A chaotic toy

Here is a fun toy illustrating chaos--the three body problem.

Lots of fun. Here are some screenshots.

Try two bodies and see for yourself sensitivity to inital conditions.

Both planets start off with almost the same initial conditions, and as time progresses they drift farther apart. The rate of this drift (which would be described by the Lyapunov exponent) is tied to the inital mass you give Sun 1 (on the left). When the value is very low, the Lyapunov exponent is similarly low, and it takes a long time for the orbits to diverge.

This is a lot like a game we used to have years ago, except you would set the initial position and velocity vector for a number of celestial bodies around a central Sun. It was great fun having them collide, and vexatious trying to make a stable solar system.