Saturnian Ring System Simulator ← All n-Body Animations

With this applet, you can investigate mass ratios that lead to stable ring systems vs. unstable ones.
Let M denote the mass of Saturn,
let m denote the mass of each of the n small orbiting bodies and
let γ = n³m/M.
For n > 1, it is a known fact that the system is stable if and only if n > 6 and γ < 2.298.
For the proof of this inequality, see:
    Linear Stability of Ring Systems.Astronomical Journal, 133:656-664, 2007.

If you set "Warp" to 100, the integrator will show the instabilities very quickly. Give it a whirl.

A fun one to watch is n=20 with 5 rings. Click on "Toggle Counter-rotation" and set "Warp" to 10.

Note: The warp parameter only controls how often the screen is updated---large values mean that many time steps of the integrator are performed between each screen update. This makes the simulation run much faster as updating the screen image is more time consuming that a step of the integrator.