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I see two aspects to your question/comment: at-rest, and two-objects. The whole point of that comment was to apply only to at-rest things (he goes on to contrast it with objects with velocity), though I think maybe you got that. If you have a marble and two other objects, the other objects make two funnels, and there is a saddle (itself curved) where the two objects's funnels are equipotent. That's the three-body case. If it were possible to balance perfectly on this line of equipotence, you'd just slide to the lowest point on that line, and stay there, out of the funnels. This, IIUC, is one of the Lagrange points... L1, I think. In theory it's possibly-stable, but its stability exhibits negative feedback, so in practice it's impossible (although with station-keeping rockets, it's cheaper to hover there than most places). As you add more funnels, you just get more of these saddle lines intersecting. There are many infinitely-fussy places in the universe where you could in-theory-but-not-in-practice hover without falling into a funnel (if it weren't for brownian motion and maybe some other quantum effects that disturb your infinitely-difficult equilibrium). Of course, this whole analogy doesn't account for the fact that all of the bodies are acting on each other, not just the funnels acting on the marble. |