Physics of the Impossible

by Michio Kaku

  On paper a mammoth light sail might be able to travel as fast as half the speed of light. It would take such a solar sail only eight years or so to reach the nearby stars. The advantage of such a propulsion system is that it could use off-the-shelf technology. No new laws of physics would have to be discovered to create such a solar sail. But the main problems are economic and technical. The engineering problems in creating a sail hundreds of miles across, energized by thousands of powerful laser beams placed on the moon, are formidable, requiring a technology that may be a century in the future. (One problem with the interstellar solar sail is coming back. One would have to create a second battery of laser beams on a distant moon to propel the vessel back to Earth. Or perhaps the ship could swing rapidly around a star, using it like a slingshot to get enough speed for the return voyage. Then lasers on the moon would be used to decelerate the sail so it could land on the Earth.)

  RAMJET FUSION

  My own favorite candidate for getting us to the stars is the ramjet fusion engine. There is an abundance of hydrogen in the universe, so a ramjet engine could scoop hydrogen as it traveled in outer space, essentially giving it an inexhaustible source of rocket fuel. Once the hydrogen was collected it would then be heated to millions of degrees, hot enough so that the hydrogen would fuse, releasing the energy of a thermonuclear reaction.

  The ramjet fusion engine was proposed by physicist Robert W. Bussard in 1960 and later popularized by Carl Sagan. Bussard calculated that a ramjet engine weighing about 1,000 tons might theoretically be able to maintain a steady thrust of 1 g of force, that is, comparable to standing on the surface of the Earth. If the ramjet engine could maintain a 1 g acceleration for one year, it would reach 77 percent of the velocity of light, sufficient to make interstellar travel a serious possibility.

  The requirements for the ramjet fusion engine are easy to compute. First, we know the average density of hydrogen gas throughout the universe. We also can calculate roughly how much hydrogen gas must be burned in order to attain 1 g accelerations. That calculation, in turn, determines how big the “scoop” must be in order to gather hydrogen gas. With a few reasonable assumptions, one can show that you would need a scoop that is about 160 kilometers in diameter. Although creating a scoop of this size would be prohibitive on Earth, building it in outer space poses fewer problems because of weightlessness.

  In principle the ramjet engine could propel itself indefinitely, ultimately reaching distant star systems in the galaxy. Since time slows down inside the rocket, according to Einstein, it might be possible to reach astronomical distances without resorting to putting the crew into suspended animation. After accelerating at 1 g for eleven years, according to clocks inside the starship, the spacecraft would reach the Pleiades star cluster, which is 400 light-years away. In twenty-three years it would reach the Andromeda galaxy, which is 2 million light-years from Earth. In theory, the spacecraft might be able to reach the limit of the visible universe within the lifetime of a crew member (although billions of years might have passed on the Earth).

  One key uncertainty is the fusion reaction. The ITER fusion reactor, scheduled to be built in the south of France, combines two rare forms of hydrogen (deuterium and tritium) in order to extract energy. In outer space, however, the most abundant form of hydrogen consists of a single proton surrounded by an electron. The ramjet fusion engine would therefore have to exploit the proton-proton fusion reaction. Although the deuterium/tritium fusion process has been studied for decades by physicists, the proton-proton fusion process is less well understood, is more difficult to achieve, and yields far less power. So mastering the more difficult proton-proton reaction will be a technical challenge in the coming decades. (Some engineers, in addition, have questioned whether the ramjet engine could overcome drag effects as it approaches the speed of light.)

  Until the physics and economics of proton-proton fusion are worked out, it is difficult to make accurate estimates as to the ramjet’s feasibility. But this design is on the short list of possible candidates for any mission contemplated to the stars.

  NUCLEAR ELECTRIC ROCKET

  In 1956 the U.S. Atomic Energy Commission (AEC) began to look at nuclear rockets seriously under Project Rover. In theory, a nuclear fission reactor would be used to heat up gases like hydrogen to extreme temperatures, and then these gases would be ejected out one end of the rocket, creating thrust.

