Many objects in stable orbit

I used the “Fracture Tools” add on to make a ton of small rock-like objects and then used the Vortex effector to spin them out into a rough ring-like formation. But now I want them to orbit in such a way that at least a majority of the rocks don’t fly out into space.

I tried using a combination of the Vortex effector (for the spin) and the Force Field effector with a negative value to keep them pulled in, but I can’t find a set of values for each to keep it stable (they always pull back in or fly away entirely). Is there a relatively easy way to do this?

Right now I’m faking it by just doing short animations with many camera cuts before they all fly away.