In 1850, Eduoard Roche demonstrated that a satellite would be torn asunder by gravitational tidal forces if it came within a certain critical distance of its primary. We can estimate what this distance is as follows:
The idea is that the gravitational force of the Moon on material at its surface has to be less than the difference in Earth's gravitational force between the center of the Moon and its surface. This will allow the Earth to pull-apart the Moon.
G M(moon) m
F(moon) = --------------
r(moon)^2
2 G M(earth) m
F(earth tidal) = ------------------ r(moon)
D^3
where D is the distance between the Earth and the Moon, r(moon) is the radius
of the moon, M(moon) is the mass of the Moon, M(earth) is the mass of the
Earth. Now, since mass is density times volume, and since the volume of a
sphere is 4/3 pi R^3, we can set these two forces equal to each other, cancel
out the little mass, m, and rewrite with some algebra the resulting equation
in terms of the density of the Earth and Moon:
D(tidal) = R(earth) x ( 2 x Density of earth/Density of moon)^3Which says that the distance to the 'Tidal Radius' depends only on the radius of the primary body, and the ratio of the densities of the two bodies. For the Earth-Moon system, an accurate determination of this distance is 2.9 times the radius of the Earth. If the Moon or any other passing asteroid came within 18,500 kilometers of the Earth, its would be tidally disrupted into small fragments. The entire ring system of Saturn is inside Saturn's tidal radius for objects made of rock and ice.