How to prove that gravity isn't homogeneous on a disk? I

>>331948
f=GMmd^2, where G is the gravitational constant and d is the distance between the centers of mass.

f=GMmg(x,y)^2, where g(x,y) gives the distance between the center of mass of the planet and the center of mass of an observer at coordinates (x,y) on whatever planet.

g_sphere(x,y) returns a constant
g_disc(x,y) returns (x^2+y^2+h^2)^-1, where h is half the average thickness of the disc.

g_disc does not return a constant, so gravity is not homogeneous on a disc, QED.

>>331957
>returns
how? sorry i'm dumb

>>331958
"p returns q" means the output of the function p (for a certain input, or for a set of inputs) is q. >g_sphere(x,y) returns a constant
this means that g_sphere(x,y) is a constant number for every ordered pair (x,y).
>g_disc(x,y) returns (x^2+y^2+h^2)^-1
this means g(x,y) = (x^2+y^2+h^2)^-1, which is obviously not constant.

>>331948

gravity always pulls you towards the center of mass, as if all mass was hypothetically concentrated in one dot at the center. At a disk this point would be at the center of the circle in the middle of its thickness.
Gravitational force is dependant on distance, if you were standing on the center you would be closest to the mass point, but if you walked around yoour distance to it would increase ind its pull waeken, therefore it is not constant.