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

• 作者: Florendia Valvi Themis Dallas Vassilis Geroyannis
• 来源期刊: 天文学与天体物理学国际期刊(英文)
• 学科: 数学
• 关键词: Complex-Plane Strategy GLOBAL Polytropic Model Jovian SYSTEM QUANTIZED ORBITS Solar SYSTEM Trans-Neptunian Objects
• 年，卷（期）: 2014,（3）
• 页码范围: 464-473
• 页数: 10页
• 分类号: O1

摘要

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.