  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.
