Roche Limit Calculator

The Roche limit is the distance from a primary body inside which the tidal forces it exerts on an orbiting satellite become stronger than the satellite’s own self-gravity. Inside this distance, a fluid satellite is torn apart. Outside it, moons can survive.

Formula (for rigid satellite):

d = 2.44 × R_M × (ρ_M / ρ_m)^(1/3)

For fluid satellite:

d = 2.455 × R_M × (ρ_M / ρ_m)^(1/3)

Where:

• R_M = radius of the primary body
• ρ_M = density of the primary body
• ρ_m = density of the satellite

Saturn’s rings: Saturn’s rings lie inside Saturn’s Roche limit for ice (ρ ≈ 900 kg/m³). This is why the rings exist — ring particles cannot coalesce into a moon there. Beyond the Roche limit (outside ~140,000 km), Saturn’s moons survive intact.

Shoemaker-Levy 9: In 1992, Comet Shoemaker-Levy 9 passed inside Jupiter’s Roche limit and was torn into 21 fragments. The fragments then collided with Jupiter in 1994 in a spectacular multi-day event.

Earth-Moon Roche limit: For a rocky moon (ρ_m = 3,000 kg/m³) orbiting Earth: d ≈ 9,492 km (inside Earth’s radius — no risk). For an icy body (ρ_m = 900 kg/m³): d ≈ 14,400 km — still below the Moon’s 384,400 km orbit.

The Roche limit is also relevant for accretion disks around black holes and neutron stars.