TIDAL EVOLUTION OF PLANETARY SYSTEMS

We review the orbital and rotational evolution of single and two-planet systems under tidal dissipation. In the framework of mutual gravitational perturbation and tidal interaction between the star and the innermost planet, we shall present the main results for the variations of eccentricities in both cases. These results are obtained through the numerical solution of the exact equations of motions. Moreover, we will also give an analysis of the planetary rotation, which can be temporarily trapped in special configurations such as spin orbit resonances. Results will be shown using a Maxwell viscoelastic deformation law for the inner planet. This rheology is characterized by a viscous relaxation time, tau, that can be seen as the characteristic average time that the planet requires to achieve a new equilibrium shape after being disturbed by an external forcing (tides of the star).