Doubly-symmetric periodic orbits in the spatial Hill's lunar problem with oblate secondary primary

TL;DR

This paper proves the existence of doubly-symmetric periodic orbits in a spatial Hill's lunar problem with an oblate secondary, using fixed point theorems and perturbation analysis.

Contribution

It introduces a novel approach to establish doubly-symmetric periodic orbits in the spatial Hill's lunar problem with an oblate secondary primary.

Findings

Existence of doubly-symmetric periodic orbits confirmed

Application of fixed point theorem to celestial mechanics

Analysis of perturbations in the Hill's lunar problem

Abstract

In this article we consider the existence of a family of doubly-symmetric periodic orbits in the spatial circular Hill's lunar problem, in which the secondary primary at the origin is oblate. The existence is shown by applying a fixed point theorem to the equations with periodical conditions expressed in Poincare-Delaunay elements for the double symmetries after eliminating the short periodic effects in the first-order perturbations of the approximated system.