# Roche limit

The Roche limit is smallest distance that a fluid satellite can orbit from the center of a planet without being torn apart by tidal forces. For a satellite of negligible mass, zero tensile strength, and the same mean density as its primary, in a circular orbit around its primary, this critical distance is 2.44 times the radius of the primary. (For the Moon, whose density is lower than that of Earth, the Roche limit would be 2.9 Earth radii.) In practice, since moons tend to be solid, the tensile force of the rock and ice of which they are composed helps prevent their breakup. Even so, the shattering of satellites in orbits well inside the Roche limit may explain the origin of some planetary ring systems. The limit is named after the French mathematician Édouard Roche (1820–1883) who first described the theory behind it.

## Examples

object | Roche limit (km) |

Earth | 18,470 |

Jupiter | 175,000 |

Saturn | 147,000 |

Uranus | 62,000 |

Neptune | 59,000 |