Roche Limit Rechner — Formel

## 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.

Lösungsbeispiel

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

  1. rho_p / rho_s = 1326 / 3346 = 0.3963
  2. (0.3963)^(1/3) = 0.7347
  3. Rigid: 1.26 × 69 911 000 × 0.7347 ≈ 64 700 km
  4. Fluid: 2.44 × 69 911 000 × 0.7347 ≈ 125 300 km