Roche Limit Calculator
Calculate the Roche limit, the distance inside which a satellite breaks apart due to tidal forces.
Explains planetary rings and comet disruption.
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 = 1.26 × R_M × (ρ_M / ρ_m)^(1/3)
For fluid satellite:
d = 2.455 × R_M × (ρ_M / ρ_m)^(1/3)
The gap between those two coefficients is the whole point, and it is nearly a factor of two. A rigid body is held together by its own material strength, so it survives much closer in. A fluid body has nothing but self-gravity, so the tide deforms it into an ellipsoid, which makes the near side stick out further, which makes the tide stronger, and the whole thing runs away. Real moons sit between the two: a rubble pile behaves closer to fluid, a solid iron fragment closer to rigid. Use the rigid answer as the optimistic bound and the fluid answer as the pessimistic one.
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, the rigid limit is about 9,840 km and the fluid limit about 19,170 km. Both sit above Earth’s own 6,371 km radius, so a rocky body really would break up if it drifted that close. For an icy body (ρ_m = 900 kg/m³) the limits are roughly 14,690 km rigid and 28,620 km fluid. Either way the Moon, at 384,400 km, is more than twenty times too far out to be in any danger.
The Roche limit is also relevant for accretion disks around black holes and neutron stars.
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This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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