Hiroaki UMEHARA

Communications Research Laboratory
893-1, Hirai, Kashima, Ibaraki, 314-0012
Japan
ume@crl.go.jp

Escape and non-escape orbits close to triple collision in the planar three-body problem

Abstract : The existence of escape and non-escape orbits arbitrarily close to the triple-collision orbits of equilateral type is considered with the aid of the blow-up analysis in the planar three-body problem with zero initial velocities and equal masses. It is found that any binary-collision orbit sufficiently close to triple collision leads to escape after the first triple encounter. In order show this, it is proved that the escape criterion is formulated in the planar isosceles problem and translated into the words of blow-up variables.