A Simple Analytical Formulation for Periodic Orbits in Binary Stars

TL;DR

This paper presents a straightforward analytical approximation for periodic orbits in binary star systems, enabling quick calculations without complex numerical integrations, based on classical mechanics with added necessary terms.

Contribution

It introduces a simple analytical formulation for periodic orbits in binary systems, improving efficiency over traditional numerical methods.

Findings

Analytical expressions closely match simulation results.

The method simplifies calculations of periodic orbits.

No numerical integration needed for these approximations.

Abstract

An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary terms to give a fairly good approximation that we compare with simulations, resulting in a simple set of analytical expressions that solve periodic orbits on discs of binary systems without the need of solving the motion equations by numerical integrations.