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

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) $T^{\ast }=T\mathrm{\mid }E{\mathrm{\mid }}^{3\mathrm{/}2}<80$. 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 $T^{\ast }<80$, corresponding to 12,409 distinct solutions, 236 of which are self-dual.