Is there some prediction of the speed of rings?

[Prometeus]

From NASA page:

The inner parts of the rings move around Saturn faster than the outer parts, all in accordance with Kepler’s third law for small objects revolving about a massive, larger one. They orbit the planet with periods ranging from 5.8 hours for the inner edge of the C ring, to 14.3 hours for the outer edge of the more distant A ring. Since Saturn spins about its axis with a period of 10.6562 hours, the inner parts of the main rings orbit at a faster speed than the planet rotates, and the outer parts at a slower speed.

Now my questions:

Why are the inner rings moving faster than rotation of Saturn?

Is there some expected relation between the rotation of a planet (or asteroid) and rotation of the particles in the rings?

Or is the speed of rings rather related to the gravity of the planet (or asteroid) and not related to rotation of the planet?

 

[russ_watters]

The rings are just particles in orbit. Their speed is a function of distance, as the NASA page says, and it has nothing to do with the planet's rotation. Just like our satellites.

 

[Chronos]

A ring is nothing more than a large number of small objects in orbit around a planet. Orbital velocity is a function of distance from the planet. At small distances the orbital velocity must be greater than at larger distances for a body to remain in orbit. A body in orbit cannot exceed escape velocity and remain in orbit, so there is a limited range of velocities permitted for objects forming a planetary ring. When orbital velocity equals the projected rotational speed of a planet at any particular distance ti achieves a synchronous orbit. Around Earth this is known as a geosynchronous orbit. This speed must increase with distance from the planet.without exceeding its escape velocity. A geostationary orbit is always in a geosynchronous orbit but not the other way around.

 

[Prometeus]

A ring is nothing more than a large number of small objects in orbit around a planet. Orbital velocity is a function of distance from the planet. At small distances the orbital velocity must be greater than at larger distances for a body to remain in orbit. A body in orbit cannot exceed escape velocity and remain in orbit, so there is a limited range of velocities permitted for objects forming a planetary ring. When orbital velocity equals the projected rotational speed of a planet at any particular distance ti achieves a synchronous orbit. Around Earth this is known as a geosynchronous orbit. This speed must increase with distance from the planet.without exceeding its escape velocity. A geostationary orbit is always in a geosynchronous orbit but not the other way around.

Thanks. So it is just a function of distance, escape velocity and gravity of the planet. The expected speed of rings has nothing to do with the rotational speed of planet.

 

[Chronos]

Correct, the ring speed is unrelated to the rotation speed of the planet it orbits

 

[LURCH]

So perhaps the question could be rephrased as, “Why is the surface of the planet rotating more slowly than the inner rings?”, right?

After all, if the planet formed from local materials that got pulled into orbit around a common center of gravity, then their speed should have been determined by the same dynamics as the materials in the rings. But that doesn’t seem to be the case. The same could be said of Earth, although I’ve heard that in our case, gravitational breaking is the reason. If we have been slowed down by the drag from our moon, is that what is believed to have happened to Saturn, as well?

 

[Bandersnatch]

So perhaps the question could be rephrased as, “Why is the surface of the planet rotating more slowly than the inner rings?”, right?

After all, if the planet formed from local materials that got pulled into orbit around a common center of gravity, then their speed should have been determined by the same dynamics as the materials in the rings. But that doesn’t seem to be the case. The same could be said of Earth, although I’ve heard that in our case, gravitational breaking is the reason. If we have been slowed down by the drag from our moon, is that what is believed to have happened to Saturn, as well?

It's been a few years since I read about rings, but from what I remember, their depletion rate is too high for them to be primordial. I think the model was along the lines of a breakup of a small orbiting body (either collisionally or tidally), and subsequent flattening of the debris through an interplay of self-gravity, collisional dynamics and tidal acceleration.