Saturday, July 19, 2008

Interplanetary billards

If you've ever wanted to play at being a god then perhaps you'll find the University of Chicago's solar system simulator to be as much fun as I did. Here you get to set up moons, planets and stars, press the start button and see what happens. Most of the time it's a demolition derby. The bodies are obviously made of glue, because nothing escapes the frequent collisions.

Making any orbital system stable with 3 or more bodies is well known to be quite difficult. However, it's easy to see in the simulator that if you keep the masses of all the bodies but the central sun down then it gets much simpler, at least on the time scales on which I can be bothered to keep watching. Starting 3 planets at distances of 142, 100 and 50 with velocities of 130, 150, 170 gets you a nice 3-planet solar system which might be OK to live in as long as the planets are much smaller than the star. Increase their sizes and things get interesting in the sorts of ways that wouldn't give evolution time to work its magic.

There are ready made systems with planets, moons and even a dual star where one of them has a planet. When I got tired of playing with them I tried making more of my own. Two planets at radius 140 and 160 with speeds of 137 and 103 will make a dual planet system that looks fairly stable. This would be something like having a moon the size of a planet, not entirely unlike the world in Ursula K. LeGuin's The Dispossessed. Again, it works best with smallish planets.

The somewhat more serious, but not nearly as fun simulations at Princeton also illustrate that making stable several-body solar systems is just not an easy thing to do. Even some of the ones that start off well, such as the 3-body Lagrange orbit or FigureEight5 quickly degenerate into what looks like a drunken game of pool, played with magnetic balls. Still, who would have thought that the figure of eight with 3 bodies was stable?

So it's vital that You budding solar system building deities note how important it is to keep the size of orbiting satellites down if You want more than two of them in your system. If You keep them small enough, You can even have a stable million-body configuration, as shown in this paper about Saturn's rings. I may be old-fashioned, but I always feel that having at least one planet with prominent rings in your solar system shows an attention to detail that is appreciated by any sentient life You manage to breed.

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