I agree with most of the stuff you have, but I don't think the shell theorem applies for flat disks in the way it applies for spheres. I tried my hand at working it out but wolframalpha doesn't like the integral I got, but when solving numerically the net force on an off-center mass in a hollow disk does not equal 0 like it would inside a hollow sphere.
blazzess t1_j13p0uy wrote
Reply to comment by Weed_O_Whirler in What assumptions are made about gravity when calculating the gravity within a galaxy? by bizzehdee
I agree with most of the stuff you have, but I don't think the shell theorem applies for flat disks in the way it applies for spheres. I tried my hand at working it out but wolframalpha doesn't like the integral I got, but when solving numerically the net force on an off-center mass in a hollow disk does not equal 0 like it would inside a hollow sphere.