the popular imagination, especially in movies, TV, and other expressions of popular culture. One important point is that space travel is commonplace even in stories in which the plot doesn’t depend on it at all. Of the novels mentioned above, both Ubik and Neuromancer could easily have been written without space travel. So pervasive was the idea of space travel as a commonplace of the future that both Dick and Gibson included it in their novels as a matter of course.

Accurate depictions of the science of space travel and rocketry began to appear in science fiction stories in the 1930s and 1940s; this is probably associated with the publication of Robert Goddard’s massive paper, “A Method of Achieving Extreme Altitudes” in 1919 [98]. He was not the first to do serious scientific work on the subject—Tsiolkovsky in Russia and Oberth in Germany anticipated his work—but his work represents the first English-language publication on the applications of rocketry to space travel. In the article he derives a number of results, including the “rocket equation” I show below. The founding of the British Interplanetary Society in the early 1920s also increased popular interest in the subject and spurred further research on these ideas. Again, the thought was that in the near future, interplanetary travel, or at least travel into orbit, would be relatively common. This didn’t happen, although in the early 2000s we began to see the beginnings of space tourism, albeit for the very rich. So, what happened? Why don’t we fly to the Moon on gossamer wings today?

6.2    ORBITAL MECHANICS

We’ll begin by considering the cheapest trip into space: a flight into orbit around the Earth. There have been seven people who have booked a vacation in orbit through Space Adventures, a company devoted to space tourism; Dennis Tito in 2001 supposedly paid $20 million for a ride to the International Space Station. This is clearly far beyond the reach of the ordinary Joe or Jane, but the flight was supposed to inaugurate the era of space tourism, with prices falling and larger numbers of people heading up and out. However, there has been little progress on this front in the last decade.

At first glance it would seem that the biggest problem with traveling into space is that of energy. It takes a lot of energy to get into orbit. The cost of this energy is expensive in today’s society. So we need to ask two questions:

1. How much energy does it take to go into space? What are the costs of this energy usage?

2. Is this the limiting factor that makes space travel expensive? If not, what other factors are important?

6.3    HALFWAY TO ANYWHERE: THE ENERGETICS OF SPACEFLIGHT

Once you’re in orbit, you’re halfway to anywhere.

—ATTRIBUTED TO ROBERT A. HEINLEIN

There seems to be a common misconception that the late, great Space Shuttle could fly to the Moon if it had needed to. This idea was fostered by the heritage of the Apollo space program and an unfamiliarity with the scale of space. The shuttle orbit was typically 350 km (about 200 miles) above the surface of the planet, or less than the distance between Washington, D.C., and New York City. The distance from the center of the Earth to the Moon is some 380,000 km (about 238,000 miles), or about a thousand times greater than the highest shuttle orbit. If Earth were shrunk to the size of a basketball, the orbit of the shuttle would be about half an inch above the surface of the ball and the Moon would be about the size of a tennis ball, 30 feet away.

If the orbit is so close, why is it so hard to put the shuttle into orbit? You don’t need huge launchers to go from Washington to New York, after all. Maybe it’s because you have to go 200 miles up, instead of horizontally. This is part of the answer, but not all of it. The big reason has to do with that word “orbit.” To simply launch the shuttle 200 miles straight up would take less energy than to put it into orbit (by my calculations, about one-fourth as much). However, such a rocket would rapidly fall back to Earth because it wouldn’t have the speed to stay in orbit once there.

6.3.1 What Goes Up

People on the surface of the Earth don’t fall through the Earth because of the solidity of the ground. The ground exerts an upward force on our feet that balances the downward force of gravity. Airplanes don’t fall out of the sky because of the lift generated by the flow of air around their wings. But what keeps the shuttle up? It does have wings, but they’re only for landing at the very end of a mission. In space, as we’re told, no one can hear you scream because there’s no air, and without air there is no lift to keep the shuttle up.

What is very interesting is that nothing keeps the shuttle up. In fact, it is continually falling toward the Earth but always missing it. The orbit of the shuttle is nearly circular: we can think of the orbit as something like a stone swing on a rope by a child at play. If the rope broke, the rock would fly off at a high speed at a right angle to the rope, following Newton’s first law: if no net force acts on an object, it moves in a straight line at a constant speed. The stone flying free moves on a straight line in the direction it was just moving in before the rope broke (fig. 6.1 has a picture of the stone’s path). However, the rope constrains it to move in a circle. The shuttle is just like that stone, with the rope being the attractive force of gravity between it and Earth.

If any object (the shuttle, a stone on a rope, a car turning around a curve) moves in a circle at some speed v, it must be acted on by a force directed toward the center of the circle. The size of the force is given by

where M is the mass of the object and r is the radius of the circle. Again, the force can be anything so long as it is centrally directed (“centripetal,” in physics jargon). The force on the shuttle is the force of gravity and is given by

Here, G is a universal constant (which has the value 6.67 × 10⁻¹¹ Nm/kg² in metric units), M is the mass of the Earth (5.98 × 10²⁴ kg), and r is the distance from the shuttle to the center of the planet, which is equal to the radius of the Earth plus the height of the shuttle orbit (about 6,800 km, or 6.8 × 10⁶ m). We can combine the two equations to solve for the speed to the keep shuttle in orbit:

One should note that the speed doesn’t depend on the mass of the shuttle. Putting the numbers in, v_orbit = 7,600 m/s (7.6 km/s, or a whopping 17,000 mph). If it were any slower it would crash into the ground. Bigger speeds lead first to noncircular orbits, and eventually to the spacecraft never coming back.

