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Tidal Disruption Distance Calculator

Enter the primary radius and densities to find the Roche limit.

How it is calculated

The tool uses the rigid-body Roche limit: d = R × (2 × ρp / ρs)1/3. R is the radius of the primary body in kilometres, ρp is its mean density and ρs is the satellite's mean density, both in kg/m³. Only the ratio of the two densities matters, so use the same unit for both. The limit comes out in km, and the same distance is also given in primary radii, d / R, to two decimals. All three inputs must be above zero. A satellite orbiting closer than d would be pulled apart by tides. It assumes a solid satellite that holds its shape; a body that deforms is disrupted farther out.

Worked example

Take a primary of radius 6,371 km and mean density 5,514 kg/m³, with a rocky satellite of density 3,344 kg/m³. The density ratio is 2 × 5,514 / 3,344 = 3.298. The cube root of 3.298 is about 1.489. Multiplying by the radius, 6,371 × 1.489 gives a Roche limit of 9,483 km, or 1.49 primary radii. A satellite of that density orbiting closer than 9,483 km from the centre would be torn apart.

Try this example →

Common mistakes

  • Entering the radius in metres or miles. The field is km, so 6,371 km must not be typed as 6,371,000.
  • Swapping the two densities. A dense satellite around a light primary gives a much smaller limit, and reversing them changes the answer.
  • Measuring the limit from the surface. The result is a distance from the centre of the primary; subtract R to get the altitude above the surface.
  • Using the rigid limit for a loose rubble pile or a liquid body. This tool assumes a solid body, and a deformable one breaks up farther from the primary than shown.
  • Forgetting that mean density is the whole-body average, not the density of the surface rock.

About this calculator

The Roche limit is the distance from a massive primary body — a planet or star — within which a smaller satellite held together only by its own gravity gets torn apart by tidal forces, because the difference in gravitational pull across the near and far sides of the satellite exceeds the self-gravity holding it in one piece. For a rigid, non-deformable satellite the limit is d = R × (2 × ρM / ρm)^(1/3), where R is the primary’s radius, ρM is the primary’s density and ρm is the satellite’s density.

This distance explains why planetary ring systems like Saturn’s sit close to the planet — material inside the Roche limit cannot clump into a moon and instead stays spread out as rings — and it also explains events like comet Shoemaker-Levy 9 breaking into fragments as it passed close to Jupiter before its 1994 impact. Astronomers and astrophysics students use the rigid-body Roche limit as a first-order estimate; the actual disruption distance for a real, deformable body is somewhat larger.

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  • Editorial team

    A quick sense check is to compare the result with a real orbit. For Earth and a rocky satellite of about 3,340 kg/m³ the limit is roughly 9,480 km from Earth's centre, and the Moon circles at about 384,400 km, around forty times farther out. Try an icy density near 900 to see how much closer a loose, light body must stay. Which planet and moon pair are you looking at?

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