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

by Adler, Charles L.

  10.4.3 NERVA

  Robert Heinlein’s novel Rocket Ship Galileo is about a group of Boy Scouts and their nuclear physicist mentor who build a spacecraft and go to the Moon, defeat a group of Nazi astronauts while there, and return triumphantly home. It is the first science fiction novel I know of to use the idea of a nuclear reactor to heat up and eject propellant, even though this predated the NERVA program by 20-odd years [109]. However, this idea hasn’t caught on as much as other propulsion ideas in the science fiction literature, principally because of the limitations of conventional nuclear reactors.

  The NERVA program was initiated by NASA in the 1960s to build a nuclear-powered spacecraft for a planned manned mission to Mars (scheduled to take place around 1970). A small nuclear reactor was designed as a power source for the spacecraft; the reactor heated liquid hydrogen to a temperature of 2,200 K and expelled it through a nozzle to generate thrust. The initial design showed some promise: the exhaust velocity was u ≈ 8,600 m/s, which is nearly twice the best value obtainable from rocket fuels. It also had a relatively high thrust of 73 kN. The NERVA propulsion system was also proposed as a potential engine for the Space Shuttle but was killed by post-detente cuts in NASA’s budget and a general distrust of nuclear power in the 1970s.

  The biggest issue with this type of propulsion system is that although a lot of energy is liberated in nuclear processes, it isn’t obvious how to use it. The limitations imposed on fission reactor spacecraft have more to do with materials science than with energy usage: for one thing, the energy liberation rate is limited by the melting point of the material one makes the reactor from (ultimately, the uranium alloy used as fuel). Also, the neutrons that are produced embrittle the spacecraft engine, which places limits on the energy generation rate. Finally, the method simply heats the reaction mass (the hydrogen fuel), which may not be the best way to use all of this energy. There should be a better way, a more clever design, that uses all the energy directly. NERVA represents an incremental advantage over chemical rockets because it is a relatively conservative design. The design of the propulsion system for the Orion project, however, represents a real departure from most rocket concepts.

  10.5 OLD “BANG-BANG”: THE ORION DRIVE

  The most interesting nuclear propulsion system was invented by the mathematician Stanislaw Ulam and C. J. Everett and developed by physicists Freeman Dyson and Ted Taylor in the 1950s [41] [75, pp. 22–24] [240, chap. 7] It is no longer taken seriously by anyone except science fiction writers; however, it does represent thinking big. The idea was to build a spacecraft with a big, highly shielded plate at the back and blow up a nuclear bomb behind it to push the ship forward. I swear to God I am not making this up. This was referred to euphemistically by NASA as a “nuclear pulse drive” [210]. Dyson, currently a fellow at the Institute for Advanced Study at Princeton University, thought it could be done safely, and ran a pilot program to study it. The full story is related in the books The Curve of Binding Energy, The Canoe and the Starship, and Project Orion [75][164]. Dyson is a firm believer in thinking big in science; we will examine the idea of a “Dyson sphere” (another science fiction fave) later on in this book. His idea to make Orion work was to use a sequence of small nuclear bombs to give a more or less uniform acceleration to the ship. One thing to note here: I realize that at this point I’ve discussed only nuclear fission (the power source of atomic bombs), whereas Orion would be using specially made hydrogen bombs.

  This idea has proved incredibly popular in the science fiction community. I’ve read two novels that use the idea, S.M. Stirling’s The Stone Dogs [228] and Larry Niven and Jerry Pournelle’s Footfall [187]. The Stone Dogs is set in an alternate–history present/future in which the world is divided between the United States and its allies and the Domination of the Draka, a highly advanced technological slave-owning society based in South Africa. Stirling assumes that because of the rivalry between the two, certain forms of military technology (especially developments in space) are accelerated relative to our own world. By the 1960s, nuclear pulse drives have been developed and are later used to put colonies on the Moon and settle the asteroid belt.

