What is the Roche limit?

The Roche limit is the orbital distance at which the tidal force exerted by a primary body equals the self-gravity of the satellite. Inside this distance, loose material cannot coalesce and existing satellites break apart into rings.

Which formula should I use?

The rigid-sphere formula (d = 1.26 × R_primary × (ρ_primary / ρ_satellite)^(1/3)) gives a lower bound for a perfectly rigid body. The fluid-body formula (d ≈ 2.44 × R_primary × (ρ_primary / ρ_satellite)^(1/3)) is more realistic for icy or rubble-pile satellites and is widely cited in planetary science.

Why does density matter and not total mass of the satellite?

The Roche limit depends on the ratio of densities, not the absolute masses. A denser satellite can survive closer to the primary because its own self-gravity is stronger relative to the tidal force acting on it.

Does this apply to artificial satellites?

Artificial satellites are held together by structural strength (not just gravity), so the Roche limit does not determine their breakup point. The calculation is relevant only for bodies held together by self-gravity, such as moons, asteroids, and comets.

What are typical densities for common bodies?

Rocky bodies: 2,500–4,000 kg/m³. Icy bodies (comets, some moons): 500–1,500 kg/m³. Water: 1,000 kg/m³. Iron-rich asteroids: 5,000–8,000 kg/m³. The lower the satellite density, the farther out its Roche limit falls.

Roche Limit Calculator

Name: Roche Limit Calculator
Availability: InStock
Author: Nham Vu

Calculate the Roche limit — the minimum orbital distance before a satellite is torn apart by tidal forces from a larger body.

Primary Body

Quick Preset

Primary Mass (kg)

Primary Radius (km)

Satellite

Satellite Density (kg/m³)

Formula

Fluid body (×2.44) Rigid sphere (×1.26)

Enter primary body and satellite parameters,
then click Calculate.

Summary

Calculate the Roche limit — the minimum orbital distance before a satellite is torn apart by tidal forces from a larger body.

How it works

Enter the primary body mass (e.g., Earth, Jupiter) and its equatorial radius.
Enter the satellite density — the bulk density of the smaller orbiting body.
Choose the formula: rigid sphere (conservative lower bound) or fluid body (real-world upper bound).
Click Calculate to get the Roche limit distance in kilometers, Earth radii, and AU.
Compare the result against a known moon or ring system to see whether it lies inside the disruption zone.

Use cases

Determine why Saturn's rings exist inside its Roche limit.
Check whether a proposed orbit for a small moon is stable.
Study tidal disruption in binary star systems.
Visualize how density affects the Roche limit for different satellite compositions.
Explore the difference between the rigid-sphere and fluid-body approximations.
Educational demonstrations of planetary science and orbital mechanics.

Frequently Asked Questions

Last updated: 2026-07-22 · Reviewed by Nham Vu