Gravitational quantization of satellite orbits in the giant planets

Abstract

A fundamental assumption in the so-called "global polytropic model" is hydrostatic equilibrium for a system of planets or statellites. By solving the Lane-Emden differential equation for such a system in the complex plane, we find polytropic spherical shells defined by succesive roots of the real part $\mathrm{Re}(\theta )$ of the Lane-Emden function $\theta$. These shells seem to be appropriate places for accomodating planets or satellites. In the present study, we apply the global polytropic model to the systems of satellites of the giant planets: Jupiter, Saturn, Uranus, and Neptune.

some parts of v1 have been removed; this modification has been achieved by systematic reference to a recent relevant investigation; some typos have been corrected; 12 pages

References in corpus (3)

• Testing the Titius-Bode law predictions for Kepler multi-planet systems
• Exact Solutions of the Isothermal Lane--Emden Equation with Rotation and Implications for the Formation of Planets and Satellites
• 55 Cancri: A Laboratory for Testing Numerous Conjectures about Planet Formation

Cited by in corpus (1)

• Gravitational quantization of exoplanet orbits in 55 Cnc, $\upsilon$ And, Kepler-11, Kepler-20, and Kepler-90