Analytical developments of rigid Mars nutation and tide generating potential series

Abstract

In this paper, series of rigid Mars nutations for the angular momentum axis, the rotation axis and the figure axis, as well as series of rigid Mars tide generating potential (TGP) are computed. The method used is based on the calculation of the forces produced by the external bodies on the rigid Mars. We have included the direct effect of the sun, Phobos and Deimos. We have also included the indirect effects associated with these bodies and planets of the Solar System which are given at the level of the ephemerides. For the nutation series, with a truncation level of 0.1 mas (milliarcsecond), related to the present-day precision of the Martian precession constant, 24 terms in longitudes (Δ*****) and 10 terms in obliquity (Δ*****) are computed. The value of the dynamical flattening used is H _D=(C−A)/C=0.00536, derived from the value p _a=−7576±35 mas/yr for the precession rate. Our results show a perfect agreement with those of Bouquillon and Souchay (1996) to the truncation level of Bouquillon and Souchary (1 mas). For the TGP series, we have set the truncation level to 10⁻⁶ m²/s² which corresponds to an effect on the vertical acceleration on Mars’ surface of about 10⁻¹² m/s²=0.1 nanogal (1 nanogal=10⁻¹¹ m/s². With this truncation level, 134 terms are computed.