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 |
Read more about this topic: Roche Limit
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