Roche Limit Calculator Formula

Understand the math behind the roche limit calculator. Each variable explained with a worked example.

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Formulas Used

Roche Limit (Rigid)

roche_rigid = primary_radius * 1.26 * pow(primary_density / satellite_density, 1/3)

Roche Limit (Fluid)

roche_fluid = primary_radius * 2.44 * pow(primary_density / satellite_density, 1/3)

Variables

VariableDescriptionDefault
primary_radiusPrimary Body Radius(m)69911000
primary_densityPrimary Density(kg/m³)1326
satellite_densitySatellite Density(kg/m³)3346

How It Works

The Roche Limit

Within the Roche limit, tidal forces from the primary exceed the self-gravity holding the satellite together.

Rigid Body

d_rigid = 1.26 R_p (rho_p / rho_s)^(1/3)

Fluid Body

d_fluid = 2.44 R_p (rho_p / rho_s)^(1/3)

Planetary rings typically exist inside the Roche limit.

Worked Example

Rocky moon (rho = 3346 kg/m³) around Jupiter (R = 69 911 km, rho = 1326 kg/m³).

primary_radius = 69911000primary_density = 1326satellite_density = 3346
  1. 01rho_p / rho_s = 1326 / 3346 = 0.3963
  2. 02(0.3963)^(1/3) = 0.7347
  3. 03Rigid: 1.26 × 69 911 000 × 0.7347 ≈ 64 700 km
  4. 04Fluid: 2.44 × 69 911 000 × 0.7347 ≈ 125 300 km

Ready to run the numbers?

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