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Tethered together
Could satellite ‘stepping stones’ solve the space elevator conundrum, asks Colin Ledsome CEng FIED
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rotating the satellite around its centre of mass. This can be used to deliberately orient a satellite with one end pointing towards the Earth. This is known as gravity-gradient or tidal stabilisation and its maintenance doesn’t require any energy. This effect can be extended by connecting a pair of satellites with a long cable or tether. They can orbit together at a velocity appropriate to their joint centre of mass, which is located part way along the tether. Since the angle of the tether changes, the upper body has further to go than the lower one, so moves faster. It would be moving too quickly for its orbital height so tries to move higher. The lower one is slower, so tries to move downwards. This puts tension in the tether, keeping the satellites structurally connected.
PHOTOBANK GALLERY/SHUTTERSTOCK
e tend to use the terms ‘centre of gravity’ and ‘centre of mass’ as if they are the same, but they aren’t. The difference becomes important when a satellite is sent into orbit. For a circular orbit, the velocity of the satellite’s centre of mass determines its orbital height. However, the pull of gravity is inversely proportional to the square of the distance from the Earth, so the pull on its base will be greater than that on its top. Hence, its centre of gravity will be slightly lower than its centre of mass. For compact satellites, this has little effect, but for larger ones, especially where one axis is longer than the others, the difference between the two centres can act like a pendulum, with the gravitational pull, acting at the centre of gravity,
This concept was taken to its extreme in 1895 by the Russianborn scientist and mathematician Konstantin Tsiolkovsky, who proposed a tether that extended down to the Earth’s surface from a large ‘counterweight’ satellite. To reach a stationary point on the Earth, the centre of mass would have to be at the level of a geostationary orbit. Since the geostationary orbital height is 35,786 kilometres, the satellite would have to be even farther out. The forces in a tether some 50,000 kilometres long, mainly generated by its own ‘weight’, causes a tension load that’s far beyond that which can be borne by any material currently available in that quantity. Even so, various proposals for a ‘space elevator’ using such an arrangement have been made, with some projecting completion by the middle of this century. How to get it all up there is a daunting challenge. I would like to suggest a more practical alternative. A pair of satellites on a much shorter tether could provide a docking station for passengers and cargo. At the lower end, the inward forces would provide some sense of weight downward. A travelling capsule could then climb the tether to the upper satellite, where the outward forces would also provide a sense of weight, but now upward. These latter forces would have a slingshot effect on any vehicle released from the upper station. With appropriate timing and small adjustments, this could allow travel to the lower end of another pair of tethered satellite stations farther out. A sequence of these pairs could allow travel to and from extremely high orbits in a series of steps without an inconveniently heavy tether. If the lowest station were close to the upper atmosphere, it would be within reach of small launch vehicles, since its velocity would be slower than orbital velocity. A high top-station would provide an initial boost for missions to the Moon and beyond. All tethers could be made from currently available materials and the launch requirements for each pair wouldn’t be excessive. If the elevator doesn’t work, use the steps. ■
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29/06/2021 20:08
