Martin Wood Complex, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU
Tidal deformation and consequent dissipation result in spin and orbital evolution of planetary and stellar systems. In this talk, we revisit the two body problem with tides and present new approaches to the tidal theory. We compute the instantaneous deformation of extended bodies using a differential equation for the inertia tensor. This method allows large eccentricities and it is not limited to quasi-periodic perturbations. It can take into account a wide class of perturbations, including chaotic motions and transient events. We also derive the secular equations of motion in a vectorial formalism, which is frame independent and valid for any rheological model. We show that for viscoelastic rheologies, which are suitable for rocky planets, spin-orbit resonances arise naturally and delay the evolution towards the synchronous state. These equilibria are very important for Earth-like planets in the habitable zone of M-dwarf stars, as they help to sustain temperate environments and thus more favourable conditions for life.