A Generalized approach for Approximate Solutions to the N Body Problem

TL;DR

This paper introduces a generalized method to approximate solutions for the classical N body problem by reducing it to multiple two-body problems, applicable to systems with symmetric mass distributions and low angular velocities.

Contribution

It presents a novel approach that approximates the N body problem using N two-body analogues, expanding the toolkit for tackling complex gravitational systems.

Findings

Applicable to systems with symmetric mass distributions

Effective for low angular velocities (< 1 rad/s)

Provides approximate solutions where exact solutions are infeasible

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.