Three-body planetary problem: study of KAM stability for the secular part of the Hamiltonian

The Hamiltonian representing the average over the mean-motion angles (i.e. the secular part) of the three-body planetary problem is considered. An efficient algorithm constructing invariant tori for the trajectories in phase space is provided. To give a possible practical application, we consider a toy-model including the main terms of the secular part of a hypothetic Sun-Jupiter-Saturn system having eccentricities and inclinations equal to 120 of the true ones. The scheme of a KAM proof of the stability of the model is sketched. The proof is “computer assisted”.