In the framework of the space mission BepiColombo, a very accurate model of rotation of Mercury is required. In this thesis, we study various causes affecting the rotation of the planet on a time span going from a few days to several decades. In the first part of this work, we describe the model of a planet constituted of an ellipsoidal mantle and a spherical liquid core (no interaction), and without planetary perturbations. We compute the libration in longitude and in latitude as well as the polar motion of Mercury. In the second part, we study the effects of the indirect planetatery perturbations in the rotation. We emphasize several potential resonances capable of enhancing the longitudinal and latitudinal librations. In the third part, we analyse the core-mantle interactions assuming that the core is an ellipsoidal cavity. We show that an additional resonance plays a major role in this case and that the observations of the rotation of the mantle can yield information on the size of the core but not its shape. Finally, we study more theoretically a resonance between a free period of the system and the orbital period of Jupiter, raising the influence of Jupiter in the rotation. All the results were obtained analytically using a Hamiltonian approach of the problem and a perturbation method based on canonical Lie transforms, and were then verified using numerical integrations and frequency analysis.
|Date of Award||21 Jun 2010|
|Supervisor||Anne LEMAITRE (Supervisor), Timoteo Carletti (Jury), Guy Terwagne (President), Véronique Dehant (Jury) & Andrea Milani (Supervisor)|