New doubly-symmetric families of comet-like periodic orbits in the spatial restricted (N + 1)-body problem

For any positive integer N ≥ 2 we prove the existence of a new family of periodic solutions for the spatial restricted (N +1)-body problem. In these solutions the infinitesimal particle is very far from the primaries. They have large inclinations and some symmetries. In fact we extend results of Howison and Meyer (J. Diff. Equ. 163:174-197, 2000) from N = 2 to any positive integer N ≥ 2. © 2009 Springer Science+Business Media B.V.