Algodoo

Pink is planet (or sun)
Orange is field of dust and rocks
Teal is moon (or planet)
Without the moon, the rings form a relatively uniform, undisturbed distribution.
With the moon, The rings form a light inner band and dense outer band, with a gap where the moon orbits. In some cases, resonant gams can form as well, gaps at distances such that objets with such distance from the planet will be in a resonant frequency with the moon. However, with so few objects, it isn't clear if this simulation forms any resonant gaps.