Roche Limit Calculator

Saturn's rings are almost entirely within Saturn's Roche limit for icy bodies (~2.44 Saturn radii ≈ 142,000 km). Any moon that drifted too close was torn apart, and material inside the Roche zone can never accrete into a moon — tidal forces undo gravity's work faster than it proceeds. The Moon orbits Earth at ~384,400 km, safely outside Earth's fluid Roche limit of ~18,400 km. The classic two-model split matters in practice: rigid bodies (rocky asteroids, solid moons) have internal structural strength that adds to self-gravity, so the disruption criterion is harder to meet — c = 1.26. Fluid bodies (comets, very porous rubble piles, molten objects) have no internal strength, so they begin deforming as soon as tidal force exceeds surface gravity — c = 2.44. Comet Shoemaker-Levy 9 broke into 21 fragments in 1992 when it passed inside Jupiter's Roche zone, then those fragments fell into Jupiter in 1994 in a famous string of impacts. Tidal disruption events (TDEs) around white dwarfs and neutron stars are the stellar-mass version: a planet strays too close, exceeds the Roche limit, and forms a bright accretion disk.

Picture a moon held together only by its own gravity. As it nears a planet, the planet tugs harder on the moon's near side than its far side, and that difference stretches the moon. Cross the Roche limit and the stretching wins, tearing the moon apart. The surprising part: the moon's mass cancels out of the equation entirely. Only the two densities and the planet's radius set the distance, so a denser moon can safely orbit closer than a fluffy one.

Phobos, the larger Martian moon, orbits below the synchronous distance, so tidal drag is spiraling it inward by roughly 2 meters per century. In about 30-50 million years it will cross Mars's Roche limit and shatter, likely spreading into a temporary ring around the planet. The strange parallel grooves scarring Phobos may already be stress fractures from tidal stretching — a moon showing its first cracks long before the final breakup.