How to Solve the Three Body Problem

Newton found Kepler's laws, which were these beautiful regularities of planetary motion emerging as an approximation. He devoted more time and a lot of space in the Principia to understanding the motion of the moon - he said it was the only problem that made his headache. Celestial mechanics is very much a living science and has been reinvigorated by the availability of high-speed computers or space probes. It's all based on Newton's laws and of motion and gravity, which again you can write down very, very simply,. but solving them gets you involved in solving those equations get you involved in very complex situations very quickly.