Orbital Regularity of Exoplanets and the Symmetries of the Kepler Problem

Abstract

We investigate the question whether or not the orbitals of exoplanets follow the symmetry-governed sequence found by Barut from the dynamical group of the Kepler problem. In particular, we consider their star distances, periods, and velocities. Previous studies have shown the validity of this regularity for our solar system, and for some selected exoplanet systems. Here, we study all the systems which are known with four or more planets. A remarkable result is found: 63 out of 100 systems show a better agreement between the theory and observation than our solar system. We discuss the relation between the symmetry-inspired transformations and the generalized Titius–Bode (gTB) rule. It turns out that the gTB rule, which has been considered purely empirical, can be obtained from the transformations corresponding to the dynamical group of the Kepler problem.