I've heard that it's apparently impossible to solve a 3-body mechanical problem, but I'd just like to know why. I'm told there are so many integrals and n'th order differential equations that you can't find an analytic solution, only a numerical one, but I want to know is it physically impossible, or just too difficult? I also know it's to do with chaos theory - that a small change in the initial condition makes a huge change in the whole system. But can supercomputers do it? For instance to find the motion between the sun, Earth and moon simultaneously.