  An approach is developed to find approximate solutions to the classical
Newtonian problem of N bodies. Sets of N gravitating bodies having spherically
symmetric mass distributions, small angular velocities (< 1 rad/s) and bounded
position vectors have been taken into consideration. In addition, it is assumed
that the masses form an isolated system in free space and perform free
gravitating motion. Although the problem is not exactly solvable, a new
approach will be developed to find approximate solutions using N number of two
body motion analogues.
