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According to the so-called "global polytropic model", hydrostatic equilibriumfor a planetary system leads to the Lane-Emden differential equation. Solvingthis equation in the complex plane, we obtain polytropic spherical shellsdefined by succesive roots of the real part $\mathrm{Re}(\theta)$ of theLane-Emden function $\theta$. Such shells provide hosting orbits for themembers of a planetary system. Within the framework of the global polytropicmodel, we study the exoplanet systems HD 40307, $\mu$ Ara, Kepler-26,Kepler-62, and Kepler-275. We give emphasis on comparing our results withobservations, and with orbit predictions derived from the "generalizedTitius-Bode relation".

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