Brian Hayes in American Scientist:
Isaac Newton’s universe was a cozy, tidy place. Gathered around the sun were six planets, a handful of moons and the occasional comet, all moving against a backdrop of stationary stars. Newton provided us with the mathematical tools needed to compute the motions of these bodies. Given initial positions and velocities, we can calculate the forces acting on each object, using Newton’s law of universal gravitation. From the forces we can determine accelerations, and then update the positions and velocities for the next round of calculations. This scheme of computation is known as the n-body method. Perhaps Newton himself could have put it to work if he had had suitable computing machinery.
Today we have the computers. On the other hand, our universe is far larger and more intricate than Newton’s. Now the solar system is merely a speck in a spiral galaxy of several hundred billion stars. Our galaxy drifts among billions of others, which form clusters and superclusters and a whole hierarchy of structures extending as far as the eye (and the telescope) can see. Those objects are getting farther away all the time because the universe is expanding, and moreover the expansion is accelerating. Strangest of all, the luminous matter of the galaxies—everything we see shining in the night sky—makes up less than one-half of 1 percent of what’s out there. Most of the universe is unseen and unidentified stuff known only as “dark matter” and “dark energy.”
Given this profound change in the nature and the scale of the known universe, I find it remarkable that computer simulations of cosmic evolution can still rely on n-body algorithms rooted in the principles of Newtonian mechanics.