… derived from those of a harmonic oscillator

P. A. Horvathy
Kepler’s laws are deduced from those valid for a harmonic oscillator, following the approach of Bohlin, Levi-Civita and Arnold

1 Introduction
Kepler’s laws of planetary motion state that
1. K-I: A planet moves on an ellipse, one of whose foci being occupied by the sun;
2. K-II: The vector drawn from the sun to the planet’s position sweeps equal areas in equal
times
3. K-III: The squares of the periods are as the cubes of the major axes of the ellipses.
These laws can be deduced from the inverse-square force law and Newton’s equations of
motion…
… Read more at http://arxiv.org/pdf/1404.2265v1.pdf