John Schutkeker wrote:

3. The bodies are point masses.

Like Brian said, this isn't necessary. In fact, that's one of the
things Newton had to invent calculus to prove.

Parts of the Earth closer to you pull on you more strongly, and parts
farther away pull more weakly. But when you add it all up, it's the
same as if all of the Earth's mass were concentrated at a point in its
center.

- Ernie http://home.comcast.net/~erniew