An Accurate Model of Mercury’s Spin-Orbit Motion

Abstract

AbstractOur work deals with the physical and dynamical causes that induce librations of Mercury around an equilibrium state defined by the 3:2 spin-orbit resonance. 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 model), 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 the main perturbations acting on the spin-orbit motion of Mercury such as the planetary interactions or the dynamical figure of the planet. Moreover, the complete rotation of Mercury exhibits two proper frequencies, namely 15.847 and 1066 years, and in addition one spin-orbit secular resonance (298 898 years). A new determination of the mean obliquity of Mercury has been proposed. Besides, we have identified in the Hermean librations the impact of the uncertainty of the greatest principal moment of inertia (C/MR2) on the obliquity as well as on the libration in longitude (2.3 mas and 0.45 as respectively for an increase of 1% on the C/MR2 value). These accurate relations have to be taken into account in the context of the two upcoming missions BepiColombo and MESSENGER.