A Generalized approach for computing the trajectories associated with   the Newtonian N Body Problem
  The Classical Newtonian problem of describing the free motions of N gravitating bodies which form an isolated system in free space has been considered. It is well known from the Poincares Dictum that the problem is not exactly solvable. Sets of N body systems composed of masses having spherical symmetry, appropriate angular velocities (< 1 rad/s) and bounded position vectors are examined. A procedure has been developed which yields expressions approximately defining the trajectories executed by the masses. 
AbuBakr Mehmood, Syed Umer Abbas Shah and Ghulam Shabbir