🪐 The Roche Limit

About this simulation

Every orbiting moon is stretched by its planet's gravity: the near side is pulled harder than the far side, creating a tidal force that tries to tear the moon apart while the moon's own self-gravity tries to hold it together. The Roche limit is the orbital distance at which those two forces balance. Cross inside it and tides win — a loosely-bound body shreds into a ring of debris, exactly as is thought to have formed Saturn's rings.

How it works

• For a fluid (self-gravitating, non-rigid) satellite the limit is d = 2.44 · R_planet · (ρ_planet / ρ_moon)^(1/3), shown here as the translucent shell around the planet.
• Every rock in the moon is also simulated with its own individual Keplerian orbit — inner chunks orbit faster than outer chunks. While the moon is intact, its self-gravity is strong enough to force all chunks to move together as one rigid body.
• Once you drag the moon inside the Roche shell, that cohesion is overwhelmed: each chunk drifts along its own orbital speed, and the differential rotation shears the moon into an elongated stream and eventually a full ring.

Controls

• Orbital distance — how far the moon sits from the planet's centre, in planet radii.
• Moon / Planet density — denser moons resist tides better (smaller Roche limit); denser planets pull harder (larger Roche limit).
• Orbit speed — time multiplier for watching the breakup unfold.
• Auto spiral-in — slowly shrinks the orbit on its own.
• Reform moon — resets the rubble back into a solid sphere.

Did you know?

Comet Shoemaker-Levy 9 was torn into a "string of pearls" by Jupiter's tides in 1992 after passing inside its Roche limit, then fell back and struck the planet piece by piece in 1994 — one of the few tidal disruptions ever directly observed.