Gravitational Bracelet

In the applet shown here, there are n masses each having the same mass m (m = 1 is one Earth mass).

The bodies are gravitationally attracted to each other.

The radius of the ring is 0.00101251 AU (which equals the radius of the orbits of Saturn's coorbiting moons Janus and Epimetheus).

In addition to gravity, each adjacent pair of bodies is attached by a spring (the springs are not shown in the applet).

Hence, each body has two springs pulling on it. The net spring force is directed toward the center of the ring. The spring constant is determined so that this net force is equivalent to the gravitational attraction of a central mass of M (the default value of 95.2 corresponds to the mass of Saturn).

Changing M changes the strength of the spring. Empirically, this "bracelet" of masses is stable if M is larger than 0.2 and unstable if M is smaller than 0.1. If you set "warp" to 100, the integrator will show the instability very quickly. Give it a whirl.

The textfield labeled gamma is the ratio m*n^3/M.

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.

     
Delay between frames = ms.   Warp = .   dt = yrs.
M =   m =   n =  
Drag mouse to rotate 3D model. Hold shift key to zoom in and out.
Updated 2011 Jan 02