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

2014/04/08 by P. A. Horváthy, Pengming Zhang, Horvathy, P. A. +1
Earth and Planetary Sciences · #Classical Physics (physics.class-ph) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1404.2265

openalex publication_date 2014/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Bohlin-Arnold-Vassiliev's duality and conserved quantities

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