The lowest orbit at which a satellite can withstand tides raised within it by its parent planet. French mathematician Edouard Roche (182083) studied rotating liquid masses, and noted in 1848 that, if a moon orbited close enough to its parent planet, the stresses would exceed the strength of rock, tearing the satellite apart. This mechanism could explain the presence of rings around some planets.
| Primary | Density (kg/m3) | Radius (m) |
|---|---|---|
| Sun | 1408 | 696,000,000 |
| Jupiter | 1326 | 71,492,000 |
| Earth | 5513 | 6,378,137 |
| Moon | 3346 | 1,738,100 |
| Saturn | 687.3 | 60,268,000 |
| Uranus | 1318 | 25,559,000 |
| Neptune | 1638 | 24,764,000 |
Using these data, the Roche Limits for rigid and fluid bodies can easily be calculated.
| 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. 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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