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awarded  Nice Question
Jun
20
awarded  Scholar
Jun
20
accepted infinite grid of planets with newtonian gravity
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awarded  Supporter
Jun
14
comment infinite grid of planets with newtonian gravity
the gravitational potential stuff, would you consider that to be a part of Newtonian mechanics? I'm willing to write off all of my assumptions as soon as we talk about general relativity, simply because I don't understand enough to have any intuition about what's going on. Does any of what you say show ill-defined-ness or non-equilibruim in a purely Newtonian/Euclidean setup?
Jun
14
comment infinite grid of planets with newtonian gravity
I can only really answer your last point here: if I understand you correctly, the integrand being an odd function means that the force on each planet is zero, but shifting the centre of the spherical coordinates to get a non-zero result is fine. This amounts to saying that the gravitation force at those points is non-zero, but there's no mass on which to act at those points so that's fine.
Jun
13
comment infinite grid of planets with newtonian gravity
I realise that equilibrium would be unstable. I still don't think anything will move without some other perturbation.
Jun
13
awarded  Student
Jun
13
asked infinite grid of planets with newtonian gravity