Two orbiting bodies are perfectly predictable forever; add a third and chaos creeps in
Newton's laws give a clean, exact formula for how two bodies orbit each other under gravity, valid for all time. Add just one more body and the same equations have no general closed-form solution at all. Henri Poincaré proved this in the 1890s while chasing a prize for solving the three-body problem, discovering instead that such systems can be chaotic: tiny changes in starting position spiral into wildly different outcomes, a finding that helped found modern chaos theory.