Roche Limit Tidal Disruption Calculator
Celestial Mechanics & Planetary Physics: Calculate the rigid ($d_{rigid}$) and fluid ($d_{fluid}$) Roche limits where gravitational tidal forces overwhelm satellite self-gravity.
Primary Central Body
Approaching Satellite / Asteroid
Roche Disruption Limit Output
The Roche Limit & Tidal Disruption Formulations
Tidal forces dictate the stability of moons, rings, and asteroids encountering planets.
1. Rigid and Fluid Roche Limits
d_rigid = R_M · [ 2 · (ρ_M / ρ_m) ]^(1/3) ≈ 1.26 · R_M · (ρ_M / ρ_m)^(1/3) d_fluid ≈ 2.44 · R_M · (ρ_M / ρ_m)^(1/3)
2. Tidal Disruption Criterion
F_tidal = ( 2 · G · M · m · r ) / d³ > F_self_gravity = ( G · m² ) / r²
Frequently Asked Questions
What is the physical meaning of the Roche limit?
The Roche limit is the minimum orbital distance to which a celestial body, held together only by its own self-gravity, can approach a second, more massive body without being torn apart by differential gravitational tidal forces. Inside the Roche limit, tidal forces overcome the satellite's gravitational cohesion, causing it to disintegrate into debris.
Why is the fluid Roche limit significantly larger than the rigid Roche limit?
A rigid monolithic body maintains its spherical shape until tensile stress exceeds material yield strength ($d_{rigid} = 1.26 R_M (\rho_M / \rho_m)^{1/3}$). A fluid or loosely bound "rubble-pile" body elongates into a prolate tidal ellipsoid. This elongation increases the tidal force difference across its ends, causing tidal disruption much farther out ($d_{fluid} = 2.44 R_M (\rho_M / \rho_m)^{1/3}$).
How are planetary rings related to the Roche limit?
Saturn's main rings lie almost entirely inside Saturn's fluid Roche limit for icy bodies ($\approx 140,000\,\text{km}$). Any icy moon that formed or migrated inside this boundary was ripped apart by tidal forces, preventing the debris from coalescing into a single moon and preserving the flat ring system.