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.
Inside the Roche limit, orbiting material disperses and forms rings whereas outside the limit material tends to coalesce. For example, the rings of Saturn lie inside Saturn's Roche limit and may be the debris of a demolished moon.
In the late 1840s, French astronomer Edouard Roche determined the distance at which a given satellite would get ripped apart by the body it was orbiting.
Roche Limit = 1.26 x (Radius of Larger Object) x (Density of the Larger Object/Density of the Smaller Object)^1/3
In this we can see that, if the radius and the density of larger object are large, no self-respecting satellite will want to get near them, because the Roche distance will be huge. If, however, the density of the orbiting object is large — if it is packed tight — it can freely wander about the universe without any worries, since it's unlikely that it will be ripped apart. A dense orbiting object shrinks the Roche distance considerably.
The best known application of Roche’s theoretical work is on the formation of planetary rings: an asteroid or comet which strays within the Roche limit of a planet will disintegrate, and after a few orbits the debris will form a nice ring around the planet (of course, this is not the only way a planetary ring can form; small moons can create rings by being bombarded by micrometeorites, or by outgassing).
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