KAM stability estimates in Celestial Mechanics

A review of KAM stability estimates in Celestial Mechanics is presented. Rotational and librational invariant surfaces are constructed to ensure confinement in the phase space of a model obtained in the spin-orbit coupling between the revolutional and rotational motions of a satellite around a primary body. Stability of invariant tori for the restricted, circular, planar three body problem is also presented. Finally, an application of Arnoldʹs theorem to the inclined planetary problem is briefly discussed.