A Generalized approach for computing the trajectories associated with the Newtonian N Body Problem

TL;DR

This paper introduces a generalized method to approximate trajectories in the Newtonian N-body problem, focusing on systems with symmetric masses and bounded motions, where exact solutions are impossible.

Contribution

It develops a new procedure to approximate trajectories for N-body systems with spherical symmetry and bounded positions, extending classical approaches.

Findings

Provides a method for approximate trajectory computation

Applicable to symmetric, bounded N-body systems

Addresses the challenge of non-solvability in the classical problem

Abstract

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.