The Three-Body and n-Body Problems

This project explores the multi-body problem according to Newton's Laws of Gravitation in two dimensions. First, I will derive and numerically solve the differential equations which govern the motion of the three-body problem. Then, I will explore the chaotic nature of the system through a variety of demonstrations, plots, animations, and Explore windows. After, I will look at a few special periodic solutions to the three-body problem. Next, I will apply this system to astronomy, exploring the gravitational orbits that comprise our solar system. Finally, I will to generalize the three-body problem into a higher order n-body system (specifically, five bodies).