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Planetary rings consist of orbiting particles (mm to km in size) held by gravity and dynamical resonances against tidal disruption. Ring structure (gaps, spokes, spiral density waves, shepherd moons) reflects orbital resonances with satellites and collisional processes; rings are transient features on billion-year timescales.
From your study of satellite formation and orbital mechanics, you understand how gravity and orbital dynamics govern the motion of bodies around a planet. Planetary rings are a natural extension of these ideas — instead of a few large moons, imagine millions of particles, each on its own orbit, collectively forming a thin, flat disk. The reason rings are flat is the same reason protoplanetary disks flatten: collisions between particles on inclined orbits dissipate vertical energy while conserving the net angular momentum, forcing the system into the orbital plane.
The existence of rings depends on a critical boundary called the Roche limit — the distance within which a planet's tidal forces exceed the self-gravity holding a body together. Inside this limit, a moon or large chunk of debris would be torn apart rather than coalescing. Ring particles persist precisely because they orbit within or near this zone: they are close enough to the planet that tidal forces prevent them from accreting into a moon, yet gravity keeps them in orbit. Saturn's main rings, for example, lie well within Saturn's Roche limit for ice.
Ring structure is far from featureless. Orbital resonances with nearby moons create some of the most dramatic features. When a ring particle orbits with a period that is a simple fraction of a moon's period (say, 2:1), it receives periodic gravitational kicks at the same point in its orbit, amplifying its eccentricity until it is swept out of that region — creating a gap. The Cassini Division in Saturn's rings is maintained this way by the moon Mimas. Conversely, shepherd moons — small satellites orbiting just inside and outside a narrow ring — gravitationally confine ring particles, keeping the ring sharp and well-defined. Uranus's epsilon ring is a classic example, bounded by the moons Cordelia and Ophelia. Other structures include spiral density waves, which propagate outward from resonance locations like ripples in a pond, and spokes — transient radial features in Saturn's B ring likely caused by electromagnetic forces on charged dust grains.
A key insight is that rings are geologically transient. Collisions between ring particles gradually dissipate energy, causing particles to spread: inner particles spiral toward the planet while outer ones drift outward. Meteoroid bombardment darkens and erodes ring material. Without some replenishment mechanism — disruption of a comet, breakup of a small moon, or ongoing volcanic supply as with Enceladus feeding Saturn's E ring — rings would disappear on timescales of tens to hundreds of millions of years. The youthful appearance of Saturn's main rings has led to serious debate about whether they formed recently (perhaps only 100 million years ago) rather than with the planet itself 4.5 billion years ago. Ring systems thus offer a window into ongoing dynamical processes, not just frozen relics of formation.