  In one of their patented cast-of-thousands novels, Larry Niven and Jerry Pournelle in Footfall present an Earth being invaded by aliens resembling miniature elephants. The aliens use a Bussard ramjet for propulsion, which I discuss in the next chapter. The humans in the story, led by a team of science fiction writers and fans, institute a crash program to build an Orion-type spacecraft to combat the aliens. There are many others examples of the genre. Science fiction writers (and readers) like space travel and things that go bang; combining them is almost irresistable.

  The energy released by a Hiroshima-sized nuclear bomb is about 1013 J. If this could be converted to kinetic energy, it would get our canonical 10,000 kg payload moving at a speed of about 50 km/s. Unfortunately, the energy is liberated in a few microseconds, meaning that everyone would be crushed to jelly from the high acceleration. Also, a payload as small as 10,000 kg is unrealistic for a manned vehicle. In reality, the initial studies were of payloads ranging in mass from 10 tons to about 400 tons, with mass ratios of about 10. They relied on small nuclear devices blown up at a rate of roughly one per second and an effective exhaust velocity of about 20,000 m/s, or about seven times what we’ve assumed for chemical propellants [9]. It’s pretty clear that if such a system could be made to work, then one could send fast rockets to the far corners of the Solar System, if not to the stars. You would need to launch the rocket from orbit, as the radioactive fallout is not something you want in your back yard. Three major technical issues have to be overcome in designing a spacecraft using nuclear bombs: shielding the passengers from the radiation produced in blowing up a nuclear bomb every second or so behind them; keeping the average thrust low enough so that people wouldn’t be smashed to jelly by the high acceleration; and designing a system to throw a nuclear bomb behind the ship once a second and detonate it there—a difficult design problem. According to George Dyson, the Orion team consulted the Coca-Cola Company on the bomb delivery system for the spacecraft [75, pp. 177–178]. A final problem is that getting Congress (or any agency) to fund such a program is improbable, to say the very least. This is what eventually killed the program. It is fun to think about, though; a lot of sweet design problems stem from trying to figure out how to launch spacecraft with nuclear bombs. A few are listed on the book website.

  The preliminary studies for Orion were for ships traveling to the Moon or on conventional Hohmann orbits to Mars; the pulse drives were to be turned on for only a few minutes during the two Δv boosts, and the total trip time was 450 days. However, Dyson and Taylor were ambitious: they wanted ships that could accelerate continuously, and it is clear that this is what they expected the Orion project to eventually deliver.

  In overall design, the main part of the ship rests on top of a “pusher plate” that serves both as radiation shielding and as something for the bomb to push against. A bomb is dropped behind the plate and blown up. The pusher is attached to the rest of the ship by an arrangement of springs and mass dampers that smooths out the inherently jerky nature of the acceleration.

  The overall (theoretical) performance is very impressive. The specific impulse is very high (Isp ≈103 s, or u ≈ 104 m/s or higher). This means that for typical Δv corrections of 1–10 km/s, the ratio of fuel mass to payload mass is of order one. As one might expect, thrust is also high.

  One thing unique to Orion is that there is no way to make a small spacecraft using this concept because of the difficulty of making low-yield nuclear bombs. The first design (for a Mars mission) called for a 4,000-ton (4×106 kg) spacecraft using 0.1 kT yield bombs specifically designed for the project. By comparison, the lunar landers for the Apollo missions massed about 14,000 kg. Several thousand of these bombs would be detonated during the round-trip mission. Because of the high impulse, one can also use faster orbits than the minimum-energy Hohmann transfer.

 
; The development of Orion came to a halt in the early 1960s when priority was given to the Apollo program, which used more standard chemical propulsion systems to reach the Moon. However, Orion is the only feasible high-impulse, high-thrust propulsion system studied in detail to date.

  10.6 PROSPECTS FOR INTERPLANETARY TRAVEL

  There are definite advantages to using nuclear propulsion; the effective exhaust velocities range from twice to about five to ten times what one can get by using traditional chemical propellants. They really are the only way one could envision large-scale manned interplanetary travel, in that they could cut the travel time between Earth and the other planets in the Solar System by about an order of magnitude. If one could use Orion to accelerate a spacecraft at 1 g indefinitely, one could cut the time by a factor of 100 or so.

