On Chenciner-Montgomery's orbit in the three-body problem

Recently A. Chenciner and R. Montgomery found a remarkable periodic orbit for a three-body problem by variational methods. On this orbit all masses chase each other along a figure-eight circuit without any collision, and the solution curve is indeed a minimizer of the action functional on a properly chosen path space. One technical difficulty, where numerical integration had been used in their proof, is to show that the minimizing orbit does not experience any collision. In this paper a short analytical proof will be presented.