Roche Limit Calculator

Calculate the orbital distance where tidal forces tear apart a satellite, for both rigid and fluid bodies.

Last reviewed: June 2026
Built and maintained by · Last updated June 2026
km
kg/m³
kg/m³
Rigid Roche Limit
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Fluid Roche Limit
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Density Ratio (ρprimary / ρsatellite)
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Important Disclaimer: This calculator gives a first-order tidal-disruption estimate from idealized bulk-density formulas. It does not model orbit shape, spin, tensile strength, internal layering, or mission-specific safety margins.

How the Roche Limit Calculator works

The Roche limit estimates how close a satellite can orbit before tidal forces from the primary body begin to pull it apart. This calculator uses the primary body's radius and bulk density plus the satellite's bulk density. It reports two useful distances: a rigid Roche limit for a body with meaningful internal strength and a fluid Roche limit for a weak, fluid, icy, or rubble-pile body.

The calculator's density ratio is rho_primary / rho_satellite. A dense primary body and a low-density satellite increase the ratio and push the Roche limit outward. A denser satellite can orbit closer before disruption becomes likely.

Formulas used

  • Rigid body: d = R_primary * (2 * density ratio)^(1/3)
  • Fluid body: d = 2.44 * R_primary * (density ratio)^(1/3)

The results are shown in kilometers and in primary-body radii. For the default Earth and rocky-satellite inputs, the rigid limit is about 1.55 Earth radii and the fluid limit is about 2.99 Earth radii. The fluid result is larger because a weak body cannot resist tidal stretching as well as a rigid one.

How to choose inputs

  • Primary radius: Use the mean radius of the planet, star, or other central body.
  • Primary density: Use average bulk density, not surface density.
  • Satellite density: Use bulk density for the moon, asteroid, comet, ring particle, or material you are modeling.
  • Rigid vs fluid: Compare both if the object is fractured, icy, porous, or partly molten.

Limits of the estimate

The Roche limit is a first-order tidal-disruption model. Spin, eccentric orbit, tensile strength, internal layering, tidal heating, and previous fractures can change the real outcome. Use this calculator for comparison and intuition, then use a detailed orbital or structural model for mission design.

Frequently Asked Questions

The Roche limit is the orbital distance where tidal forces from a primary body can overcome a satellite body's self-gravity or structural strength.
A rigid body can hold together somewhat closer to the primary body. A fluid or rubble-pile body has less structural strength, so the fluid Roche limit is farther out.
It uses d_rigid = R_primary * (2 * density ratio)^(1/3) and d_fluid = 2.44 * R_primary * (density ratio)^(1/3), where density ratio is primary density divided by satellite density.
Use average bulk density for each body. Rock, ice, iron, and gas-giant presets are approximations; custom values are better for a specific moon, asteroid, comet, or planet.
No. Composition, internal strength, spin, orbit shape, and prior fractures all matter. The result is a first-order tidal-disruption estimate, not a full orbital simulation.