The difficulty of putting the shuttle into orbit isn’t mainly how high its orbit is but how fast the shuttle is moving. The payload mass of the shuttle is about 100,000 kg (roughly 100 tons). The kinetic energy of any object moving at a speed v is given by the formula

Using this formula, the kinetic energy of the shuttle is about 3 × 10¹² J, or about 3 million MJ (megajoules). The energy density of a gallon of gasoline is roughly 100 MJ per gallon, meaning that about 30,000 gallons of gasoline contain the equivalent energy. At an average U.S. gasoline cost of $3.50 per gallon, we get a cost of about $105,000 for the amount of gasoline containing the equivalent kinetic energy. However, that isn’t the entire story.

6.3.2 The Rocket Equation

The tricky part is that a rocket burns fuel to reach such a high speed. A lot of fuel. Typically, the mass of the fuel is much more than the mass of the payload for any rocket; for example, the total liftoff mass of the shuttle orbiter plus solid rockets plus tanks is about 2,000,000 kg, or twenty times the payload mass. The reason for this is that when you burn fuel to move a spaceship, you’re moving not only the spaceship itself but also the mass of the fuel you are carrying. How rockets work is pretty straightforward and has to do with Newton’s third law that for every action there is an equal but oppositely directed reaction. To give an analogy, let’s say you are standing on a patch of frictionless ice with your little sister. You have a mass of 80 kg, she has a mass of 40 kg. She’s bugging you, so you give her a shove so that she goes flying off at a speed of 4 m/s to the right. You will find yourself moving at a speed of 2 m/s to your left. Because you exerted a force on her to push her away, she automatically exerted a force on you of exactly the same size but in the opposite direction. Because you have a great mass than she does, you end up moving more slowly than she does, but you still move.

This is how a rocket works: the engine of a rocket burns fuel. The combustion of the fuel supplies the energy to move the combustion products at high speed; the engine is designed to channel the rapidly moving gases “backward”; action and reaction dictate that the ship experiences a force that moves it forward. The fuel is characterized by an ejection speed, u, which is typically a few thousand meters per second. The ejection speed is the speed at which the burned fuel is thrown from the back of the rocket. The thrust (net force pushing the rocket forward) is then given by the product of the exhaust velocity and the rate at which fuel is being burned, which we label dm/dt. We can use Newton’s second law to write down a differential equation for the speed, v, of the rocket:

where m is the mass of the fuel + payload of the rocket at any given time and dm/dt is the rate at which the fuel is being consumed. Two points need to be made here:

1. The acceleration of the rocket isn’t constant because the mass is continually changing.

2. We are ignoring the effects of gravity on the speed of the rocket. In fact, getting to some final velocity will require more fuel than we will calculate using this equation, but the difference is relatively small in the case of the shuttle.

We can now solve the equation using elementary calculus. Assuming that the rocket started with zero speed and ended up with speed v_f, we find

Here, m_f is the total fuel mass and m_r is the mass of the rocket minus its fuel. This is the famous “rocket equation,” which should be memorized by any serious science fiction writer (or fan, for that matter). The shuttle booster rockets have an exhaust speed of about 2,600 m/s. Table 6.1 shows final speeds given various initial fuel mass to rocket mass ratios.

Note that for large fuel ratios, the rocket can travel faster than its exhaust speed. It turns out that the shuttle needs a mass ratio of 20:1 to achieve orbital speed, according to the rocket equation. This estimate is pretty accurate: the total liftoff mass is about 2 million kg, or about twenty times the mass of the orbiter. We’re off by a bit because we’ve assumed only one stage; that is, we’ve assumed that our rocket burned all of its fuel in one continuous burn, whereas the shuttle has three stages (three separate fuel burns) as it goes into orbit.¹.

Two other concepts are important for rocketry:

•  Specific impulse (I_sp): This is just the ejection speed, u, in disguise: I_sp = u/g, where g is the acceleration of gravity. I’m not sure why rocket scientists use this instead of u, but there you are.

•  Thrust (T): The net force that pushes the rocket forward, which is given by the formula

This is also essentially a materials characteristic, determined by the type of fuel you are using. Rockets are characterized by these two concepts: some rockets have high thrust but low specific impulse, like chemical propellants; low thrust but high specific impulse, like ion rockets; or high impulse, high thrust, such as the Orion propulsion system. Low-impulse, low-thrust rockets are useless for spaceflight. I mostly discuss high-thrust propulsion systems since they are the only ones capable of lifting materials from Earth into orbit.

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]