N-dimensional elliptic invariant tori for the planar (N + 1)-body problem

For any N ≥ 2 we prove the existence of quasi-periodic orbits lying on N-dimensional invariant elliptic tori for the planetary planar (N + 1)-body problem, For small planetary masses, such orbits are close to the limiting solutions given by the N planets revolving around the sun on planar circles. The eigenvalues of the linearized secular dynamics are also computed asymptotically. The proof is based on an appropriate averaging and KAM theory which overcomes the difficulties caused by the intrinsic degeneracies of the model. For concreteness, we focus on a caricature of the outer solar system.