Since Daphnis is pulling at the ring material, and the ring material is also pulling at Daphnis, won’t the effect eventually die away as the drag from the rings forces Daphnis’ orbit to become a circular, in-plane one?

Not necessarily. It’s hard to predict a priori. The main effect of the pull back from the ring material is to shift the node of Daphnis’ orbit around and to make Daphnis’ vertical motions a bit faster. Beyond that, it actually appears to depend on the gap size and the mass of the ring. (Joe Hahn, now of the Space Science Institute, did some very nice work on this in 2007.) Our simulations more or less agree with his conclusion, that it’s too close to tell if Daphnis’ orbital inclination should be pumped up or damped down. (On the other hand, I consider that a weaker conclusion of the paper since there are a lot of variables there that I think are iffy.)

If it is being damped/pumped? Thousands of years or so.

And yep, the waves do enhance collisions in the rings. (This is why you get those wonderful wakes near Pan: http://ciclops.org/view.php?id=1108.) And no, they probably don’t let to welding the particles together. Collision speeds are about 1 mm/sec. in most of the A ring. Even if you jump that up by a factor of ten (and remember, the particles near each other are generally moving more or less together), that’s 1 cm/sec, which isn’t fast and doesn’t produce a lot of energy. Rough calculation: assuming that *all* of that kinetic energy goes into heat, you produce around 1.6×10^6 ergs, or 0.04 calories, for two 1-m sized bodies. Even if you’re just heating a thin, thin layer, one gram, of water at the point of contact, that’s only 0.04 Kelvins hotter. Not likely to melt.

Since Daphnis is pulling at the ring material, and the ring material is also pulling at Daphnis, won’t the effect eventually die away as the drag from the rings forces Daphnis’ orbit to become a circular, in-plane one?

How long will this take?

Also, does all the relative motion of the ring material significantly increase the number of ring particle collisions in the region? And if so does that cause the particles to stick together to become larger chunks (energy from impact momentarily liquifying and re-freezing the particles), or do they get sand-blasted into a fine dust?

Thanks,
Brian.

Gravitational collapse is entropy in action,

Physicist John Baez has written a FAQ (sort of) on the complexities of gravitation and entropy:

If you weren’t careful, you might think gravity could violate the 2nd law of thermodynamics. Start with a bunch of gas in outer space. Suppose it’s homogeneously distributed. If it’s big enough, it will start clumping up thanks to its gravitational self-attraction. So starting from complete disorder, it looks like we’re getting some order! Doesn’t this mean that the entropy of the gas is dropping?

Well, it’s a bit trickier than you might think. First of all, you have to remember that a gas cloud heats up as it collapses gravitationally! The clumping means you know more and more about the positions of the atoms in the cloud. But the heating up means you know less and less about their velocities. So there are two competing effects. It’s not obvious which one wins!

Let’s do a little calculation to see how this works. [...]

and so we see the entropy DECREASES as the volume of the ball decreases.

Yikes! Does this mean that gravity violates the 2nd law of thermodynamics? No, not really. Before we jump to that conclusion, we have to think a bit harder – there some things we still haven’t taken into account. [...]

In the calculation I just did, it’s a bit hard to see exactly why the entropy of the gas cloud goes down as it shrinks. As the gas cloud shrinks, each atom roams around a smaller region in position space. That tends to *reduce* the entropy. But as the gas cloud shrinks, it gets hot – so each atom roams around a bigger region in momentum space. That tends to *increase* the entropy.

To figure out which effect wins, we need to [...]

Here we see quite clearly how as the cloud shrinks, the *position* uncertainty the atoms decreases faster than the *momentum* uncertainty grows. This is why the entropy of the gas cloud decreases when the cloud shrinks. [...]

So far, we’ve seen the entropy of a gas cloud actually DECREASES as it collapses under its own gravity. At this point, you should be dying to see how I’m going to rescue the 2nd law of thermodynamics! But before I do that, I want to point out another odd fact: our gravitationally bound ball of gas has a NEGATIVE SPECIFIC HEAT! In other words, the less energy it has, the hotter it gets.

To see why, [...]

In other words: THE LESS ENERGY THE GAS HAS, THE HIGHER ITS TEMPERATURE BECOMES. [...]

In fact, it’s typical for a gravitationally bound system to have a negative specific heat. Imagine a satellite so low that it starts running into the earth’s atmosphere and spiralling down. As it loses energy, it gets hotter, and finally burns up! [...]

It follows that though some of the inequalities (1)-(3) are a bit surprising, if we switched the direction of any one of these inequalities, we’d get a contradiction with things we know.

Saving the Second Law of Thermodynamics

As our gas cloud shrinks, its entropy goes down… so the entropy of something else must go up, or the 2nd law of thermodynamics is in deep trouble! [...]”

… and then he finishes off with a tease. The answer is, I guess, that thermal radiation will take the entropy in a gravitationally bound gas and deliver it to infinity (i.e. space).

Now you may wonder if this somehow messes with the universe expansion towards infinity, which after all is the driver of entropy’s constraints. (Without expansion, the universe would get stuck in maximum allowable entropy at its outset.)

We now know that standard cosmology has the fate to expand forever. But we also know that black holes (and, I think, atoms by way of the nucleus inherent quantum instability – they will eventually tunnel nucleons away, with a looo…ooong decay time) are quasi-static objects. They too will radiate energy and displace entropy until they are gone, leaving but a Pompous POOF of the Big Bang.