Gravitational quantization of satellite orbits in the giant planets

Gravitational quantization of satellite orbits in the giant planets

Author:

Geroyannis

Abstract:

A fundamental assumption in the so-called "global polytropic model" is global hydrostatic equilibrium for a system of planets or statellites. In the framework of the polytropic models and the induced (by hydrostatic equilibrium) Lane-Emden differential equation, a polytropic sphere of polytropic index n and radius R1 represents the central component S1(star or planet) of a polytropic configuration, of which further components are the polytropic spherical shells S2, S3, ..., defined by the pairs of radii (R1,R2), (R2,R3), ..., where R1,R2,R3, ..., are the roots of the real part Re(θ) of the complex Lane-Emden function θ. Such shells are appropriate places for accomodating planets or satellites. The Lane-Emden equation is solved by the Fortran code DCRKF54, which can integrate complex initial value problems along complex paths. In the present study, we treat numerically the systems of satellites of the giant planets: Jupiter, Saturn, Uranus, and Neptune.