Planetary perturbations on the rotation of Mercury

The space missions MESSENGER and BepiColombo require precise short-term studies of Mercury's rotation. In this scope, we perform analytically and numerically by Hamiltonian approach a synthetic 2-dimensional representation of its rotation, using complete ephemerides of the orbital motions of the planets of the Solar System. This representation allows us to derive the librations in longitude and latitude of the resonant arguments. We point out that the contributions of Venus and Jupiter cannot be neglected in the study of the librations in longitude. We also show that the librations in latitude are much smaller, with an amplitude of about 0.2 arcsec, whereas the librations in longitude have an amplitude of about 40 arcsec. Moreover, we mention the possibility of a resonance involving the free libration in longitude and the orbital motion of Jupiter. All these results are compared to those given by SONYR model, which integrates simultaneously the orbital motions of the planets and the rotation of Mercury, and therefore gives the full spin-orbit coupling motion of Mercury.