Comet and moon solutions in the time-dependent restricted $(n+1)$-body problem
Abstract
The time-dependent restricted -body problem concerns the study of a massless body (satellite) under the influence of the gravitational field generated by primary bodies following a periodic solution of the -body problem. We prove that the satellite has periodic solutions close to the large-amplitude circular orbits of the Kepler problem (comet solutions), and in the case that the primaries are in a relative equilibrium, close to small-amplitude circular orbits near a primary body (moon solutions). The comet and moon solutions are constructed with the application of a Lyapunov-Schmidt reduction to the action functional. In addition, using reversibility technics, we compute numerically the comet and moon solutions for the case of four primaries following the super-eight choreography.
Keywords
Cite
@article{arxiv.2001.03702,
title = {Comet and moon solutions in the time-dependent restricted $(n+1)$-body problem},
author = {Carlos Barrera and Abimael Bengochea and Carlos García-Azpeitia},
journal= {arXiv preprint arXiv:2001.03702},
year = {2024}
}