To analytical theory of Mercury rotation: planetary perturbations

Now the new and wideopportunities for the accurate determination anddescription of the Mercury gravitational field andits rotation are opened in the Messenger mission tothe planet. Therefore theoretical estimations ofexpected effects in rotation of Mercury frominfluence of the liquid core represent the importa ntinterest [1], [2]. In the work the analytical theoryof rotational motion of Mercury which isconsidered as a celestial body with a liquid coreand rigid non-spherical mantle is developed. Weconsider orbital motion of Mercury on ellipticalprecessing orbit and in more general treatment ofproblem we take into account planetaryperturbations of forced orbital motion of planet.For the basic variables: Andoyer, Poincare andEulerian angles, and also for various dynamiccharacteristics of Mercury the tables foramplitudes, periods and phases of perturbations ofthe first order have been constructed. Resonantperiods of free librations of given model ofMercury have been estimated. The influence of aliquid core results in decreasing of the period offree librations in longitude approximately on 30%,and in change of the period of free pole wobble ofMercury on 50%. In the first approximation theliquid core does not render influence on the valueof Cassini’s inclination and on the period ofprecession of the angular momentum vector.However it causes an additional quasi-diurnal”librations with period about 27.165 days. Incomparison with model of rigid non-spherical ofMercury the presence of a liquid core should resultin remarkable increase of amplitudes of Mercurylibrations in longitude on 50 %. The theory hasbeen constructed by the full taking into accountplanetary perturbations in orbital motion ofMercury. For this purpose the spesialtrigonometric developments of the spericalfunctions of spherical coordinates of Mercury andfull force function of the problem have beenconstructed. Cassini’s laws are formulated in firstin given exect treatment of the problem asgenerating periodic solution for intermediateconditionally-periodic solution of the problem.The main perturbations in librations are analized.