On the periodic orbits of the circular double Sitnikov problem

TL;DR

This paper extends the classical Sitnikov problem to a four-body scenario with two secondary bodies, analyzing the existence and properties of periodic orbits on energy surfaces using symplectic regularization.

Contribution

It introduces a novel 2+2 restricted four-body problem extending the Sitnikov problem and studies periodic orbits on energy surfaces with regularization techniques.

Findings

Identification of energy surfaces with periodic orbits

Extension of solutions beyond collisions via symplectic regularization

Analysis of the set of energy surfaces containing periodic orbits

Abstract

We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries evolve, so almost every solution is a collision orbit. We extend the solutions beyond collisions with a symplectic regularization and study the set of energy surfaces that contain periodic orbits.