Roche Limit Estimate Calculator

Advanced Roche limit estimator for planetary rings disruption and tidal stability. Enter primary radius and density plus satellite density or mass and size. Choose fluid or rigid model with flexible units. Get clear results safety flags and explanations for scientists students educators and space enthusiasts researchers engineers hobbyists learners astronomers mission planners observers analysts

Inputs
Examples: Earth 6371 km · Jupiter 69911 km · Saturn 58232 km
Ice ≈ 900 kg/m³ · Rock ≈ 3000 kg/m³
Results
Quantity Value In primary radii
Rigid body Roche limit 9,833.165 km 1.5434 × Rₚ
Fluid body Roche limit 19,042.002 km 2.9889 × Rₚ
Derived satellite density 3,000.000 kg/m³ —

Selected model: FLUID ⇒ 19,042.002 km (2.9889 × Rₚ)

Tip Try presets:
Formulae & Notes

Rigid body: rR,rigid = 1.26 Rp (ρp / ρs)1/3

Fluid body: rR,fluid = 2.44 Rp (ρp / ρs)1/3

  • These are classical approximations for spherical bodies, circular orbits, and negligible satellite self-strength.
  • Real outcomes depend on spin, internal cohesion, shape, eccentricity, and tidal evolution; use results as first-order guidance.
  • Primary density is the mean bulk density. Satellite density can be direct or derived from mass and radius.
  • Outputs are shown in kilometers and as a multiple of the primary radius for quick intuition.
Quick reference
  • Inside the rigid limit ⇒ almost all weak satellites disrupt.
  • Between rigid and fluid ⇒ rubble piles and fluids likely disrupt.
  • Outside the fluid limit ⇒ bodies are generally stable against disruption.
Unit reminders
  • 1 g/cm³ = 1000 kg/m³.
  • 1 Earth radius = 6371 km.
  • 1 Solar radius = 695700 km.
About this tool

Built for astrophysics learners and practitioners who need a fast, unit-aware estimate with clear assumptions and presets for common bodies.

FAQs
The Roche limit is the critical distance from a massive primary where tidal forces overcome a satellite’s self-gravity and structural strength, leading to disruption or ring formation.
Use the rigid coefficient (1.26) for cohesive, strong bodies and the fluid coefficient (2.44) for rubble piles or fluid-like bodies. Selecting “show both” helps bracket realistic outcomes.
Strong, monolithic bodies may briefly resist disruption inside the rigid limit, but rubble piles and weak or fluid bodies are unlikely to remain intact. Long-term survival is generally not expected.
The classical formula neglects spin, eccentricity, shape, internal strength, and tidal evolution. It is best for order‑of‑magnitude estimates and scenario screening rather than precise mission design.
The Roche distance scales with the primary’s physical radius as well as the density ratio. Expressing results in units of the primary radius makes it easy to compare different systems.
You can enter radii in meters, kilometers, or common planetary radii, and densities in kg/m³ or g/cm³. The tool converts everything consistently and reports distances in kilometers and primary radii.
Yes. Rapid rotation, elongation, internal structure, and orbital eccentricity can shift the effective disruption distance. Use mission‑specific modeling for critical decisions.

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.