0

Possible Duplicate:
What nonlinear deformations will a fast rotating planet exhibit?

This is really a basic physics question that I wanted to check myself on because I'm not entirely sure of the correct answer. I asked a puzzler question on the last episode of my podcast about hollow Earth claims. I asked people to imagine a sphere with a solid shell that was filled with a compressible material, and this was spun very rapidly. (1) Would a hollow form, and (2) what shape would that hollow take on if it did form?

My thinking is that, yes, a hollow would form, but it would not be spherical as the hollow Earthers claim. It would be a biaxial ellipsoid with the short axis oriented along the poles and the long axes to the equator. This is because the centrifugal forces at the equator due to the spin would be much greater than at the poles, so there would be no "outward force" at the poles.

Is this correct? If so, is that a good explanation for a lay audience? If not correct, then what is the solution (it's been a long time since I took classical mechanics)? Thanks!

Community
  • 1
Stuart Robbins
  • 4,437
  • 22
  • 19
  • Soort answer: without at high tensile strength skin there can be no hollow. If the force at radius $r_1$ is outward, the force at radius $r_2 > r_1$ will be more outward and the body flies apart. (Because the centrifugal pseudo-force grows as $r$, and the gravitation attraction gets smaller (more distance, but not more mass because there is a hollow). – dmckee --- ex-moderator kitten Oct 28 '11 at 18:55
  • I see you closed this as a duplicate of something else. I tried searching a few times but didn't come up with anything that similar. Could you point me to where this duplicate is? – Stuart Robbins Oct 28 '11 at 19:07
  • The prior question you link to considers incompressible, not compressible, but that detail matters very little. Your podcast addressed conspiracy theories that planets are hollow - obviously we have consensus on that. If you spin an ordinary blob of matter fast enough, a torus is a valid solution, although the stability for any period of time is disputable. It's harder to ask if one could you make a planet with a closed cavity, because my own creativity may be insufficient. However, even if you did come up with something, it's a purely academic exercise. – Alan Rominger Oct 28 '11 at 19:12
  • Ah, okay, I see the duplicate. I swear that wasn't linked before? Or I just didn't see it ... anyway, yeah, while the podcast episode was about hollow Earth, the puzzler question specifically set up the scenario that you have a solid (read: sturdy) shell that won't deform, and then you have material inside that could deform. So, it could be that it's because I asked the question here, but I don't think it's an exact duplicate. – Stuart Robbins Oct 28 '11 at 19:24
  • I will definitely mention when I record the solution this weekend, though, that in reality the whole planet would deform and, if spun fast enough, would form a torus. – Stuart Robbins Oct 28 '11 at 19:25
  • @StuartRobbins I guess one thing I don't get is, if you had a outer shell with sufficient strength (which is impossible with ordinary materials by the way), why would a theory even bother with an inner fluid? The rotation of the Earth isn't enough to create proposed hollow cavity. You could propose that the fluid in the middle is spinning faster, which would be absurdly unsustainable, not to mention worsen the material strength requirements of the strong shell. – Alan Rominger Oct 28 '11 at 19:47
  • Well, it was a thought experiment. That's what I try to do with the puzzlers in my 'cast is to have a thought experiment loosely based off of one small aspect of the main topic of the episode. So I'd like to present the actual solution to it, but I'll then add that it's completely artificial due to everything posted above. – Stuart Robbins Oct 28 '11 at 19:51

0 Answers0