Saturn’s rings flatten because collisions dissipate energy while angular momentum stays fixed

Evidence

Why should orbiting debris around a planet collect into a flat ring in the first place? Presumably, the debris around Saturn was originally much more broadly distributed, continuously colliding like a swarm of blindfolded bumper car drivers. The explanation for the formation of rings appeals to angular momentum, which must be preserved in each collision. Conservation of angular momentum, appropriate to rotating bodies, is related to the more familiar conservation of ordinary (linear) momentum: add up the masses times their velocities before the collision, and it will be the same after the collision, with the new masses and the new velocities. The whole swarm of particles, collisions and all, must maintain a constant total angular momentum. Total energy is conserved too, but collisions are messy: part of the energy of motion before the collision becomes heat, eventually radiated into space and removed from the orbital energy. The orbital energy therefore declines as long as there are collisions, but it cannot decline forever: a minimum of orbital energy is required to maintain the fixed angular momentum. So the decline of orbital energy and therefore the collisions must stop at some point. The only way to keep collisions from happening is freeways in the shape of rings, with particles in the same lane going the same direction with the same speed. If the lanes were not flat, particle orbits would have to cross and collisions would still happen. A flat ring structure, therefore, results from the requirements of minimizing the orbital energy while keeping the angular momentum fixed. Flat indeed: the rings are for the most part only 10 meters thick! — Eric J. Heller, Why You Hear What You Hear- An…, 923

Categorization

• XREF: Connects to conservation laws and resonance mechanics broadly — the same energy-minimization-under-fixed-constraint reasoning used elsewhere in physics, and a good concrete analogy for how systems settle into minimum-energy configurations.