The laws of planetary motion, derived from those of a harmonic oscillator (following Arnold)
arXiv:1404.2265
Abstract
Kepler's laws of planetary motion are deduced from those of a harmonic oscillator following Arnold. Conversely, the circular orbits through the Earth's center suggested by Galilei are consistent with an potential as found before by Newton. Both the Kepler/oscillator correspondance and circular orbits are examples of dual potentials.
Corrected and substantially extended version, with the collaboration of P.-M. Zhang (Zhuhai). To be published in "Physics Education (India)". (13 pages, 5 figures)