TITLE:
Gravitationally Quantized Orbits in the Solar System: Computations Based on the Global Polytropic Model
AUTHORS:
Vassilis Geroyannis, Florendia Valvi, Themis Dallas
KEYWORDS:
Complex-Plane Strategy, Global Polytropic Model, Jovian System, Quantized Orbits, Solar System, Trans-Neptunian Objects
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.4 No.3,
August
19,
2014
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 indexnand radiusR1represents the central
componentS1(Sun or planet) of a polytropic
configuration with further components the polytropic spherical shellsS2,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 functionθ.
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.