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

P. A. Horvathy, Pengming Zhang

School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China

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 correspondence and circular orbits are examples of dual potentials.