N-body problem

Next time you need some entertainment, check out this Planet simulation game. Although "solving" the three-body problem is not possible, simulations are trivial. For a couple goals, try to get a "Mercury" type planet - closer to the Sun than the Earth, highly elliptical orbit. When you get it, it will precess naturally due to Earth's gravitation (rather than due to general relativity as Einstein proved). And a harder goal is getting a Moon to orbit the Earth (I haven't managed yet).