The aim of this project was to numerically simulate the orbital motion of Saturn's co-orbital moons — Janus and Epimetheus — using the Runge-Kutta 4th Order (RK4) method in Julia. This simulation highlights the fascinating orbital swap mechanism these two moons exhibit, despite sharing nearly the same orbit.
Janus and Epimetheus are two small moons of Saturn that share a similar orbit and exchange positions approximately every four years due to gravitational interaction. This makes them a natural example of a restricted three-body problem. To simulate their motion, Newton's laws of motion and universal gravitation were applied.
The simulation successfully captured the orbital swap behavior of Janus and Epimetheus. Their mutual gravitational interaction results in one moon moving slightly inward and speeding up, while the other moves outward and slows down — effectively causing them to exchange orbits without collision.