Refresher: three masses interacting under gravity. But unlike two-body motion (think Earth–Sun), add just one more mass—and Newton’s equations can’t be solved neatly anymore. That’s because the system becomes nonlinear and chaotic: tiny changes in initial conditions explode into huge differences over time. There’s no closed-form equation that predicts all future motion for arbitrary starting positions. Still, physicists have found workarounds: • Numerical simulations: approximate trajectories step-by-step; useful but sensitive to rounding errors and limited by computing power. • Special analytical solutions: a few rare configurations (like Lagrange points or figure-eight orbits) that stay stable—mathematically elegant, physically fragile. • Perturbation methods: assume one mass is much smaller, expanding around the two-body case (used in celestial mechanics and spaceflight). Each “solution” works only within boundaries—outside them, chaos reigns again. The three-body problem is ...