Variational proof of the existence of periodic orbits in the spatial Hill problem and its constrained problems

摘要

Abstract The Hill problem models the motion of a particle near a planet. In this paper, we show the existence of symmetric periodic orbits in the spatial Hill problem by using the variational method. We also study the problem under a constraint on a prescribed plane and show the existence of periodic orbits in the problem. The obtained orbits are applicable to artificial satellites around the Earth and other planets.