three-body problem

The three-body problem involves predicting the motions of three objects under their mutual gravitational attraction, like three planets or stars. Unlike two objects, whose paths can be precisely calculated, three objects create complex, often unpredictable movements due to their gravitational influences on each other. Small changes in initial conditions can lead to vastly different outcomes, making precise long-term predictions extremely difficult. This problem is fundamental in celestial mechanics and highlights how systems with three or more interacting bodies can exhibit chaotic behavior, where exact solutions are generally impossible, and scientists rely on computer simulations to understand their dynamics.