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

For any $Ngeq 2$ 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/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.