The spin-orbit resonant problem including core-mantle gravitational coupling

Abstract

In this work, we numerically study an improved model of the spin-orbit resonances with applications in the exoplanetary dynamics. While in the classical model the planetary rotation is characterized by the motion of the whole planet around the axis with the largest moment of inertia, the model which we revisit here considers differential rotation and gravitational coupling between distinct internal layers of the planet. We have prepared a numerical code with the equations of motion of differential rotation of an inner core and an outer mantle. We apply the model to the exoplanet Kepler-10b. Supposing a terrestrial-like interior structure for the planet, numerical exploration of the rotational phase space shows that the effects of the gravitational forces of the external layers of the planet on the rotation of a solid inner core may be not negligible.