Quantitative conditions for the existence of low-order spin-orbit resonances

We consider (p, q)−periodic orbits of a dissipative spin-orbit model, i.e. during q revolutions about the central planet the satellite does p rotations on its own spin-axis. L. Biasco and L. Chierchia in [2] give a sufficient condition for the existence of such orbits for q = 1, 2 and 4. Here we give explicit upper bounds on the eccentricity and, in the case q = 4, also on the dissipation, such that this condition is satisfied.