Variational Minimizing Parabolic Orbits for the 2-Fixed Center Problems

TL;DR

This paper proves the existence of a symmetric parabolic orbit in the 2-fixed center problem using variational methods, expanding understanding of orbital dynamics under weak force potentials.

Contribution

It introduces a variational approach to establish the existence of specific parabolic orbits in the 2-fixed center problem with weak force potentials.

Findings

Existence of an odd symmetric parabolic orbit proven.

Application of variational minimizing methods to orbital problems.

Results extend understanding of weak force potential dynamics.

Abstract

Using variational minimizing methods,we prove the existence of an odd symmetric parabolic orbit for the 2-fixed center problems with weak force type homogeneous potentials.