  In this paper, an approach is developed to solve the three body problem
involving masses which posses spherical symmetry. The problem dates back to the
times of Poincare, and is undoubtedly one of the oldest of unsolved problems of
classical mechanics. The Poincares Dictum comprehensively proves that the
problem is truly insolvable as a result of the nature of the instabilities
involved. We therefore refute the idea of finding exact solutions. Instead, we
develop closed form analytical approximations in place of exact solutions. We
will solve the problem for the case when all the masses involved have
spherically symmetric mass distributions. The method of solution would include
the use of a single mass to replicate the effect of two individual masses on
each body. The derivation of solutions will involve the use of the Lamberts
wave function and the solution will comprise of the position vectors expressed
as explicit time functions.
