If Saturn's rings cannot coalesce into a moon because of tidal forces, then how are shepherd moons able to exist?

Question

From Wikipedia:

In celestial mechanics, the Roche limit, also called Roche radius, is the distance within which a celestial body, held together only by its own force of 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.

However if tidal forces are strong enough to prevent the rings from coalescing, then how are shepherd moons such as Pan and Daphnis able to exist without being disintegrated by Saturn's tidal forces despite literally orbiting within the rings themselves?

Answer 1

The Roche limit is calculated on the assumption that the orbiting body is held together only by its gravitation i.e. there are no cohesive forces with the body that help hold it together. For large bodies this is a reasonable assumption, and indeed it is why large celestial bodies are approximately spherical. Their gravitation is so much stronger than any cohesive forces that the material from which they are made flows like a liquid to form a sphere. When you put a large body inside the Roche limit the tidal forces will also make it flow and ultimately pull it apart.

However as you decrease the size of the body the gravitational forces decrease until they become smaller that the cohesive forces. The reason that Mount Everest can exist is that the strength of its rock resists the gravitational forces trying to flatten it, and if you put Mount Everest inside (for example) the Roche limit of Saturn those same cohesive forces would stop it being pulled apart.

And this is why small satellites can exist within the rings. Those satellites are small enough that the strength of the material from which they are made can resist the tidal forces trying to pull them apart.