A database of high precision trivial choreographies for the planar three-body problem

TL;DR

This paper introduces a high-precision database of 462 trivial choreographies in the planar three-body problem, including 397 new solutions, with detailed stability analysis and decimal accuracy.

Contribution

It develops a modified Newton's method with high precision arithmetic to discover and catalog new trivial choreographies in the three-body problem.

Findings

Computed 462 trivial choreographies with 180 decimal digits accuracy.

Identified 108 linearly stable choreographies, including 99 new ones.

Provided initial conditions and periods for all solutions.

Abstract

Trivial choreographies are special periodic solutions of the planar three-body problem. In this work we use a modified Newton's method based on the continuous analog of Newton's method and a high precision arithmetic for a specialized numerical search for new trivial choreographies. As a result of the search we computed a high precision database of 462 such orbits, including 397 new ones. The initial conditions and the periods of all found solutions are given with 180 correct decimal digits. 108 of the choreographies are linearly stable, including 99 new ones. The linear stability is tested by a high precision computing of the eigenvalues of the monodromy matrices.