Three Body Problem―Its Past and Present

Abstract

The three body problem is reviewed. Euler and Lagrange found collinear and equilateral triangular solutions, respectively. However, attempts for searching a general solution for the three body problem finished soon after Poincare discovered chaotic behaviors in the restricted three body problem. In the general relativistic gravity, the three body problem is revisited. The post-Newtonian counterparts of the collinear and triangular solutions are obtained. The relativistic hierarchical triple system including a millisecond pulsar J0337+1715 allows a direct test of the strong equivalence principle. Moreover, a possible relevance of the three body system to gravitational wave astronomy is also mentioned.