Steven and Mauro, I think you'd like how Ellipitical orbits are explained in these links. They are based on Feynman's so called "lost lectures", where he showed how to use geometry without calculus to derive elliptic orbits.
paper: http://journal.geometryexpressions.com/pdf/kep.pdf video tutorial in several parts: http://www.youtube.com/user/nymathteacher#p/u/17/ObVDk7WPm9Y harry
