Planetary theories with the aid of the expansions of elliptic functions (Q1363503)

The mutual perturbations between two bodies moving initially on coplanar circular unperturbed orbits are expressed in terms of the argument of elliptic functions. This expression improves the convergence, compared to the classical expansion in the difference of mean longitudes. The method is extended to any order of planetary masses and is applied to the case of Jupiter and Saturn. In this case, a unique angular variable can be used by taking advantage of the close commensurability of the mean motions of the planets.