# The three body problem

# The three body problem

This chapter derives the consequences of scale invariance in the three body problem. Jacobi co-ordinates are introduced. The orbits are geodesics in a certain metric. The three body problem with inverse cube force is shown to be more symmetric. Montgomery's ‘pair of pants’ metric is derived. The orbits are geodesics in a metric of negative curvature on the plane with three points removed. The Virial Theorem is suggested as an exercise.

*Keywords:*
three body problem, Jacobi co-ordinates, negative curvature, geodesics

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