Librations of a 2-layer Mercury

International audienceWith the space missions MESSENGER and BepiColombo, there has been a renewed interest for Mercury. In this framework, we study the longitudinal and latitudinal librations of a 2-layer Mercury. We apply Hamiltonian mechanics to determine the effects of planetary perturbations on the librations (using both analytical and numerical methods). The libration in longitude is dominated by the 88-day and 11.86-year period effects, while other planetary perturbations have smaller contributions. The libration in latitude (under 1 arcsec) should not be detected by the space missions. However, we point out that the latitudinal librations could be much larger (up to several tens of arcsec) if the free precession period approaches the Jupiter-Saturn Great Inequality period. With the large uncertainties on the planetary parameters, this new resonant forcing on Mercury's libration in latitude should be borne in mind. Finally we state our early results of the wobble motion of Mercury (i.e. the angle between the angular momentum and the axis of inertia)