  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.
