## Saturnian Ring System Simulation

If the Java applet fails to start due to *Java Security* issues,
click
here.

With this applet, you can investigate mass ratios and eccentricities that lead to stable ring
systems vs. unstable ones.

The parameter *ecc* controls the eccentricity. A value of zero produces circular orbits. Positive values produce an eccentric ring.

For a circular ring,
if the mass of each ring body is no more than
2.3 times the mass of Saturn divided by the cube of the number of ring
particles, then the system can be expected to be stable; otherwise not. See
Linear Stability of Ring Systems
for the derivation of this inequality.

In the applet below, *M* is the mass of Saturn (in Earth-masses), *m* is the
mass of an individual ring body, and *n* is the
number of ring bodies.

The textfield labeled gamma is the ratio *m*n^3/M*. If
this value is smaller than 2.3, the system will be stable. Large values will
be unstable.

You will find that you don't need to increase m very much to
make the system unstable. If you set "warp" to 100,
the integrator will show the instability very quickly.
Give it a whirl.

Notes: (1) 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.

(2) Due to unresolved technicalities, the time-step parameter *dt* can only be changed
if *'ecc'* is set to zero (i.e., circular orbits).

(3) For WebGL version of applet,
click here.