About the Roche Limit Calculator
This Roche limit calculator finds the closest distance a satellite held together only by its own gravity can orbit a larger body before tidal forces pull it apart. Choose a primary — Earth, Mars, the giant planets or the Sun — or enter a custom radius and density, then enter the satellite’s density, and it returns the Roche limit for both a rigid and a fluid (easily deformed) satellite, in kilometres and in primary radii.
It helps astronomy students, writers and space enthusiasts understand why Saturn has rings instead of a moon close in, why comets such as Shoemaker–Levy 9 broke up near Jupiter, and how close Mars’s moon Phobos is getting to its own break-up. The chart compares limits for comets, ice, rock and iron.
The rigid formula treats the satellite as a perfect sphere that does not deform; the fluid formula lets it stretch into an elongated shape, which makes it easier to disrupt. Real moons lie between the two, and small bodies with material strength — such as spacecraft or solid rocks a few kilometres across — can survive well inside the Roche limit.
With the default inputs, the roche limit (fluid satellite) is 18,373 km. Change any value above to recalculate instantly.
How to use the roche limit calculator
- 1Choose the primary body, or select Custom and enter its radius and density.
- 2Enter the satellite’s density in g/cm³.
- 3Read the fluid and rigid Roche limits in kilometres.
- 4Compare them in primary radii to see how close to the surface they are.
- 5Use the chart to see how density changes the limit.
Formula and method
The Roche limit is where the tidal force stretching a satellite — the difference in the primary’s pull between its near and far sides — equals the satellite’s own gravity holding it together. Writing both in terms of radius and density makes the satellite’s size cancel, so the limit depends only on the primary’s radius and the ratio of the two densities.
For a rigid, spherical satellite this gives 2^(1/3) ≈ 1.26 times the primary radius times the cube root of the density ratio. A fluid satellite deforms into an elongated shape, which amplifies the tidal effect; Édouard Roche’s fluid result is about 2.44 instead of 1.26. Distances are measured from the centre of the primary. Planet radii and densities are NASA fact-sheet values.
- d
- Roche limit, distance from the primary’s centre
- R_M
- Radius of the primary (planet or star)
- ρ_M
- Mean density of the primary
- ρ_m
- Mean density of the satellite
Worked examples
Earth and the Moon
The density ratio 5.514 ÷ 3.34 = 1.651 has a cube root of 1.1819. The fluid limit is 2.44 × 6,371 × 1.1819 ≈ 18,370 km and the rigid limit 1.26 × 6,371 × 1.1819 ≈ 9,490 km — far inside the Moon’s 384,400 km orbit.
Icy moonlets around Saturn
Saturn is less dense than water ice, so the ratio is 0.747. The fluid limit is about 128,900 km from Saturn’s centre — close to the outer edge of its main rings, which is why ice there stays as rings rather than forming a moon.
A comet passing the Sun (density 0.6)
With a density ratio of 2.35, a loosely bound comet would be torn apart within about 2.26 million km (3.24 solar radii) of the Sun’s centre — the fate of many sungrazing comets.
Jupiter and a rocky moon like Io (3.53 g/cm³)
Io is much denser than Jupiter, so its fluid limit is only 1.76 Jupiter radii (123,100 km), and the rigid limit falls inside Jupiter itself. Io actually orbits at about 421,700 km, well outside.
Frequently asked questions
What is the Roche limit?+
It is the minimum distance at which a satellite held together only by its own gravity can orbit a larger body without being pulled apart by tidal forces. It was first calculated by French astronomer Édouard Roche in 1848.
What is the Roche limit of Earth?+
For a satellite with the Moon’s density (3.34 g/cm³), about 9,500 km for a rigid body and about 18,400 km for a fluid one, measured from Earth’s centre. Denser satellites can come closer.
Why don’t satellites and the ISS get torn apart inside the Roche limit?+
The Roche limit applies to bodies held together by their own gravity. Spacecraft, people and small rocks are held together by chemical bonds and material strength, which are vastly stronger than the tidal forces at those distances.
Are Saturn’s rings inside its Roche limit?+
Largely, yes. The main rings lie within about 2.3 Saturn radii, close to the fluid Roche limit for icy material, so tidal forces stop ring particles from clumping into a single moon.
What is the difference between the rigid and fluid Roche limit?+
A rigid satellite keeps its spherical shape, giving the smaller limit (factor 1.26). A fluid or rubble-pile satellite stretches toward the primary, which strengthens the tidal pull and roughly doubles the limit (factor 2.44). Real bodies fall in between.