That is, until Einstein comes along and ruins it. Check out this thought experiment that shows how, under Newtonian physics, five bodies can complete a task an infinite number of times in a finite amount of time.

The physics of two planets orbiting each other in a stable system is easy to work out with math. Simply take the speed of the planets, and their relative masses, and you can find a stable orbit for them. Introduce a third planet, and things get tricky. Although relatively stable systems of multiple masses are possible - look at the solar system - they're tought to puzzle out on paper. With gravity, speed, and location changing with every motion of three different bodies, they're very volatile. Forces pull on each body in surprising ways. Often, one of the objects gets kicked out of system, taking energy with it, leaving the other two objects to drop into a lower, but stable, orbit.

Ah, but what happens if there are five bodies? This is an idea that physicist Jeff Xia thought of in the late nineties. First, take two stable systems. Each consists of two orbiting bodies of equal weight. One system spins one direction, while the other spins the other direction. They both lie in planes that are parallel to each other, as if they were rolling in circles on separate shelves of a bookcase. Now take a fifth body, a considerably lighter one, and set it moving back and forth between the two systems. As it moves through the center of mass of one system, it destabilizes the whole thing and gets kicked back towards the other system. Once it reaches the other system, the same thing happens.