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The "orbits" in this case have no closed-form in terms of circular or elliptic functions. The locus of the body will tend to fill space in an annular region around the central point. This image of a $F=-1/r$ orbit was produced by "central force workbench" by Juan M. Aguirregabiria. The potential is now of the form $V= \ln|r|$. The only ...

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You can't. An N-body system with n>2 is (in general) chaotic. This means that any inaccuracy in the initial state of the system will grow exponentially. You can't get a rough estimate of any planets position at a future time. So you can't predict roughly where a body will be a long way into the future, even if you numerically predict frame by frame. In ...

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I think if the satellite doesn't rotate about its own axis the centrifugal force will be of the same strength for each point of the satellite because the radius of each trajectory is the same. But if the satellite rotates synchronously there should be different centrifugal forces causing the Roche limit to decrease by a factor of $\sqrt[3]{2}$ Edit: Okay, I ...

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For those who wanted a complete mathematical answer and were also dissatisfied with the previous answers, see answers to How high can a mountain possibly get? in Earth Science SE. I adjusted a few numbers in the linked equation to more accurately reflect compression strength and density of granite ($2.5 \times 10^8$ and $2.75 \times 10^3$ respectively). A ...

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