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The "Lord of the Rings" has more than 60 moons, some of which are larger than Mercury. My question is, wouldn't the ring, which is mostly comprised of rocks, experience tidal effect whenever a moon is near?

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Most of the 60 moons in the Saturn system are far away from the rings and very small, so their effect on the rings is negligible. But larger ones that are closer in (Enceladus) do have a rather significant effect on the rings, but as the gravitational pull of these moons is radially outward, it is hardly visible. On the other hand, small moons inside the rings that are a few kilometers in diameter cause significant changes in the ring system.


(source: magicgate.eu)

The orbits of those giant rocks are slightly inclined relative to the rings, which causes the rings to create a bulge in the direction of the small moon as seen in the picture. And these effects are fairly significant as the rings are mostly just a few hundred meters thick or less without a moon present, but with one, they are possibly hundreds of kilometers spread out.

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