What is the gravitational potential of an ellipsoid at $0$?
Given an ellipsoid: $\frac{x^2+y^2}{a^2} +\frac{z^2}{c^2} \leq 1,$ and a uniform density of mass:
Using spherical coordinates, and the transformation $(x,y,z) \rightarrow (ax,ay,cz)$ I got: $= \int\frac{a^2c \sin \phi}{ \sqrt{ a^2sin^2\theta +c^2cos^2\theta }} $
I'm not sure how to continue from here..