A new solution to the three body problem - and more

by Bill Casselman

2. The figure-eight

Here is the basic animation of the figure-eight configuration (using Carlos Simó's data):

The motion of the three bodies looks plausible as the track of a system of three bodies interacting through Newton's law of gravitation.But this could be an illusion.There is much numerical evidence that this is indeed a good picture of a real three-body system.But numerical evidence cannot distinguish between a real periodic motion of three bodies and one that very closely approximates this one for a while and then diverges away from it. The current mathematical interest of this topic is that Chenciner and Montgomery have recently proven that there is a choreographic system that has many features in common with the orbit suggested by computation and is in fact plausibly approximated by the techniques that produced the picture above.

These web essays are designed for those who have already discovered the joys of mathematics as well as for those who may be uncomfortable with mathematics.
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