Saturn Rings: Orbital Mechanics (2D)

Ring Particles

Particle count 3000

Outer edge (ring spread) 2.30 R♄

Roche Limit

Moon/particle density ρ_m 1.00 g/cm³

Shepherd Moon (2:1 resonance)

Shepherd moon present

Moon mass (perturbation strength) 1.50×

Live Readout

Roche limit

0.00 R♄

Resonance gap

0.00 R♄

Particles in gap band

Elapsed time

0.0 s

Inner period T(r_in)

0.0 s

Outer period T(r_out)

0.0 s

How it works

Every particle orbits Saturn on its own circle of radius r (in Saturn radii R☿). Kepler's third law fixes its angular speed purely from r — no forces are faked:

ω(r) = ω0 · r^(-3/2)     (T ∝ r^1.5)

so inner particles sweep around faster than outer ones — real differential rotation, the same reason the rings shear into a spiral instead of rotating as a rigid disk. Particles are colored by their starting angular sector so you can watch the shear happen.

Roche limit — the radius inside which tidal stretching from Saturn's gravity exceeds a body's self-gravity, so loose ring material can never clump into a moon there:

d_Roche = R♄ · (2·ρ_Saturn / ρ_moon)^(1/3)

ρ_Saturn is fixed at Saturn's real mean density (0.687 g/cm³); the density slider sets ρ_moon. Denser candidate moons have a smaller Roche limit — icy material (~1 g/cm³) gives a limit close to the real inner rings.

Resonance gap — a shepherd moon orbiting at r_moon perturbs any particle whose orbital period is a simple ratio of its own. At the 2:1 inner Lindblad resonance (period = T_moon / 2, so r_gap = r_moon·(1/2)^(2/3), the same relation behind Mimas carving the real Cassini Division) repeated resonant kicks push particles away from r_gap every orbit, clearing a gap that widens as moon mass increases. Set moon mass to 0 or uncheck the moon and the gap fills back in.

Saturn Roche limit Resonance gap Shepherd moon