Multistability and Gibbs entropy in the planar dissipative spin-orbit problem

In this work, we numerically investigate and visually illustrate the dynamical properties of the dissipative spin-orbit problem such as the co-existence of multiple periodic and quasi-periodic attractors, and the complexity of the corresponding basins of attraction. Our model is composed by a triaxial satellite (planet) orbiting a planet (star) in a fixed Keplerian orbit with zero obliquity. A dissipative tidal torque that is proportional to its rotational angular velocity is assumed to be acting on the satellite. We use Hyperion as a toy model to characterize the methodology used, since this system has a very rich conservative dynamical scenario, and we later apply our methodology to the Moon and Mercury. Our results show that the basins of attraction may possess an intricate structure in all cases which changes with the orbital eccentricity, and that the Gibbs entropy is a good measure on how dominant one basin is over the others in the phase space.