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

Abstract

Li and Liao announced (New Astron 70:22–26, 2019, arXiv:1805.07980v1) 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∗<80. We revisited this work with the intention to improve both, its logical consistency and the numerical efficiency of the method. 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.