In 1848 Eduoard Roche of Montpellier worked out the necessary physics by noting that a satellite is subjected to gravitational stresses as the parts of it nearer the planet try to orbit faster that more distant parts. These stresses eventually exceed the strength of the rock holding the satellite together, and the satellite is first deformed into a football shape, then fragmented into pieces that orbit as separate satellites. The exact distance is in the neighborhood of 2.5 times the radius of the planet, but it varied depending on the density of the satellite. The rings of Saturn are inside the Roche Limit for bodies made of ice.