A general theory of motion for the eight major satellites of Saturn. II, Short-period perturbations

We give a representation of the long-period perturbations of the following satellites of Saturn : Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus. The first order partial derivatives of this representation with respect to the physical parameters and the initial conditions have been also computed. The internal precision, obtained by comparison with numerical integration, has been estimated to a few kilometers for all satellites except Iapetus for which discrepancies reach 100 km over 100 years. Important new terms due to the orbital precession of Iapetus, and some terms coming from indirect perturbations by Jupiter have been found in the solution of Rhea, Titan and Iapetus