New families of periodic orbits for the planar three-body problem computed with high precision

TL;DR

This paper introduces a high-precision numerical method to discover 123 new periodic orbits in the planar three-body problem, significantly expanding the known solutions and demonstrating the effectiveness of parallel computation.

Contribution

The paper presents a novel high-precision numerical approach using a modified Newton's method and parallel computing to find new periodic orbits in the three-body problem.

Findings

Found 123 new periodic solutions

Identified 105 new topological families

Demonstrated effective parallel computation

Abstract

In this paper we use a Modified Newton's method based on the Continuous analog of Newton's method and high precision arithmetic for a general numerical search of periodic orbits for the planar three-body problem. We consider relatively short periods and a relatively coarse search-grid. As a result, we found 123 periodic solutions belonging to 105 new topological families that are not included in the database in [Science China Physics, Mechanics and Astronomy 60.12 (2017)]. The extensive numerical search is achieved by a parallel solving of many independent tasks using many cores in a computational cluster.