Fermilab

You wrote:

I have heard there is a proof of Kepler's law that involves geometry only -- no calculus. Can you help me find it?

Joseph,

As you might know, Kepler himself did not derive his laws using strict mathematics. He found the laws by guessing and trying to fit his guesses to the observational data left by Tycho Brahe. We still use this approach today!

As to the proof of Kepler's laws ... I found a very nice web page showing a proof of Kepler's laws assuming Newton's Laws of motion and gravity. It appears to be mostly geometry based.
It is at: http://www.alcyone.com/max/physics/kepler/index.html

Another nice web site gives some historical overview:
http://plus.maths.org/issue8/features/proof2/

Hopes this helps,

William Wester