Gravitational potential inside spherical shell

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Gravitational potential inside spherical shell Anonymous Sat Dec 16 08:02:50 2017 No.9371791 [Reply] [Original]

How can I derive it using Poisson's equation? The outer region is easy, but the inner is causing me problems and I don't want to do it the "classical" way.

>>	Anonymous Sat Dec 16 08:08:04 2017 No.9371794 Easy: use Gauβ's theorem instead.

>>	Anonymous Sat Dec 16 09:15:02 2017 No.9371854 >>9371794 no

Anonymous Sat Dec 16 18:41:17 2017 No.9372987

>>9371791
Write out the spherical form of the laplacian on the left side, -rho over epsilon naught on the right.
You have spherical symmetry, so only the radial part of the laplacian survives. Thus you have an ordinary differential equation that's second order. You just have to write it out.

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