juststrange wrote:Blatm wrote:juststrange wrote:Stuff

It seems like you're making up your mind before doing any physics, and then trying to use physics to justify your (often incorrect) guess (as are a number of other posters in this thread). All of phlip's answers are correct and well justified.

No. First, philp and I had most of the same answers. Two, I staunchly disagree with his take on problem #1. Cycloids do not apply here, atleast in my understanding of the problem.

If you need more convincing, there's a fair few youtube videos that have been linked in the thread demonstrating this. But yeah, phlip is quite right. Also, you might want to check the working from other people for q.5 - an answer has been found that's a bit more qualitative then 'fast'.

Oh, and for people thinking about the Dyson sphere (q.7) - the easiest analogy here is to electromagnetism - like gravity it's an inverse square law so the maths is the same. Gauss's law gives that the integral of the dot product over any closed surface of the electric field and the surface normal is equal to the charge contained by that surface divided by the permeability of free space. If we assume a uniform spherical surface of charge, and take a spherical surface of smaller radius, then we can immediately say the integral is equal to zero, which means by symmetry arguments the electric field is equal to zero. Obviously, if you can't make those symmetry arguments, then you can't claim this, so it's not true that any system is unperturbed by an external electric charge (or else there'd be none whatsoever). But for a spherical shell, then it works out quite well.