  However, the nearest stars are thousands of times more distant than the farthest planets in the Solar System. To get to the stars we need even more energy than even Orion can provide, but for this saga, we take up the story again in the next chapter.

  CHAPTER ELEVEN

  SPECULATIVE PROPULSION SYSTEMS

  As far as we know, nothing travels faster than light. Aside from energy issues, it takes a long time to get anywhere interesting. The nearest star apart from the Sun is the triple-star system Alpha Centauri, located 4.3 light-years away. There are about 32 star systems within 15 light-years of the Sun, and roughly 600 within 100 light-years. This means it will take years to get to the nearest stars even traveling at speeds close to light. There is one saving grace: because of relativity, the trip won’t seem as long to the voyagers. However, to get to these speeds, even the Orion drive is insufficient.

  11.1 MORE SPECULATIVE PROPULSION SYSTEMS

  11.1.1 Fusion Reactors

  Fusion reactions generate energy from building up heavier nuclei from lighter ones. Again, there is net energy produced in the reaction because the reaction products are lighter than the reactants. This is the energy source inside the Sun. The reaction there is the proton-proton cycle,

  This reaction needs high densities and is relatively slow, making it unusable for Earth-based fusion applications. Most researchers concentrate on the deuterium-deuterium reaction:

  or the deuterium-tritium reaction:

  The latter process has (in principle) an energy density of 3×1014 J/kg of total fuel, or one to two orders of magnitude greater than fission processes [246]. If you used the reaction products as ejection mass for the spacecraft, you would have an exhaust velocity of about 2×107 m/s, or 20,000 km/s, roughly 7% of the speed of light. In principle, half a kilogram of this fuel could send a 1,000 kg spacecraft to the Moon. The proton-proton cycle has a higher exhaust velocity of approximately 12% of the speed of light. One tricky part is that while deuterium is pretty common, tritium is not: it is an unstable isotope with a half-life of 12 years. Even given this issue, a 1974 study of how to build a spacecraft capable of interstellar flight, Project Daedalus, fixed on a deuterium-tritium fusion reactor as the only feasible means of powering the spacecraft.

  Fusion energy can only be generated at temperatures of millions of degrees and high densities, which is why it is difficult to generate it controllably; however, if one could harness it, it would supply an essentially limitless source of power. This is why the development of controllable fusion has been something of a holy grail for physicists for the past fifty years; commercial fusion power plants would essentially solve the world’s energy problems. However, it is a holy grail in many senses: no one really has any idea how to do it, although much work has been done on the problem. As the joke goes, fusion power is always 20 years away. Needless to say, no one knows how to build a fusion-powered rocket either, although there have been suggestions on that issue as well.

  So fusion rockets are a good way to go, if we had any idea how to make them. The first study I know of on making an interstellar probe using a fusion engine was Project Daedalus in 1975. This was a serious study undertaken by a number of scientists and engineers to put together a “proof-of-principle” design for a probe capable of a flyby mission to Barnard’s star, six light-years from Earth. The speed chosen was 15% of light-speed, making it an approximately 40-year journey. There are definitely some science-fictiony aspects of the project; for example, it called for mining Jupiter for tritium for the fuel supply. This seems to be on the borderline of possible, but exactly which side is anyone’s guess.

  However, the implication of an interstellar probe like this one is that we possess an extremely energy-rich society. The cost of Project Daedalus was estimated at $10 trillion. Using the rule of thumb that prices for everything double every 20 years, the estimate comes in at about $40 trillion today, dwarfing the U.S. GDP. This amount of money is about equal to the GDP of the entire world. Energetics tell us why this is so: the total energy contained in the payload is about 10% of the total world energy usage for one year. This is too expensive for any current world civilization to undertake, and it may well be too expensive for any civilization to undertake under any circumstances.

