The best surprises come from unexpected places

This time I’m back with some more physics visualizations with a flat 2d canvas. I’m skipping over some demos of basic physics to get at some orbital mechanics animations that I found surprising. I’ve derived and calculated solutions for two objects gravitationally bound to each other from my freshman physics classes back in college. Then I did it again with more sophisticated mathematics, and again when I did quantum mechanics of the atom. As I think about it, I was writing BASIC programs back in high school to simulate the 3 body problem. All of those equations and simulations had some pretty severe limits. For one they only involved one or two bodies in motion. What you are looking at here are roughly 185 test particles orbiting one massive object like planets in circular orbits around the sun. While each of these test particles start close to each other, their mutual interactions are ignored. If they weren’t there would be much more complicated dynamics going on. What caught me off guard was how fast the inner bodies were moving in relation to the outer planets. Whenever I had pictured the slow ponderous motion of the planets, I had pictured them moving more or less like a uniform disk. Whoa, was I wrong. The inner bodies are just whipping around at a frenetic pace, while the outer ones just plod along at a snail’s pace. In fact there is a rather conspicuous divergence in the speed of motion as the distance between the particles decreases. I plan to have something more to say about that in the future. You might be wondering why I picked 185 test bodies? In this case it comes from looking at orbits in the range of 5 to 375. Which corresponds to Mercury (.4AU) to Neptune (30AU) a ratio of 1 to 75. If our solar system was build from evenly spaced bodies in circular orbits, this is what it would look like. So when I set this up, I never expected the slow graceful curve of the spiral slowly winding around the center. As I play with it, it seems so obvious, but that’s why I find this stuff so fascinating. I’ve calculated and simulated these same orbits for well over 20 years now, and they can still surprise and awe me with just the slightest change of perspective.

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