  Because of the danger of an explosion in the Earth’s atmosphere involving toxic nuclear fuel, early versions of nuclear rocket engines were placed horizontally on railroad tracks, where the performance of the rocket could be carefully monitored. The first nuclear rocket engine to be tested under Project Rover was the Kiwi 1 in 1959 (aptly named after the Australian flightless bird). In the 1960s NASA joined with the AEC to create the Nuclear Engine for Rocket Vehicle Applications (NERVA), which was the first nuclear rocket to be tested vertically, rather than horizontally. In 1968 this nuclear rocket was test-fired in a downward position.

  The results of this research have been mixed. The rockets were very complicated and often misfired. The intense vibrations of the nuclear engine often cracked the fuel bundles, causing the ship to break apart. Corrosion due to burning hydrogen at high temperatures was also a persistent problem. The nuclear rocket program was finally closed in 1972.

  (These atomic rockets had yet another problem: the danger of a runaway nuclear reaction, as in a small atomic bomb. Although commercial nuclear power plants today run on diluted nuclear fuel and cannot explode like a Hiroshima bomb, these atomic rockets, in order to create maximum thrust, operated on highly enriched uranium and hence could explode in a chain reaction, creating a tiny nuclear detonation. When the nuclear rocket program was about to be retired, scientists decided to perform one last test. They decided to blow up a rocket, like a small atomic bomb. They removed the control rods [which keep the nuclear reaction in check]. The reactor went super-critical and blew up in a fiery ball of flames. This spectacular demise of the nuclear rocket program was even captured on film. The Russians were not pleased. They considered this stunt to be a violation of the Limited Test Ban Treaty, which banned above-ground detonations of nuclear bombs.)

  Over the years the military has periodically revisited the nuclear rocket. One secret project was called the Timberwind nuclear rocket; it was part of the military’s Star Wars project in the 1980s. (It was abandoned after details of its existence were released by the Federation of American Scientists.)

  The main concern about the nuclear fission rocket is safety. Even fifty years into the space age, chemical booster rockets undergo catastrophic failure about 1 percent of the time. (The two failures of the Challenger and Columbia Space Shuttles, tragically killing fourteen astronauts, further confirmed this failure rate.)

  Nonetheless, in the past few years NASA has resumed research on the nuclear rocket for the first time since the NERVA program of the 1960s. In 2003 NASA christened a new project, Prometheus, named for the Greek god who gave fire to humanity. In 2005 Prometheus was funded at $430 million, although that funding was significantly cut to $100 million in 2006. The project’s future is unclear.

  NUCLEAR PULSED ROCKETS

  Another distant possibility is to use a series of mini-nuclear bombs to propel a starship. In Project Orion, mini-atomic bombs were to be ejected out the back of the rocket in sequence, so that the spacecraft would “ride” on the shock waves created by these mini-hydrogen bombs. On paper such a design could take a spacecraft close to the speed of light. Originally conceived in 1947 by Stanislaw Ulam, who helped to design the first hydrogen bombs, the idea was further developed by Ted Taylor (one of the chief designers of nuclear warheads for the U.S. military) and physicist Freeman Dyson of the Institute for Advanced Study at Princeton.

  In the late 1950s and 1960s elaborate calculations were made for this interstellar rocket. It was estimated that such a starship could make it to Pluto and back within a year, with a top cruising velocity of 10 percent the speed of
light. But even at that speed it would take about forty-four years to reach the nearest star. Scientists have speculated that a space ark powered by such a rocket would have to cruise for centuries, with a multigenerational crew whose offspring would be born and spend all their lives on the space ark, in order that their descendants could reach the nearby stars.

  In 1959 General Atomics issued a report estimating the size of an Orion spacecraft. The largest version, called the super Orion, would weigh 8 million tons, have a diameter of 400 meters, and be energized by over 1,000 hydrogen bombs.

