Closed Form Approximations for the Trajectories of the Three Body Problem

The problem of describing the free motions of three gravitating bodies under each others gravitational influence is one of the oldest of unsolved problems of classical mechanics. Henry Poincare proved in his dictum that due to the nature of the instabilities involved in the problem, it could not be solved. Yet closed form approximations for the problem can be found and it is on these lines that we will explore the problem. It will be shown that closed form approximations for the associated trajectories can be found.