Contribution to the study of the resonant rotation in the Solar System

This HDR-thesis is devoted to the study of the rotation of the natural satellites of the giant planets and of Mercury. These bodies have a resonant rotation. Most of the natural satellites rotate synchronously, showing the same hemisphere to their parent planet (1:1 spin-orbit resonance). The case of Mercury is unique since its spin rate is exactly 1.5 its mean motion (3:2 spin-orbit resonance). These two configurations are dynamical equilibria, reached after damping of the initial rotation of the relevant bodies. Thus, the rotation quantities are a signature of the interior, in particular of a putative global ocean. This manuscript divides into 3 parts. The first part is devoted to the synchronous resonance. It presents different models of rotation from a fully rigid body to a one with a global subsurfacic ocean. We always consider all the degrees of freedom simultaneously, using analytical and numerical resolutions. These models are applied on Titan, Callisto, Janus, Epimetheus, Mimas, Hyperion, and Io. The second part presents the resonant rotation of Mercury, target of the two space missions MESSENGER and BepiColombo. We reveal in particular how it got trapped into its 3:2 resonance. The final part presents an algorithm I have elaborated to tackle the rotational problems.