Three-body periodic collisionless equal-mass free-fall orbits revisited

TL;DR

This paper revisits the search for periodic collisionless three-body orbits with equal masses, significantly expanding the known solutions and addressing previous issues in logical consistency and numerical efficiency.

Contribution

The authors conducted a new, more efficient search that identified over 12,000 distinct equal-mass periodic orbits with scale-invariant periods, vastly increasing the known solutions.

Findings

Found 12,409 distinct equal-mass periodic orbits

Identified 236 self-dual solutions

Expanded the catalog of known three-body orbits

Abstract

Li and Liao announced (2019) discovery of 313 periodic collisionless orbits' initial conditions (i.c.s), 30 of which have equal masses, and 18 of these 30 orbits have physical periods (scale-invariant periods) $T^{*}=T|E|^{3/2}<80$. That work left a lot to be desired, however, both in terms of logical consistency and of numerical efficiency. We have conducted a new search for periodic free-fall orbits, limited to the equal-mass case. Our search produced 24,582 i.c.s of equal-mass periodic orbits with scale-invariant period $T^{*}<80$, corresponding to 12,409 distinct solutions, 236 of which are self-dual.