Three bodies, one dance. Newton’s three-body problem has no general solution, and almost every start ends in chaos, with one star thrown out. These are the rare exceptions: periodic orbits found by computer, where three equal stars chase each other along a closed path for ever. Click to nudge the stars and watch the dance fall apart.
Three bodies, one dance
Two stars orbit each other for ever. Add a third and, almost always, the dance turns to chaos.
How it works
An unsolvable problem. Since Newton, the motion of three bodies under gravity has had no general formula. Henri Poincaré showed in the 1890s why: tiny changes in the start grow without limit. Almost every start ends with one star thrown out.
The exceptions. A few starting points are perfect. In 2000 Alain Chenciner and Richard Montgomery proved that three equal stars can chase each other along a figure eight, and in 2013 Milovan Šuvakov and Veljko Dmitrašinović found new families by computer search: butterflies, moths, a yin-yang, a dragonfly. Each one closes on itself after one period.
How fragile. Click near a star to give it a tiny push. The pattern holds for a while, then frays.