The N-Body Problem

by Brandon Warburton
Faculty advisor: Dr. Shawn Stone

The study of orbital dynamical systems has been of interest since the time of Newton.  The problem of solving for the motion of two bodies under mutual gravitation can be solved in closed form.  However, this is not the case when three or more bodies are considered. These mutually attractive systems are called N-body systems (N being the number of discrete bodies in the system) and the process of determining the motion of the bodies’ is called the N-body problem.  Thanks to the development of numerical methods and the advent of the computer, the N-body problem has become much easier to investigate and understand. 

The goal of this project is to evaluate three numerical methods that are used to solve the equations of motion for a simple N-body system (in this case, a special 3 body problem). The methods evaluated are the Euler, Runge-Kutta Order Four, and an adaptive Runge-Kutta Order Four.  It will be shown that the former two lack the accuracy required to produce a satisfactory result and that the adaptive Runge-Kutta Order Four, though slower, is the best choice for accuracy when solving the N-body problem..