Gravitational quantization of satellite orbits in the giant planets

TL;DR

This paper applies the global polytropic model, solving the Lane-Emden equation in the complex plane, to analyze satellite orbits around giant planets, suggesting a gravitational quantization pattern in their orbital arrangements.

Contribution

It introduces a novel application of the complex-plane Lane-Emden solution to model satellite orbits as quantized shells in giant planet systems.

Findings

Identification of polytropic shells corresponding to satellite orbits

Potential quantization pattern in satellite orbital distances

Application to multiple giant planet systems

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.