You know, regarding my question to Lonesome in Massachussets about a theoretical upper limit on the number of possible orbits, we may be looking at a situation where there are an infinite number of possible three-body orbits out there. Wouldn’t that be wonderful? Could you imagine the possibilities for life, and all the different environments it might inhabit?
Laplace, in Mécanique Céleste claimed to have "proven" that the solar system is stable. Newton thought that God had to intervene periodically to prevent chaotic disintegration of the solar system. When Napolean asked Laplace about the place of God in his universe, Laplace is said to have replied, "Sire, je n'ai pas besoin de cette hypothèse". (Sire, I have no need of that hypothesis.) We know now that Laplace was wrong, but wrong with style. He was very right about a great number of other things.
I don't think you can properly introduce the three body problem without at least a mention of Poincaré.