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

P. A. Horvathy; P. -M. Zhang

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arXiv · 1404.2265

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

P. A. Horvathy·P. -M. Zhang

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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.

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P. A. Horvathy, P. -M. Zhang. 2014-04-08. The laws of planetary motion, derived from those of a harmonic oscillator (following Arnold). https://arxiv.org/abs/1404.2265

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