Why not moons instead of rings?

What would be wrong with all that snow and rock making a couple of moons?

The snow and rock can stick together to make bigger objects.
These objects can attract more material to join them by their gravitational attraction.
We know that planets and moons exist, so this must work.
Even Saturn has lots of moons. They are just further out from the planet.

But we should worry about the tidal force . When is the gravitational attraction between two snowballs bigger than the tidal force pulling them apart?

The exact answer depends on lots of things: density of the moonlets, density of the planet, shape of the moonlets.
But clearly, the closer they are to the planet, the bigger the tidal forces are, so the harder it is to form moons.
The limiting distance from the planet is called the Roche limit.
Depending on the assumptions, it is about 2 times the planet radius.

So at least qualitatively we can understand why Saturn has rings close to the planet and moons farther out.

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Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA soper@bovine.uoregon.edu