Every moon, comet, and star has a distance below which a larger body's tides exceed its self-gravity. Cross the Roche limit and you disintegrate — this is where Saturn's rings come from, where Shoemaker-Levy 9 fragmented, where stars become tidal-disruption flares around black holes.
01Pick a systemprimary · satellite
Tidal scenarios
Saturn + ice particle
The textbook case — ice in Saturn's ring system
Primary radius58,232 km
Density ratio0.749
Tidal diagram · primary, Roche limit, and satellite's actual position
02Roche limitd = R√[2(ρ₁/ρ₂)]¹⃗³
Fluid Roche limit
128,857 km
Distance from Saturn's center at which a fluid ice particle is torn apart by tidal forces.
Saturn's main ring system extends to ~140,000 km — the outer edge sits right at the Roche limit, where particles can finally clump into moons.
Rigid Roche limit
66,624 km
Actual distance
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Distance ratio
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Status
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03Tidal characteristicsat the Roche limit
Rigid Roche limit
66,624 km
Distance at which a solid body held only by gravity (no internal cohesion, spherical) is pulled apart. Inner edge of ring systems sits near here.
d = R₁(2ρ₁/ρ₂)¹⃗³
Fluid Roche limit
128,857 km
Distance for a fluid body that can deform under tides — the more realistic limit for rubble piles, ice particles, and comets. Marks the outer edge of stable rings.
d ≈ 2.44 R₁ (ρ₁/ρ₂)¹⃗³
Tidal acceleration gradient
5.9 × 10⁻⁸ s⁻²
Tidal acceleration per meter at the Roche limit. The greater this is, the more violently a body is stretched along the radial axis.
2GM/d³
Self-gravity at satellite surface
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Acceleration holding the satellite together. When this is exceeded by tidal force at the Roche limit, the body disintegrates.
g = GM/r²
Synchronous orbit radius
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Where orbital period matches the primary's rotation. Below this, orbits decay inward (Phobos around Mars); above, they spiral out (the Moon).
a_sync = (GM T²/4π²)¹⃗³
Outcome at Roche limit
Disrupted
A fluid body crossing this radius breaks into pieces over a single orbital period. The result is rings, a debris stream, or in the case of stars near a black hole, a tidal disruption event.