The Two-body problem

The two-body problem is a fundamental issue in physics and astronomy that involves predicting the motion of two objects who exert gravitational force on each other. For example, consider the Earth and the Moon. The challenge is to determine their paths based on their positions, masses, and the gravitational force between them. While the equations governing their motion are straightforward, finding precise solutions can be complex, especially over long periods, due to the influence of factors like speed and distance. This problem serves as a foundation for understanding more complicated interactions in astrophysics.