In Pursuit of the Unknown by Ian Stewart Page A

spacecraft must be boosted out of Earth orbit and slowed again to enter lunar orbit; this wastes fuel. There arealternatives involving many loops round the Earth, a transition through the point between Earth and Moon where their gravitational fields cancel, and many loops round the Moon. But trajectories like that take longer than Hohmann ellipses, so they were not used for the manned Apollo missions where food and oxygen, hence time, were of the essence. For unmanned missions, however, time is relatively cheap, whereas anything that adds to the overall weight of the spacecraft, including fuel, costs money.
    By taking a fresh look at Newton’s law of gravity and his second law of motion, mathematicians and space engineers have recently discovered a new, and remarkable, approach to fuel-efficient interplanetary travel.
    Go by tube.
    It’s an idea straight out of science fiction. In his 2004 Pandora’s Star , Peter Hamilton portrays a future where people travel to planets encircling distant stars by train, running the railway lines through a wormhole, a short cut through space-time. In his Lensman series from 1934 to 1948, Edward Elmer ‘Doc’ Smith came up with the hyperspatial tube, which malevolent aliens used to invade human worlds from the fourth dimension.
    Although we don’t yet have wormholes or aliens from the fourth dimension, it has been discovered that the planets and moons of the Solar System are tied together by a network of tubes, whose mathematical definition requires many more dimensions than four. The tubes provide energy-efficient routes from one world to another. They can be seen only through mathematical eyes, because they are not made of matter: their walls are energy levels. If we could visualise the ever-changing landscape of gravitational fields that controls how the planets move, we would be able to see the tubes, swirling along with the planets as they orbit the Sun.
    Tubes explain some puzzling orbital dynamics. Consider, for example, the comet called Oterma. A century ago, Oterma’s orbit was well outside that of Jupiter. But after a close encounter with the giant planet, the comet’s orbit shifted inside that of Jupiter. After another close encounter, it switched back outside again. We can confidently predict that Oterma will continue to switch orbits in this way every few decades: not because it breaks Newton’s law, but because it obeys it.
    This is a far cry from tidy ellipses. The orbits predicted by Newtonian gravity are elliptical only when no other bodies exert a significant gravitational pull. But the Solar System is full of other bodies, and they can make a huge – and surprising – difference. It is here that the tubes enter the story. Oterma’s orbit lies inside two tubes, which meet near Jupiter. One tube lies inside Jupiter’s orbit, the other outside. They enclose specialorbits in 3 : 2 and 2 : 3 resonance with Jupiter, meaning that a body in such an orbit will go round the Sun three times for every two revolutions of Jupiter, or two times for every three. At the tube junction near Jupiter, the comet can switch tubes, or not, depending on rather subtle effects of Jovian and solar gravity. But once inside a tube, Oterma is stuck there until the tube returns to the junction. Like a train that has to stay on the rails, but can change its route to another set of rails if someone switches the points, Oterma has some freedom to change its itinerary, but not a lot ( Figure 15 ).

    Fig 15 Left : Two periodic orbits, in 2 : 3 and 3 : 2 resonance with Jupiter, connected via Lagrange points. right : Actual orbit of comet Oterma, 1910–1980.
    The tubes and their junctions may seem bizarre, but they are natural and important features of the gravitational geography of the Solar System. Victorian railway-builders understood the need to exploit natural features of the landscape, running railways through valleys and along contour lines, and