N-Body Problem

As described above, there is no analytic solution for the N-body problem. However, it is possible—at least in principle—to solve the N-body problem numerically. A qualitative description of this is as follows. Suppose you have four bodies stars for instance—all moving around one another under the influence of each other's gravity. At a given time, we can calculate the gravitational force felt by star 1 using Newton's law of universal gravitation; this force is simply the sum of the forces exerted by the three other stars. We could do the same calculation for the other three stars. Knowing the force acting on the star, we can predict its motion, but only for a short period of time, since all the stars are moving and the gravitational force they exert on one another is constantly changing. Once the stars have moved a short distance, we need to recalculate the force, rederive the direction and velocity of each star, and allow them to move some more—again, only for a short distance, at which point yet another calculation of the various forces will be required.

If the description above sounds tedious, it is! This is what scientists call an iterative process, a process in which the same steps are repeated many times. To predict the evolution of a cluster of stars, one might have to repeat the process described above thousands, even hundreds of thousands of times. Obviously, it would be sheer madness to attempt this on paper, and indeed, significant N-body calculations were nonexistent prior to the invention of computers.