Saturn Rings: Orbital Mechanics (2D)

This 2D companion strips the 3D Saturn scene down to the celestial mechanics actually driving it. Thousands of ring particles each get their own orbital radius and their own angular speed set purely by Kepler's third law (ω ∝ r⁻¹·⁵), so instead of spinning as one rigid disk the ring visibly shears into a spiral — a direct, real demonstration of differential rotation. A dashed Roche-limit circle is computed live from Saturn's real mean density against an adjustable moon/particle density, showing exactly why loose material inside that radius can never pull itself together into a moon. And a Mimas-style shepherd moon, orbiting outside the ring, carves a real Cassini-Division-style gap at its 2:1 inner Lindblad resonance radius through repeated resonant kicks each orbit — raise the moon's mass and watch the gap visibly widen; drop it to zero or uncheck the moon and the gap fills back in.