An Accurate Model of Mercury's Spin-Orbit Motion

Our work deals with the physical and dynamical causes that induce librations around an equilibrium state defined by the 3:2 spin-orbit resonance of Mercury. In order to integrate the spin-orbit motion of Mercury we have used our gravitational model of the solar System including the Moon's spin-orbit motion. This model called SONYR (acronym of Spin-Orbit N-bodY Relativistic) was previously built by Bois Journet and Vokrouhlicky in accordance with the requirements of the Lunar Laser Ranging observational accuracy. Using the model we have identified and evaluated the main perturbations acting on the spin-orbit motion of Mercury such as the planetary interactions and the dynamical figure of the planet. Moreover the complete rotation of Mercury exhibits two proper frequencies namely 15.825 and 1089 years and one secular variation of 271043 years. Besides we have computed in the Hermean librations the impact of the variation of the greatest principal moment of inertia C/MR2 on the obliquity and on the libration in longitude (1.4 and 0.4 milliarseconds respectively for an increase of 1% on the C/MR2 value). We think that these accurate relations are also significant and useful in the context of the two upcoming missions BepiColombo and MESSENGER