Closed Form Approximations for the Trajectories of the Three Body Problem

TL;DR

This paper explores the classical three-body problem, demonstrating that despite its inherent instabilities, closed-form approximations for the trajectories of three gravitating bodies can be derived.

Contribution

The paper introduces a method to obtain closed-form approximations for the trajectories in the three-body problem, addressing a long-standing challenge in classical mechanics.

Findings

Closed-form approximations for three-body trajectories are achievable.

The approach provides insights into the motion despite the problem's inherent instabilities.

The results offer a new perspective on classical gravitational dynamics.

Abstract

The problem of describing the free motions of three gravitating bodies under each others gravitational influence is one of the oldest of unsolved problems of classical mechanics. Henry Poincare proved in his dictum that due to the nature of the instabilities involved in the problem, it could not be solved. Yet closed form approximations for the problem can be found and it is on these lines that we will explore the problem. It will be shown that closed form approximations for the associated trajectories can be found.