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arXiv · 1501.04189

Gravitational quantization of exoplanet orbits in HD 40307, $μ$ Ara, Kepler-26, Kepler-62, and Kepler-275: Comparing predicted orbits

Vassilis S. Geroyannis
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Abstract

According to the so-called "global polytropic model", hydrostatic equilibrium for a planetary system leads to the Lane-Emden differential equation. Solving this equation in the complex plane, we obtain polytropic spherical shells defined by succesive roots of the real part $\mathrm{Re}(θ)$ of the Lane-Emden function $θ$. Such shells provide hosting orbits for the members of a planetary system. Within the framework of the global polytropic model, we study the exoplanet systems HD 40307, $μ$ Ara, Kepler-26, Kepler-62, and Kepler-275. We give emphasis on comparing our results with observations, and with orbit predictions derived from the "generalized Titius-Bode relation".

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Vassilis S. Geroyannis. 2015-01-17. Gravitational quantization of exoplanet orbits in HD 40307, $μ$ Ara, Kepler-26, Kepler-62, and Kepler-275: Comparing predicted orbits. https://arxiv.org/abs/1501.04189

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