Roche Limit

Bring a moon too close and its planet's tides win — the moon shatters into a ring. That boundary is the Roche limit, and it is why Saturn has rings.

Roche LimitLive

when tides tear a moon apart

Controls

Presets

Density ratio ρ_primary/ρ_sat

Orbit distance (primary radii)

Inside the Roche limit, tidal forces from the primary exceed the satellite's own gravity and pull it apart — the origin of planetary rings. The rigid-body limit is d = R·(2·ρ_primary/ρ_sat)^(1/3). Drag the moon inside the red ring to shred it.

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Data Inspector

Roche limit1.26 R

Orbit2.5 R

Statusstable

Governing equation

d = R (2 \frac{ρ _{M}}{ρ _{m}})^{1/3} = 1 (2 \cdot 1.0)^{1/3} = 1.26 R

Reading this result: Outside the Roche limit: at 2.5 R the moon has a 98% margin above the 1.26 R threshold, so its own gravity holds it together.

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How it works

The Roche limit is the orbital distance inside which tidal forces from the primary exceed the satellite's self-gravity. For a rigid body it is d = R·(2·ρ_primary/ρ_satellite)^(1/3). Drag the moon inside the limit to watch it disrupt into a debris ring.

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Frequently asked questions

Is this Roche limit calculator tool really free?▾

Yes. Roche Limit runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.

Do I need to install anything?▾

No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.

Can I save or share my simulation?▾

Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.

How accurate are the results?▾

The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.