On the Figure-of-Eight and Nearby Solutions of the Three-Body Problem
The figure-of-eight solution is unusual in being a stable solution of the planar three-body problem. To study its stability, we first implement a numerical integrator, the Runge-Kutta-Fehlberg method, and demonstrate that it is accurate enough to integrate the figure-of-eight for thousands of periods. To examine what effect initial perturbations have on it, we define two perturbation schemes, one
