Periodic orbits in the restricted four-body problem with two equal masses

TL;DR

This paper investigates symmetric periodic orbits in a restricted four-body problem with two equal masses, focusing on configurations near Routh's critical value, extending understanding of orbital dynamics in multi-body gravitational systems.

Contribution

It introduces analysis of symmetric periodic orbits in the restricted four-body problem with two equal masses near Routh's critical value, a novel exploration in multi-body orbital dynamics.

Findings

Identification of symmetric periodic orbits near Routh's critical value

Extension of orbital dynamics understanding in four-body systems

Potential applications to celestial mechanics and space mission design

Abstract

The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian configuration of the three-body problem i.e., they remain fixed at the apices of an equilateral triangle in a rotating coordinate system. A massless fourth body moves under the Newtonian gravitational law due to the three primaries, as in the Restricted three-body problem (R3BP), the fourth mass does not affect the motion of the three primaries. In this paper we explore symmetric periodic orbits of the restricted four-body problem (R4BP) for the case of two equal masses where they satisfy approximately the Routh's critical value.