Abstract
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.
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Llibre, J., Roberto, L.A. New doubly-symmetric families of comet-like periodic orbits in the spatial restricted (N + 1)-body problem. Celest Mech Dyn Astr 104, 307–318 (2009). https://doi.org/10.1007/s10569-009-9213-6
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DOI: https://doi.org/10.1007/s10569-009-9213-6
Keywords
- Comet-like periodic orbits
- Spatial restricted (N + 1)-body problem
- Doubly symmetric periodic orbits
- Continuation method