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http://dx.doi.org/10.1016/j.icarus.2006.05.026

has been cited by the following article:

• 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.