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
(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
Cite this paper
Geroyannis, V. , Valvi, F. and Dallas, T. (2014) Gravitationally Quantized Orbits in the Solar System: Computations Based on the Global Polytropic Model. International Journal of Astronomy and Astrophysics
, 464-473. doi: 10.4236/ijaa.2014.43042
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