Roche limit

In celestial mechanics, the Roche limit, also called Roche radius, is the distance within which a celestial body, held together only by its own force of gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction. Inside the Roche limit, orbiting material disperses and forms rings whereas outside the limit material tends to coalesce. The term is named after Édouard Roche (pronounced (French), /rɔːʃ/ rawsh (English)), who was the French astronomer who first calculated this theoretical limit in 1848. In celestial mechanics, the Roche limit, also called Roche radius, is the distance within which a celestial body, held together only by its own force of gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction. Inside the Roche limit, orbiting material disperses and forms rings whereas outside the limit material tends to coalesce. The term is named after Édouard Roche (pronounced (French), /rɔːʃ/ rawsh (English)), who was the French astronomer who first calculated this theoretical limit in 1848. Typically, the Roche limit applies to a satellite's disintegrating due to tidal forces induced by its primary, the body about 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.) The Roche limit is not the only factor that causes comets to break apart. Splitting by thermal stress, internal gas pressure and rotational splitting are other ways for a comet to split under stress. The table below shows the mean density and the equatorial radius for selected objects in the Solar System. The equations for the Roche limits relate the minimum sustainable orbital radius to the ratio of the two objects' densities and the Radius of the primary body. Hence, using the data above, the Roche limits for these objects can be calculated. This has been done twice for each, assuming the extremes of the rigid and fluid body cases. The average density of comets is taken to be around 500 kg/m³. The table below gives the Roche limits expressed in kilometres and in primary radii. The mean radius of the orbit can be compared with the Roche limits. For convenience, the table lists the mean radius of the orbit for each, excluding the comets, whose orbits are extremely variable and eccentric.