*Explain* Roche Limit
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For the limits at which an orbiting object will be captured, see Roche lobe. For the gravitational sphere of influence of one astronomical body in the face of perturbations from another heavier body around which it orbits, see Roche sphere.

An orbiting mass of fluid held together by gravity, here viewed from above the orbital plane. Far from the Roche limit the mass is practically spherical.

Closer to the Roche limit the body is deformed by tidal forces.

Within the Roche limit the mass's own gravity can no longer withstand the tidal forces, and the body disintegrates.

Particles closer to the primary move more quickly than particles farther away, as represented by the red arrows.

The varying orbital speed of the material eventually causes it to form a ring.
In celestial mechanics, the Roche limit, also called Roche radius, is the distance in which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction.[1] 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 [ʁɔʃ] (French), /rɔːʃ/ rawsh (English)), who is the French astronomer who first calculated this theoretical limit in 1848.[2]
ExplanationEdit

Comet Shoemaker-Levy 9 was disintegrated by the tidal forces of Jupiter into a string of smaller bodies in 1992, before colliding with the planet in 1994.
Typically, the Roche limit applies to a satellite's disintegrating due to tidal forcesinduced 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, Saturn's E-Ring and Phoebe ring being notable exceptions. They could either 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.
Selected examplesEdit
The table below shows the mean density and the equatorial radius for selected objects in the Solar System.
PrimaryDensity (kg/m3)Radius (m)Sun1,408696,000,000Earth5,5136,378,137Moon3,3461,737,100Jupiter1,32671,493,000Saturn68760,267,000Uranus1,31825,557,000Neptune1,63824,766,000
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.
BodySatelliteRoche limit (rigid)Roche limit (fluid)Mean orbital radius (km)Distance (km)RDistance (km)REarthMoon9,4921.4918,3812.88384,399Earthaverage comet17,8872.8034,6385.43N/ASunEarth556,3970.801,077,4671.55149,597,890SunJupiter894,6771.291,732,5492.49778,412,010SunMoon657,1610.941,272,5981.83149,597,890 ApproxSunaverage comet1,238,3901.782,398,1523.45N/A
These bodies are well outside their Roche limits by various factors, from 21 for the Moon (over its fluid-body Roche limit) as part of the Earth–Moon system, upwards to hundreds for Earth and Jupiter.
The table below gives each satellite's closest approach in its orbit divided by its own Roche limit. Again, both rigid and fluid body

An orbiting mass of fluid held together by gravity, here viewed from above the orbital plane. Far from the Roche limit the mass is practically spherical.

Closer to the Roche limit the body is deformed by tidal forces.

Within the Roche limit the mass's own gravity can no longer withstand the tidal forces, and the body disintegrates.

Particles closer to the primary move more quickly than particles farther away, as represented by the red arrows.

The varying orbital speed of the material eventually causes it to form a ring.
In celestial mechanics, the Roche limit, also called Roche radius, is the distance in which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction.[1] 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 [ʁɔʃ] (French), /rɔːʃ/ rawsh (English)), who is the French astronomer who first calculated this theoretical limit in 1848.[2]
ExplanationEdit

Comet Shoemaker-Levy 9 was disintegrated by the tidal forces of Jupiter into a string of smaller bodies in 1992, before colliding with the planet in 1994.
Typically, the Roche limit applies to a satellite's disintegrating due to tidal forcesinduced 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, Saturn's E-Ring and Phoebe ring being notable exceptions. They could either 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.
Selected examplesEdit
The table below shows the mean density and the equatorial radius for selected objects in the Solar System.
PrimaryDensity (kg/m3)Radius (m)Sun1,408696,000,000Earth5,5136,378,137Moon3,3461,737,100Jupiter1,32671,493,000Saturn68760,267,000Uranus1,31825,557,000Neptune1,63824,766,000
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.
BodySatelliteRoche limit (rigid)Roche limit (fluid)Mean orbital radius (km)Distance (km)RDistance (km)REarthMoon9,4921.4918,3812.88384,399Earthaverage comet17,8872.8034,6385.43N/ASunEarth556,3970.801,077,4671.55149,597,890SunJupiter894,6771.291,732,5492.49778,412,010SunMoon657,1610.941,272,5981.83149,597,890 ApproxSunaverage comet1,238,3901.782,398,1523.45N/A
These bodies are well outside their Roche limits by various factors, from 21 for the Moon (over its fluid-body Roche limit) as part of the Earth–Moon system, upwards to hundreds for Earth and Jupiter.
The table below gives each satellite's closest approach in its orbit divided by its own Roche limit. Again, both rigid and fluid body
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