Orbital Resonance

Abstract

Henri Poincare showed in 1887 that the general three-body problem has no analytical solution. Three-body systems can be chaotic, meaning that small variations in initial conditions can cause large variations in outcomes. This can lead to systems that have counterintuitive behavior. Here we investigate a specific case where two Earthlike ‘planets’ with the same radius and period are placed in orbit around a ‘Sun’. Intuition would suggest that the two small bodies would attract due to gravitational forces and eventually collide. What is observed is that the separation distance between the two planets oscillates and never drops to zero. This phenomenon of satellites affecting each other’s orbits in a periodic pattern is known as orbital resonance. The aim of this study is to investigate and analyze this orbital resonance.