Abstract
There is a great deal of planets in close-in orbits and low mass on order of magnitude less than 10 Earth mass. Valencia et al. (2006) call them Super-Earths. Recently, several efforts have been done in order to understand the dynamics of rotation of these planets, including spin-orbit resonance and spin tidal evolution (Rodríguez et al. (2012), Callegari and Rodríguez (2013)). In the referred papers, it is considered a single planet whose motion around the star is governed by the rules of the two-body problem. However, many Super-Earths are present in systems where other terrestrial or giant planets are present, and that problem must be checked. In this work we study the dynamical effects of mean-motion commensurabilities on rigid body rotation and spin-orbit resonances. Emphasis is given in the cases of the multi-planetary systems Kepler-11, KOI-55 and KOI-961, where the mean motions of several pairs of planets are commensurable. In some cases we have observed that the period associated to a particular commensurability is close to the period of the free libration of the rotation of one of the super-Earths. Thus, we investigate the role of the mean motion resonance on the synchronous rotation. Depending on the initial conditions inside the synchronous domain, the stable librations induced by the torque of the central star on the figure of the planet can lead to instabilities on its rotation which are not expected in such regular regions of rotational phase space. This phenomenon has been observed in the cases of Kepler-11 b (disturbed by Kepler-11 c), KOI-55 b (disturbed by KOI-55 c), KOI-961c (disturbed by KOI-961b and KOI-961d).
