Rick Moeckel
The planar three-body problem describes the motion of three point masses in the plane moving under the influence of their mutual gravitational attraction. Since specifying the positions of all three masses requires 6 coordinates, an alternative point of view is that we are trying to understand a single point moving in a six-dimensional "configuration space". Fortunately, one can use the symmetries of the problem to reduce the number of dimensions to 3. The process of reduction involves some unexpected mathematical objects like complex projective spaces and the Hopf map. To illustrate the ideas, some computer animations of interesting solutions will be shown from both points of view: as three masses in a plane and as a moving point in the three-dimensional reduced configuration space.
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