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

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.

16 pages

References in corpus (3)

• The 3-dimensional architecture of the Upsilon Andromedae planetary system
• Stability of the Kepler-11 System and its Origin
• Gravitational quantization of satellite orbits in the giant planets

Cited by in corpus (1)

• Gravitational quantization of exoplanet orbits in HD 10180, Kepler-32, Kepler-33, Kepler-102, and Kepler-186