Three Classes of Newtonian Three-Body Planar Periodic Orbits

TL;DR

This paper numerically identifies and classifies periodic three-body orbits with equal masses and zero angular momentum into four classes based on symmetry, revealing new orbit families and initial conditions.

Contribution

It introduces a topological classification of three-body orbits into four classes, expanding the known families and providing initial conditions for multiple new orbits.

Findings

Identified 15 initial conditions for periodic orbits.

Classified orbits into four symmetry-based classes.

Discovered new orbit families within the classes.

Abstract

We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic three-body orbits into families, which fall into four classes, with all three previously known families belonging to one class. The classes are defined by the orbits geometric and algebraic symmetries. In each class we present a few orbits initial conditions, 15 in all; 13 of these correspond to distinct orbits.