Periodic orbits of the two fixed centers problem with a variational gravitational field

TL;DR

This paper proves the existence of periodic orbits in the two fixed centers problem, deriving explicit formulas for small mass parameters, thus advancing understanding of gravitational orbital dynamics.

Contribution

It establishes the existence of bifurcating periodic orbits from the Kepler problem and provides analytical expressions for these orbits in the small mass regime.

Findings

Existence of bifurcating periodic orbits proven.

Analytical formulas derived for small mass parameters.

Enhanced understanding of gravitational orbit structures.

Abstract

We prove the existence of periodic orbits of the two fixed centers problem bifurcating from the Kepler problem. We provide the analytical expressions of these periodic orbits when the mass parameter of the system is sufficiently small.