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In the framework of the so-called "global polytropic model", we assumehydrostatic equilibrium for a planetary system, and solve the resultingLane--Emden differential equation in the complex plane. We thus obtainpolytropic spherical shells defined by succesive roots of the real part$\mathrm{Re}(\theta)$ of the Lane-Emden function $\theta$. These shells seem toprovide hosting orbits for the planets of the system(s) under consideration. Inthe present investigation, we study within this framework the exoplanet systems55 Cnc, $\upsilon$ And, Kepler-11, Kepler-20, and Kepler-90.

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