I'm not the best person to talk about this, gmPhil. I'll talk at length about blue stars and starforming galaxies, but about Saturn... not so much.
Still, let's look at the picture again. You can see that there are some strange "ring shapes" on the "disk" or "body" of Saturn itself. However, what we see here is mostly the
shadows of the rings, not so much the rings themselves.
Here you can see a man's feet and lower legs and the shadows of his feet and lower legs. They are not in the same plane. You could photograph the man so that you see little of his shadow, and you could photograph the shadow so that you see little of the man.
I think we see both the dark unlit rings across the very faintly lit "disk" of Saturn, but we also see the shadows of the rings on the "disk" of Saturn. However, the rings also seem to be "backlighting" Saturn, faintly reflecting the sunlight they receive on the dark night side of Saturn.
I think it is this complex "shadow play" with dark shadows as well as reflected light that makes the rings appear to be "broken" over Saturn. Note that the rings are "tilted" from our point of view, further complicating the "shadow play".
Why is the outer "rim" of Saturn so bright? I would guess that it has to do with the mist above the cloudtops of Saturn. Jupiter doesn't have this kind of mist, which is why the cloud features of Jupiter are so stark and dramatic. The cloud tops of Saturn are so much more muted, because they are covered by mist. I would guess that this mist acts as a reflection nebula, spreading the light of the Sun around the circumference of the planet. But the mist is almost certainly semi-transparent, which is why you can see the Sun peeking through.
I also think that the shadow of Saturn itself is falling on the brightly lit rings, so that the rings seem to "disappear" before they "reach" the disk of Saturn.
I have no idea if I answered your question, gmPhil, but if not, why don't you ask, say, Chris or Art?
Ann
