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In his popular youtube channel, Scott Manely addressed a question of whether an astronaut can orbit a space station. The provided answer is negative since such an orbit would require the space station to be impractically dense.

This got me wondering if similar arguments can limit the number of nested orbits in general. For example, say you are free to choose any solid bodies A, B, C,... s.t. A orbits B, B orbits C, etc. Is there a maximal number of such bodies and do we know it?

hilberts_drinking_problem
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  • Hi @hilberts_drinking_problem what do you think about my previous comment? Some Astronomy SE folks may not appreciate what "non-trivial" means to a mathematician, perhaps you could add something to the question explaining what you mean by non-trivial and mention if the answers in the proposed duplicate (2 close votes at this point) answer your question or not? Personally when I think of rotations accross widely different scales I think of Terry Tao's exploding water problem which we can probably agree is non-trivial :-) – uhoh Apr 16 '22 at 20:51
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    @uhoh It's been a while. If I remember correctly, I asked the question on a whimsy and "trivial" might not have been the best word to choose. I suppose I was wondering if there was a concrete upper bound number of orbits, say 12 for whatever reason. While hill spheres might be trivial, I think that the accepted answer to the linked question is great! – hilberts_drinking_problem Apr 17 '22 at 04:45

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There is no theoretical maximum. It would be possible for the solar system to orbit a sufficiently large mass, (while the planets' orbits remain stable). And it would be possible for that large mass to orbit another, even larger mass. The process could, in theory, be repeated without limit. The masses of the central bodies would have to be exponentially larger with each embedding, and so could not be conventional stars, beyond a certain point. (They could be black holes)

This is the absence of theoretical limit imposed by the theory of gravitation. In practice, multiple levels of orbits don't exist, since there does not exist a mechanism that can create the massive central bodies in the right orbits.

James K
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  • I think the Ringworld Engineers could do this in a couple weeks. – Carl Witthoft Jan 16 '17 at 13:54
  • As has been suggested elsewhere, it might be possible to do some kind of calculation based on hillspheres and see how far you get before hitting "mass of the observable universe or "diameter of the observable universe. – James K Apr 13 '22 at 17:32