Periodic orbits in the free-fall three-body problem

Periodic solutions of the general free-fall three-body problem are investigated for the case of equal masses. The initial conditions are chosen on a Hill surface in form space. The use of the form space reduces the dimension of the problem and makes it possible to represent the region of possible initial conditions on the Hill surface, together with a color scale. The regions obtained can be used to improve the precision of the initial conditions for the periodic orbits in the free-fall three-body problem.