Roche Limit - Roche Limits For Selected Examples

Roche Limits For Selected Examples

The table below shows the mean density and the equatorial radius for selected objects in the Solar System.

Primary Density (g/cm³) Radius (m)
Sun 1,408 696,000,000
Jupiter 1,326 71,492,000
Earth 5,513 6,378,137
Moon 3,346 1,738,100
Saturn 0.687 60,268,000
Uranus 1,318 25,559,000
Neptune 1,638 24,764,000

Using these data, the Roche Limits for rigid and fluid bodies can easily be calculated. The average density of comets is taken to be around 500 kg/m³.

The table below gives the Roche limits expressed in metres and in primary radii. The true Roche Limit for a satellite depends on its density and rigidity.

Body Satellite Roche limit (rigid) Roche limit (fluid)
Distance (km) R Distance (km) R
Earth Moon 9,496 1.49 18,261 2.86
Earth average Comet 17,880 2.80 34,390 5.39
Sun Earth 554,400 0.80 1,066,300 1.53
Sun Jupiter 890,700 1.28 1,713,000 2.46
Sun Moon 655,300 0.94 1,260,300 1.81
Sun average Comet 1,234,000 1.78 2,374,000 3.42

If the primary is less than half as dense as the satellite, the rigid-body Roche Limit is less than the primary's radius, and the two bodies may collide before the Roche limit is reached.

How close are the solar system's moons to their Roche limits? The table below gives each inner satellite's orbital radius divided by its own Roche radius. Both rigid and fluid body calculations are given. Note Pan, Metis, and Naiad in particular, which may be quite close to their actual break-up points.

In practice, the densities of most of the inner satellites of giant planets are not known. In these cases, shown in italics, likely values have been assumed, but their actual Roche limit can vary from the value shown.

Primary Satellite Orbital Radius / Roche limit
(rigid) (fluid)
Sun Mercury 104:1 54:1
Earth Moon 41:1 21:1
Mars Phobos 172% 89%
Deimos 451% 234%
Jupiter Metis ~186% ~94%
Adrastea ~188% ~95%
Amalthea 175% 88%
Thebe 254% 128%
Saturn Pan 142% 70%
Atlas 156% 78%
Prometheus 162% 80%
Pandora 167% 83%
Epimetheus 200% 99%
Janus 195% 97%
Uranus Cordelia ~154% ~79%
Ophelia ~166% ~86%
Bianca ~183% ~94%
Cressida ~191% ~98%
Desdemona ~194% ~100%
Juliet ~199% ~102%
Neptune Naiad ~139% ~72%
Thalassa ~145% ~75%
Despina ~152% ~78%
Galatea 153% 79%
Larissa ~218% ~113%
Pluto Charon 12.5:1 6.5:1

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