The global polytropic model for the solar and jovian systems revisited

The "global polytropic model" (Geroyannis) 1993 [P1]; Geroyannis and Valvi 1994 [P2]) is based on the assumption of hydrostatic equilibrium for the solar/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/Jupiter) of a polytropic configuration with further components the polytropic spherical shells S2, S3, ..., defined by the pairs of radii (R1,R2), (R2,R3), ..., respectively. R1, R2, R3, ..., are the roots of the real part Re(theta(R)) of the complex Lane-Emden function theta(R). Each polytropic shell is assumed to be an appropriate place for a planet/satellite to be "born" and "live". This scenario has been studied numerically for the case of the solar system (P1) and the jovian system (P2). In the present paper, the Lane-Emden differential equation is solved numerically in the complex plane by using the Fortran code dcrkf54.f95 (Geroyannis and Valvi 2012; modified Runge-Kutta- Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane). We include in our numerical study some trans-Neptunian objects. We emphasize on computing distances and comparing with previous results. REFERENCES: V.S. Geroyannis 1993, Earth, Moon, and Planets, 61, 131-139. V.S. Geroyannis and F.N. Valvi 1994, Earth, Moon, and Planets, 64, 217-225. V.S. Geroyannis and F.N. Valvi 2012, International Journal of Modern Physics C, 23, No 5, 1250038:1-15.