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