Dynamics of tidal synchronization and orbit circularization of celestial bodies

PACS number s : 05.45.Xt, 05.45.Gg, 95.10.Ce, 96.15.DeWe take a dynamical-systems approach to study the qualitative dynamical aspects of the tidal locking of the rotation of secondary celestial bodies with their orbital motion around the primary. We introduce a minimal model including the essential features of gravitationally induced elastic deformation and tidal dissipation that demonstrates the details of the energy transfer between the orbital and rotovibrational degrees of freedom. Despite its simplicity, our model can account for both synchronization into the 1:1 spin-orbit resonance and the circularization of the orbit as the only true asymptotic attractors, together with the existence of relatively long-lived metastable orbits with the secondary in p:q synchronous rotationWe acknowledge projects OTKA T72037 Hungary , Hielocris Spain , the Human Frontier Science Program I.T. , MCI project CGL-2008-06245-C02-02 Spain , and the Spanish-Hungarian Binational project TeT ESP-34/2006.Peer reviewe