Roche Limit Calculator
The Roche limit is the closest a satellite can orbit a planet or star before tidal forces tear it apart, and it explains why ring systems hug their parent worlds. It depends only on the primary's radius and the ratio of the two bodies' densities, not on the satellite's size. This calculator returns both the rigid limit, for a solid body held by strength, and the larger fluid limit, for a body that deforms under tides. Enter the primary radius and the mean density of each body in consistent units.
Roche limit formulas
Rigid: d = R * (2 * rho_M / rho_m)^(1/3)
Fluid: d = 2.44 * R * (rho_M / rho_m)^(1/3)
R = primary radius, rho_M = primary density
rho_m = satellite density
Both limits are measured from the centre of the primary. The fluid limit is larger because a deformable body stretches and breaks up further out than a rigid one. Real satellites fall between the two.
Tidal breakup context
- The Roche limit depends only on the primary radius and the density ratio, not satellite size.
- Saturn's main rings lie inside its fluid Roche limit, which is why they have not formed a moon.
- Earth's mean density is about 5,514 kilograms per cubic metre.
- Water ice has a density of about 917 kilograms per cubic metre.
- Comet Shoemaker-Levy 9 broke apart after passing inside Jupiter's Roche limit in 1992.
Roche limit: frequently asked questions
What is the Roche limit?
The Roche limit is the distance from a massive body within which a smaller body held together only by its own gravity will be torn apart by tidal forces. Inside this limit the difference in the primary's pull across the satellite exceeds the satellite's self-gravity, so loose material cannot stay bound.
What is the difference between the rigid and fluid Roche limits?
The rigid limit treats the satellite as a solid sphere held by material strength, giving d = R * (2 * rho_M / rho_m)^(1/3). The fluid limit treats it as a deformable fluid body that stretches under tides, giving d = 2.44 * R * (rho_M / rho_m)^(1/3). Real bodies lie between these two estimates.
What does the Roche limit explain?
It explains why planetary rings sit close to their planet: ring material orbits inside the Roche limit, where tides prevent it from coalescing into a moon. It also predicts where a comet or moon that wanders too close will break into fragments, as comet Shoemaker-Levy 9 did near Jupiter.
What densities should I enter?
Enter the mean density of the primary body and of the satellite in the same units, kilograms per cubic metre. Earth's mean density is about 5,514 and water ice is about 917. Densities are measured properties of each body, so they ship as user-editable inputs you set for your case.
Does the satellite's size matter?
No. Strikingly, the Roche limit depends only on the primary's radius and the ratio of the two densities, not on the satellite's size. A pebble and a large moon of the same density are torn apart at the same distance, because both self-gravity and tidal stretching scale the same way with size.
Official sources
- NASA Planetary Fact Sheet: Planetary radii and densities.
- NASA Science: Saturn and its rings.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.