Gravitationally Quantized Orbits in the Solar System: Computations Based on the Global Polytropic Model

Vassilis Geroyannis, Florendia Valvi, Themis Dallas

Department of History, Archaeology and Social Anthropology, University of Thessaly, Volos, Greece.
Department of Mathematics, University of Patras, Patras, Greece.
Department of Physics, University of Patras, Patras, Greece.

DOI: 10.4236/ijaa.2014.43042                

Abstract

The so-called “global polytropic model” is based on the assumption of hydrostatic equilibrium for the solar system, or for a planet’s system of statellites (like the Jovian system), described by the Lane-Emden differential equation. A polytropic sphere of polytropic index n and radius R₁ represents the central component S₁ (Sun or planet) of a polytropic configuration with further components the polytropic spherical shells S₂, S₃, ..., defined by the pairs of radi (R₁, R₂), (R₂, R₃), ..., respectively. R₁, R₂, R₃, ..., are the roots of the real part Re(θ) of the complex Lane-Emden function θ. Each polytropic shell is assumed to be an appropriate place for a planet, or a planet’s satellite, to be “born” and “live”. This scenario has been studied numerically for the cases of the solar and the Jovian systems. In the present paper, the Lane-Emden differential equation is solved numerically in the complex plane by using the Fortran code DCRKF54 (modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane along complex paths). We include in our numerical study some trans-Neptunian objects.

Keywords

Complex-Plane Strategy, Global Polytropic Model, Jovian System, Quantized Orbits, Solar System, Trans-Neptunian Objects

Conflicts of Interest

The authors declare no conflicts of interest.

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