Breakdown of librational invariant surfaces

A numerical investigation of the stability of invariant librational tori is presented. The method has been developed for a model describing the spin-o rbit coupling in Celestial Mechanics. Periodic orbits approaching the libra tional torus are computed by means of Newton's method. According to Greene' s criterion, their stability is strictly related to the survival of invaria nt tori. We consider librational tori around the main spin-orbit resonances (1:1, 3: 2). Their existence provides the stability of the resonances, due to the co nfinement properties in the three-dimensional phase space associated to our model. The results are consistent with the actual observations of the ecce ntricity and of the oblateness parameter. A different behavior of the Moon and Mercury around the main resonances is evidenced, providing interesting suggestions about the different probabilities of capture in a resonance.