In celestial mechanics, the Roche limit, also called Roche radius, is the distance from a celestial body within which a second celestial body, held together only by its own force of gravity, will disintegrate because the first body's tidal forces exceed the second body's self-gravitation. Inside the Roche limit, orbiting material disperses and forms rings, whereas outside the limit, material tends to coalesce. The Roche radius depends on the radius of the first body and on the ratio of the bodies' densities.
The term is named after Édouard Roche (ʁɔʃ, rɒʃ ), the French astronomer who first calculated this theoretical limit in 1848.
The Roche limit typically applies to a satellite's disintegrating due to tidal forces induced by its primary, the body around which it orbits. Parts of the satellite that are closer to the primary are attracted more strongly by gravity from the primary than parts that are farther away; this disparity effectively pulls the near and far parts of the satellite apart from each other, and if the disparity (combined with any centrifugal effects due to the object's spin) is larger than the force of gravity holding the satellite together, it can pull the satellite apart. Some real satellites, both natural and artificial, can orbit within their Roche limits because they are held together by forces other than gravitation. Objects resting on the surface of such a satellite would be lifted away by tidal forces. A weaker satellite, such as a comet, could be broken up when it passes within its Roche limit.
Since, within the Roche limit, tidal forces overwhelm the gravitational forces that might otherwise hold the satellite together, no satellite can gravitationally coalesce out of smaller particles within that limit. Indeed, almost all known planetary rings are located within their Roche limit. (Notable exceptions are Saturn's E-Ring and Phoebe ring. These two rings could possibly be remnants from the planet's proto-planetary accretion disc that failed to coalesce into moonlets, or conversely have formed when a moon passed within its Roche limit and broke apart.
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Neptune is the eighth planet from the Sun and the farthest IAU-recognized planet in the Solar System. It is the fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 times the mass of Earth, and slightly more massive than its near-twin Uranus. Neptune is denser and physically smaller than Uranus because its greater mass causes more gravitational compression of its atmosphere. Being composed primarily of gases and liquids, it has no well-defined solid surface.
The Hill sphere of an astronomical body is the region in which it dominates the attraction of satellites. It is sometimes termed the Roche sphere. It was defined by the American astronomer George William Hill, based on the work of the French astronomer Édouard Roche. To be retained by a more gravitationally attracting astrophysical object—a planet by a more massive sun, a moon by a more massive planet—the less massive body must have an orbit that lies within the gravitational potential represented by the more massive body's Hill sphere.
The rings of Saturn are the most extensive ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometers to meters, that orbit around Saturn. The ring particles are made almost entirely of water ice, with a trace component of rocky material. There is still no consensus as to their mechanism of formation. Although theoretical models indicated that the rings were likely to have formed early in the Solar System's history, newer data from Cassini suggested they formed relatively late.
Explores the Roche limit, the critical distance at which celestial bodies break apart due to tidal forces, using examples from Saturn's rings and comet disintegration.
Explores slope stability analysis using the limit equilibrium method and the Kerisel Chart for determining critical slip surfaces and factors of safety.
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