Abstract
We treat the restricted (n+1)-body problem with a non-Newtonian homogeneous potential where the n primaries move on an arbitrary 2π-periodic orbit. We prove that the satellite equation has infinitely many periodic solutions that emerge from the infinity, asymptotically homothetic to the circular solutions of a central force problem. These solutions are obtained as critical solutions of a family of time-dependent perturbed Lagrangian systems, bifurcating uniformly from a compact set of periodic solutions of the unperturbed Lagrangian system.
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