Binary and triple collisions causing instability in the free-fall three-body problem

Dominant factors for escape after the first triple-encounter are searched for in the three-body problem with zero initial velocities and equal masses. By a global numerical survey on the whole initial-value space, it is found that not only a triple-collision orbit but also a particular family of binary-collision orbits exist in the set of escape orbits. This observation is justified from various viewpoints. Binary-collision orbits experiencing close triple-encounter turn out to be close to isosceles orbits after the encounter and hence lead to escape. Except for a few cases, binary-collision orbits of near-isosceles slingshot also escape.