Teaching the Kepler Laws for Freshmen

One of the highlights of classical mechanics is the mathematical derivation of the three experimentally observed Kepler laws of planetary motion from Newton's laws of motion and of gravitation. Newton published his theory of gravitation in 1687 in the Principia Mathematica. After two short introductions, one with definitions and the other with axioms, Newton discussed the Kepler laws in the first three sections of Book 1. Kepler's second law (motion is planar and equal areas are swept out in equal times) is an easy consequence of the conservation of angular momentum L=rxp, and holds in greater generality for any central force field. Here, van Haandel and Heckman present a proof of the Kepler laws for which a priori the reasoning is well motivated in both physical and geometric terms. Then, they review the hodographic proof as given by Feynman in his "Lost Lecture", and finally they discuss Newton's proof from the Principia.