Variational existence proof for multiple periodic orbits in the planar circular restricted three-body problem

Abstract

The restricted three-body problem (R3BP) is an important research area that deals with significant issues in celestial mechanics, such as analyzing asteroid movement behavior and orbit design for space probes. We aim to show the existence of periodic orbits in the planar circular R3BP. To find these orbits, we adapt a variational approach and symmetry.

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

“…The structure of the collision singularity (X, Y, Z) = (0, 0, 0) is essential same as ones of the restricted three-body problem. We [4] established a method to avoid the collision singularities in the restricted three-body problem. We can apply the method to the Hill problem and show that the obtained minimizers have no collision.…”