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For Students · Roche Limit

Roche Limit for a cosmic expansion

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a cosmic expansion live below — adjust the inputs and watch it respond, right in your browser.

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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Frequently asked questions

Is this good for students?: Yes — this version of "Roche Limit for a cosmic expansion" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.