%0 Journal Article %T Gravitational quantization of exoplanet orbits in 55 Cnc, $\upsilon$ And, Kepler-11, Kepler-20, and Kepler-90 %A Vassilis S. Geroyannis %J Physics %D 2014 %I arXiv %X 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. %U http://arxiv.org/abs/1411.5390v1