Integration of Few Body Celestial Systems Implementing Explicit Numerical Methods

TL;DR

This paper revisits the classical N-body problem for small N, using a fourth order Runge-Kutta explicit method to compute trajectories, achieving results consistent with known planetary data.

Contribution

It demonstrates the application of explicit numerical methods to small celestial systems, providing a modern approach to classical orbital calculations.

Findings

Good agreement with planetary trajectories online

Effective use of fourth order Runge-Kutta method

Validates explicit methods for small N celestial systems

Abstract

The $N$-body problem is of historical significance because it was the first implementation of the Newtonian dynamical laws for the description of our Solar System. Motivated by this, the project's goal is to revisit this problem for small $N$ and find a solution for the trajectories of specific two-body and three-body configurations as well as the planetary orbits of our Solar System using a fourth order Runge-Kutta explicit iterative method. We find an adequate agreement in our results with planetary trajectories found online.