The laws of planetary motion, derived from those of a harmonic oscillator (following Arnold)

TL;DR

This paper explores the derivation of Kepler's laws from harmonic oscillator principles and discusses dual potentials, highlighting the mathematical connections between planetary motion and harmonic oscillators.

Contribution

It demonstrates how Kepler's laws can be derived from harmonic oscillator dynamics following Arnold, and discusses the concept of dual potentials in planetary motion.

Findings

Kepler's laws derived from harmonic oscillator principles

Circular orbits consistent with an $r^{-5}$ potential

Examples of dual potentials in planetary motion

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 $r^{-5}$ potential as found before by Newton. Both the Kepler/oscillator correspondance and circular orbits are examples of dual potentials.