Planetary Rings (2D) — Keplerian Shear & Cassini Division

Preset

Ring

Particles 14000

Inner radius 1.30

Outer radius 2.30

Time speed 1.0×

Shepherd moon

Enable (opens a gap)

Moon radius 1.95

Live state

Particles

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FPS

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Inner period

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Outer period

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Keplerian shear (outer / inner)

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How it works

Each particle orbits at a fixed radius a with angular speed (mean motion) ω = a^−3/2 — Kepler's third law in units where the planet's radius is 1. Inner particles complete far more orbits per second than outer ones, the differential shear visible as the ring spins.

The shepherd moon does not compute real gravity: when the ring is rebuilt, any sampled radius that falls inside a fixed band around the moon's position is rejected, leaving a clean, empty annulus — the same visual result as the resonant gap-clearing Mimas produces around Saturn's real Cassini Division.

Orbital period follows T ∝ a^3/2; the "shear" stat below is the outer-edge period divided by the inner-edge one, i.e. how many inner-edge orbits pass per single outer-edge orbit.

Planet Shepherd moon Ring particle