  But one major problem with the project was the possibility of contamination via nuclear fallout during launch. Dyson estimated that the nuclear fallout from each launch could cause fatal cancers in ten people. In addition, the electromagnetic pulse (EMP) for such a launch would be so great that it could cause massive short circuits in neighboring electrical systems.

  The signing of the Limited Test Ban Treaty in 1963 sounded the death knell of the project. Eventually the main driving force pushing the project, nuclear bomb designer Ted Taylor, gave up. (He once confided to me that he finally became disillusioned with the project when he realized that the physics behind mini-nuclear bombs could also be used by terrorists to create portable nuclear bombs. Although the project was canceled because it was deemed too dangerous, its namesake lives on in the Orion spacecraft, which NASA has chosen to replace the Space Shuttle in 2010.)

  The concept of a nuclear-fired rocket was briefly resurrected by the British Interplanetary Society from 1973 to 1978, with Project Daedalus, a preliminary study to see if an unmanned starship could be built that could reach the Barnard’s Star, 5.9 light-years from Earth. (Barnard’s Star was chosen because it was conjectured that it might have a planet. Since then astronomers Jill Tarter and Margaret Turnbull have compiled a list of 17,129 nearby stars that could have planets supporting life. The most promising candidate is Epsilon Indi A, 11.8 light-years away.)

  The rocket ship planned for Project Daedalus was so huge that it would have had to be constructed in outer space. It would weigh 54,000 tons, nearly all of its weight in rocket fuel, and could attain 7.1 percent of the speed of light with a payload of 450 tons. Unlike Project Orion, which used tiny fission bombs, Project Daedalus would use mini-hydrogen bombs with a deuterium/helium-3 mixture ignited by electron beams. Because of the formidable technical problems facing it, as well as concerns over its nuclear propulsion system, Project Daedalus was also shelved indefinitely.

  SPECIFIC IMPULSE AND ENGINE EFFICIENCY

  Engineers sometimes speak of “specific impulse,” which enables us to rank the efficiency of various engine designs. “Specific impulse” is defined as the change in momentum per unit mass of propellant. Hence the more efficient the engine, the less fuel is necessary to boost a rocket into space. Momentum, in turn, is the product of the force acting over a period of time. Chemical rockets, although they have very large thrust, operate for only a few minutes, and hence have a very low specific impulse. Ion engines, because they can operate for years, can have high specific impulse with very low thrust.

  Specific impulse is measured in seconds. A typical chemical rocket might have a specific impulse of 400–500 seconds. The specific impulse of the Space Shuttle engine is 453 seconds. (The highest specific impulse ever achieved for a chemical rocket was 542 seconds, using a propellant mixture of hydrogen, lithium, and fluorine.) The thruster for the Smart 1 ion engine had a specific impulse of 1,640 seconds. And the nuclear rocket attained specific impulses of 850 seconds.

  The maximum possible specific impulse would be a rocket that could attain the speed of light. It would have a specific impulse of about 30 million. Following is a table showing the specific impulses of different kinds of rocket engines.

  TYPE OF ROCKET ENGINE

  SPECIFIC IMPULSE

  Solid fuel rocket

  250

  Liquid fuel rocket

  450

  Ion engine

  3,000

  VASIMR plasma engine

  1,000 to 30,000

  Nuclear fission rocket

  800 to 1,000

  Nuclear fusion rocket

  2,500 to 200,000

  Nuclear pulsed rocket

  10,000 to 1 million

  Antimatter rocket

  1 million to 10 million

  (In principle, laser sails and ram-jet engines, because they contain no rocket propellant at all, have infinite specific impulse, although they have problems of their own.)

