What is the Roche limit?

The minimum distance a body can orbit another before tidal forces overcome its own gravity and tear it apart.

How is the Roche limit calculated?

It depends on the radius and density of both bodies, using tidal force balance formulas.

Why do some planets have rings inside their Roche limit?

Material within the limit gets torn apart before it can coalesce into a moon, forming rings instead.

Roche Limit Calculator - CalculatorLabs.net

Roche Limit Calculator

The Roche limit is the distance from a planet within which a moon or satellite held together only by its own gravity would be torn apart by tidal forces — it's why planets like Saturn have rings instead of a moon in that zone..

Primary Body Radius (m)

Primary Body Density (kg/m³)

Satellite Density (kg/m³)

Instant Result

Roche Limit Distance -

What Is a Roche Limit Calculator?

How to Use This Roche Limit Calculator

Enter the radius of the primary body (the planet), in meters.
Enter the average density of the primary body, in kg/m³.
Enter the average density of the satellite (moon), in kg/m³.
Click Calculate to get the Roche limit distance (for a rigid body approximation).

Formula

Roche Limit = R × ∛(2 × ρ_planet / ρ_satellite)

Worked Example

A planet with radius 7×10⁷ m and density 1300 kg/m³, and a satellite with density 3000 kg/m³. Roche Limit = 7×10⁷ × ∛(2×1300/3000) ≈ 6.53×10⁷ m — inside this distance, tidal forces would break the satellite apart.