Roche limit
The minimum orbital distance at which tidal forces overcome self-gravity; closer than this, a moon is torn apart.
Definition
The Roche limit is the orbital radius inside which the tidal force from a planet exceeds the self-gravity holding a satellite together. For a fluid body, the Roche limit is approximately d = 2.44 R_p (ρ_p / ρ_s)^(1/3), where R_p is the planet's radius and ρ_p, ρ_s are the densities of planet and satellite.
Édouard Roche derived this result in 1848 while studying the stability of satellites. Saturn's rings lie almost entirely within Saturn's Roche limit — they are the debris of a moon (or moons) that ventured too close, or material that could never accrete into a moon in the first place. When comet Shoemaker-Levy 9 passed inside Jupiter's Roche limit in 1992, it broke into a chain of fragments that slammed into Jupiter two years later. The Roche limit sets a fundamental boundary: inside it, rings; outside it, moons.