  SPACE ELEVATORS

  One severe objection to many of these rocket designs is that they are so mammoth and heavy that they could never be built on the Earth. That is why some scientists have proposed building them in outer space, where weightlessness would make it possible for astronauts to lift impossibly heavy objects with ease. But critics today point out the prohibitive costs of assembly in outer space. The International Space Station, for example, will require upwards of one hundred launches of shuttle missions for complete assembly and costs have escalated to $100 billion. It is the most expensive scientific project in history. Building an interstellar space sail or ramjet scoop in outer space would cost many times that amount.

  But as science fiction writer Robert Heinlein was fond of saying, if you can make it to 160 kilometers above the Earth, you are halfway to anywhere in the solar system. That is because the first 160 kilometers of any launch, when the rocket is struggling to escape the Earth’s gravity, cost by far the most. After that a rocket ship can almost coast to Pluto and beyond.

  One way to reduce costs drastically in the future would be to develop a space elevator. The idea of climbing a rope to heaven is an old one, for example, as in the fairy tale “Jack and the Beanstalk,” but it might become a reality if the rope could be sent far into space. Then the centrifugal force of the Earth’s rotation would be enough to nullify the force of gravity, so the rope would never fall. The rope would magically rise vertically into the air and disappear into the clouds. (Think of a ball spinning on a string. The ball seems to defy gravity, because the centrifugal force pushes it away from the center of rotation. In the same way, a very long rope would be suspended in air because of the spinning of the Earth.) Nothing would be needed to hold up the rope except the spin of the Earth. A person could theoretically climb the rope and ascend into space. We sometimes give the undergraduates taking physics courses at City University of New York the problem of calculating the tension on such a rope. It is easy to show that the tension on the rope would be enough to snap even a steel cable, which is why building a space elevator has long been considered to be impossible.

  The first scientist to seriously study the space elevator was Russian visionary scientist Konstantin Tsiolkovsky. In 1895, inspired by the Eiffel Tower, he envisioned a tower that would ascend into space, connecting the Earth to a “celestial castle” in space. It would be built bottom-up, starting on Earth, and engineers would slowly extend the space elevator to the heavens.

  In 1957 Russian scientist Yuri Artsutanov proposed a new solution, that the space elevator be built in reverse order, top-down, starting from outer space. He envisioned a satellite in a geostationary orbit 36,000 miles in space, where it would appear to be stationary, and from which one would drop a cable down to Earth. Then the cable would be anchored to the ground. But the tether for a space elevator would have to be able to withstand roughly 60–100 gigapascals (gpa) of tension. Steel breaks at about 2 gpa, making the idea beyond reach.

  The idea of a space elevator reached a much wider audience with the publication of Arthur C. Clarke’s 1979 novel, The Fountains of Paradise, and Robert Heinlein’s 1982 novel, Friday. But without any further progress, the idea languished.

  The equation changed significantly when carbon nanotubes were developed by chemists. Interest was suddenly sparked by the work of Sumio Iijima of Nippon Electric in 1991 (although evidence for carbon nanotubes actually dates back to the 1950s, a fact that was ignored at the time). Remarkably, nano
tubes are much stronger than steel cables, but also much lighter. In fact, they exceed the strength necessary to maintain a space elevator. Scientists believe a carbon nanotube fiber could withstand 120 gpa of pressure, which is comfortably above the breaking point. This discovery has rekindled attempts to create a space elevator.

  In 1999 a NASA study gave serious consideration to the space elevator, envisioning a ribbon, about 1 meter wide and about 47,000 kilometers long, capable of transporting about 15 tons of payload into Earth’s orbit. Such a space elevator could change the economics of space travel overnight. The cost could be reduced by a factor of ten thousand, an astonishing, revolutionary change.

  Currently it costs $10,000 or more to send a pound of material into orbit around the Earth (roughly the cost, ounce for ounce, of gold). Each Space Shuttle mission, for example, costs up to $700 million. A space elevator could reduce the cost to as little as $1 per pound. Such a radical reduction in the cost of the space program could revolutionize the way we view space travel. With a simple push of an elevator button, one could in principle take an elevator ride into outer space for the price of a plane ticket.