A Generalized approach for Approximate Solutions to the N Body Problem

Abstract

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.