Check this out, seniors: Gravity for Sticks and Rings

When it comes to the math, what we are working on in EM as far as electric potential and electric fields for charge distributions should be the same as gravity. Check out the following videos if you want to see some fancier math and strange situations for gravity, as they just follow the analyses we have done for electric charges. It is neat to see what happens with a hollow earth, or digging a tunnel through the earth and jumping in. Then there is Gauss's law for gravity, and the NON-Gauss geometries. Keep in mind you can also check out the main concepts Einstein used to come up with general relativity.