Roche Limit Calculator

About this calculator

The Roche limit is the minimum distance a smaller celestial body (a moon or satellite) can orbit a larger one before the larger body's tidal forces exceed the smaller body's self-gravity and pull it apart. This calculator uses the rigid Roche limit formula, d = R · (2 · ρM/ρm)^(1/3), where R is the primary body's radius, ρM is its density and ρm is the satellite's density — it assumes the satellite holds together only by gravity, not by any internal tensile strength.

The concept, named after French astronomer Édouard Roche, explains why planets like Saturn have ring systems rather than a single large moon close in — any moon that formed or wandered inside the Roche limit would be shredded into a debris ring by tidal stress. Astronomers and astrophysics students use the Roche limit to predict whether a close-orbiting moon or asteroid is stable, to understand the origin of planetary rings, and to model tidal disruption events around stars and black holes.