Analytical Development of Rigid Mercury Nutation Series

In this paper, series of a rigid model of Mercury nutations are computed. The method used is based on the calculation of the forces produced by the Sun on Mercury as considered as a rigid body. In order to take into account the indirect effects coming from the orbit perturbations of Mercury, we used the ephemerides VSOP87 (Bretagnon and Francou, 1988). Due to non-negligible difference between the principal moment of inertia A and B in the case of Mercury, we compute also terms due to the triaxiality in addition to the general terms coming from J₂. With a truncation level of 10^–3 mas (milliarcsecond), related to the present-day precision of the Mercury precession constant, 173 terms in longitude ( sin ) and 166 terms in obliquity () are computed. The value of the dynamical flattening used is H_D = (C – A)/C = 2.3 × 10^–4 (Anderson, 1987).