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A quick calculation for 1g spin gravity at a leisurely 1 round per 20min gives a radius of 360km.

Assume, we find a strong enough material for lightweight cables, what are the challenges for building a Bola-style habitat (i.e. two stations rotating around a common center of mass)?

In particular:

  • Is the large radius a problem on "habitable" earth orbits (tidal forces)?
  • Is it difficult to maintain the common center of mass of such a large (but comparatively lightweight) structure?
  • Is it difficult to start the desired rotation?

Which radius is practically possible?

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  • $\begingroup$ Do you exclude moving things to orbit as part of your question ? $\endgroup$ – Antzi Aug 15 '16 at 6:44
  • $\begingroup$ Yes, I assume a lightweight cable, so I assume achieving orbit is covered. $\endgroup$ – choeger Aug 15 '16 at 11:41
  • $\begingroup$ @choeger: For what it's worth, the standards for cables light enough to serve in a rotating habitat are far lower than for space elevators. In fact, we could probably do a perfectly serviceable job 50 years ago. $\endgroup$ – Nathan Tuggy Aug 19 '16 at 4:28
  • $\begingroup$ How would visiting spacecraft manage docking with no central hub? $\endgroup$ – Mike H Aug 19 '16 at 5:23
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If you are talking about one in earth orbit you have to think about it's orientation. If the axis is north / south then the habitats would be rotating into higher and lower orbits. So tidal forces would probably try to impose vibration. Not to say this couldn't be overcome. The entire system would have a center of mass and I would think if you had enough stiffening structure, it might be manageable. You might think of pointing the axis at the earth so the habitats would be at the same altitude all the time, they would effectively be changing inclination. But I believe a rotating mass would want to stabilize it's axis and you couldn't point it at earth unless the axis rotated once every orbit. The further you are out, the less the tidal forces would matter. Wernher von Braun wanted to put a spinning torus station a thousand miles out. Maybe that is why. Another interesting point in this is that a rotating object wants to spin around it's long axis. So if you built a long spinning weenie as a space colony, after a while it would wind up spinning end over end. That is why Gerard O'Neill proposed space colonies in counter rotating pairs with a truss connecting at the axis. That way the whole system acts as a non spinning object.

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