In a previous blog entry, I described various solar system simulations I played around with in high school. These were perhaps more properly termed "gravity simulations" since what I simulated was not a solar system per se but rather Newton's laws of gravity and motion as applied to a bunch of swirling rocks, which would produce a solar system if the conditions were set up correctly. The orbits that you saw in these programs appeared naturally out of the math, as emergent properties of the equations - they were not explicitly programmed.
This is a key feature of the simulation; I did not start out by assuming that the orbit would be an ellipse, or that there would even be an orbit at all. Rather, I started from the basics: the laws of gravity and motion, and saw what came out of them.Read more