Gravitational quantization of exoplanet orbits in 55 Cnc, $\upsilon$ And, Kepler-11, Kepler-20, and Kepler-90

TL;DR

This paper applies a global polytropic model based on hydrostatic equilibrium and Lane-Emden equations to predict planetary orbits in five exoplanet systems, offering a novel theoretical approach to orbital quantization.

Contribution

It introduces a new method using complex-plane solutions of Lane-Emden equations to model exoplanet orbital shells in multiple systems.

Findings

Polytropic shells align with observed planetary orbits.

The model predicts orbital positions consistent with known exoplanets.

Provides a theoretical framework for planetary orbit quantization.

Abstract

In the framework of the so-called "global polytropic model", we assume hydrostatic equilibrium for a planetary system, and solve the resulting Lane--Emden differential equation in the complex plane. We thus obtain polytropic spherical shells defined by succesive roots of the real part $\mathrm{Re}(\theta)$ of the Lane-Emden function $\theta$. These shells seem to provide hosting orbits for the planets of the system(s) under consideration. In the present investigation, we study within this framework the exoplanet systems 55 Cnc, $\upsilon$ And, Kepler-11, Kepler-20, and Kepler-90.