  11.1.2 The Bussard Ramjet

  The nearest star apart from our sun, Alpha Centauri, is about 4.3 light-years away, At an average speed of 10% of the speed of light, it would take 43 years for a spacecraft to get there and the same to return, if we want it to return. This speed is possible for a fusion-powered craft; assuming the exhaust speed is as stated above, 2×107 m/s, the mass ratio isn’t too prohibitive. The spacecraft needs about 3.5 kg of fuel for every kilogram of payload if we don’t decelerate. If we do decelerate, then we need this quantity squared, or about 12 for a fuel/payload ratio; if we want it to return, then the quantity is raised to the fourth power (about 144). However, the round trip is clearly longer than any human life, and even relativistic time dilation will not help us much. Unfortunately, going much faster gets very difficult. At this point, for speeds near the speed of light, our original formula for the rocket equation doesn’t work any more, so we need to use a version that is corrected to take the special theory of relativity into account. This was first derived by Ackeret in a 1946 paper; you can find a derivation of the same formula in English in the paper “Relativistic Rocket Theory” by Bade in The American Journal of Physics [17][29]:

  The variables are:

  • u: exhaust velocity (assumed to be 2×107 m/s);

  • v: final velocity reached by the spacecraft;

  • mi: initial (payload + fuel) mass of the spacecraft;

  • mf: final (payload) mass of the spacecraft;

  • c: speed of light (3×108 m/s).

  I’ll going to define three new variables, to make life easy on us:

  • R: mass ratio mi/mf;

  • α: ratio of exhaust speed to speed of light (= u/c);

  • β: ratio of final speed to speed of light (= v/c).

  We can then solve for the mass ratio needed to get to any fraction of the speed of light:

  The issue is that nothing can go faster than the speed of light. The nonrelativistic rocket equation doesn’t take this into account; basically, as you go faster and faster, the mass ratio increases more and more, to the point that going at the speed of light would require an infinite mass ratio. Simply to get to 90% of the speed of light with the exhaust velocity given above, we would need a mass ratio of 3.9 billion.

  This clearly won’t work. So what are we to do? In 1960 the physicist Robert Bussard had an ingenious idea: “empty” space isn’t really empty. There is very thinly spread matter in interstellar space, mostly hydrogen. On average, there is about one atom per cubic centimeter in interstellar space (or about 106/m3), although in dense molecular clouds, there can be as much as 109/m3, or even much more [130, pp. 435–438]. So: en route, scoop up the material between the stars and use it as fuel [44].

  Bussard envisioned a large “scoop” or funnel of some kind extending for hundreds or even thousands of kilometers ahead of the ship, gathering and compressing the hydrogen to the point that it underwent fusion, serving as
fuel for the spacecraft. Figure 16 shows a schematic of a Bussard ramjet. This idea has proved incredibly popular in the science fiction literature as it seems to be the only plausible way, apart from matter-antimatter reactions, to get a spacecraft to travel at an appreciable fraction of the speed of light. The idea has been used by a large number of science fiction writers (including Poul Anderson in his novel Tau Zero), but it was certainly used most extensively and popularized enormously by the writer Larry Niven in his Known Space stories. Indeed, it is almost easier to list his stories that don’t use this concept. A sampling:

  • In the novel Protector, Phssthpok the Pak uses a ramjet to get from the center of the galaxy to Earth (over the course of 30,000 years). Later in the novel, the Brennan-monster and the Pak scouts use ramjets to fight their extended interstellar skirmishes [179].

  • In A Gift From Earth (and other novels and stories), it is mentioned that unmanned Bussard ramjets explore interstellar space for inhabitable planets (or, as mentioned in the novel, “inhabitable points”), which are later settled by “slowboats” carrying human settlers.

  • In the story “The Ethics of Madness,” a paranoid steals a spacecraft and kills a friend’s family using it, and is then literally chased to the ends of the universe by the other in a second ramjet.

  • In the non-Known Space novel A World out of Time, the world government known as “The State” uses revived “corpsicles” to pilot ramjets to seed potentially Earth-like planets with bacterial life in the hopes of terraforming them for settlement.1

  And this is just a sampling.

  I’m going to present a nonrelativistic analysis of the Bussard ramjet: for a fully relativistic one, see Bussard’s original paper or any of the references below.