Tidal Disruption Distance Calculator

About this calculator

The Roche limit is the distance from a massive primary body — a planet or star — within which a smaller satellite held together only by its own gravity gets torn apart by tidal forces, because the difference in gravitational pull across the near and far sides of the satellite exceeds the self-gravity holding it in one piece. For a rigid, non-deformable satellite the limit is d = R × (2 × ρM / ρm)^(1/3), where R is the primary’s radius, ρM is the primary’s density and ρm is the satellite’s density.

This distance explains why planetary ring systems like Saturn’s sit close to the planet — material inside the Roche limit cannot clump into a moon and instead stays spread out as rings — and it also explains events like comet Shoemaker-Levy 9 breaking into fragments as it passed close to Jupiter before its 1994 impact. Astronomers and astrophysics students use the rigid-body Roche limit as a first-order estimate; the actual disruption distance for a real, deformable body is somewhat larger. Enter the primary’s radius and both densities to find the Roche limit.