Many planets have satellites revolving around them. While rotating around the planet, maximum extent for any satellite to go closer to it, is always limited. The minimum distance beyond which a satellite can not come closer to the planet is called ‘Roche limit’ named after “Edward Roche”, the scientist who discovered it. Whenever any satellite crosses this limit, the forces acting on it due to high & low tide will break it into pieces.
Satellite rotates around the planet in spherical orbit, it has a very low mass compared to the planet and its density is same as the planet, The Roche limit for a satellite is 2.46 times the radius of the planet. Thus for a satellite to balance with its own gravitation, it will have to rotate away from the planet at a distance more than 2.46 times its diameter. If it crosses this limit than due to gravitation pull of the planet, the low tide-high tide force developed on the surface of the planet will make it egg shaped. It will move further closer to the planet. Thus the elliptical shape of the satellite will go on increasing and at a particular moment will break into pieces.
The question, Why there are rings around Saturn ? can also be solved by using the concept of Roche limit. Very long ago, some satellite on Saturn must have crossed the Roche limit and due to the high tide-low tide forcees, it must have broken into pieces which are now seen as ring by us. As 4 major rings of Saturn are inside its Roche limit. The same is true with Earth and moon. the Roche limit for moon is 16,000 km. Moon should not cross this or else it will also break into pieces.
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