Saturn's Rings - Perfect circles?

[Gaius.Cornelius]

My first post…

In discussing the Cassini mission with some friends, the subject of those implausable rings came up. On the basis of no evidence at all, I found myself saying: “woudn’t those rings have to be perfectly circular, if they were at all eliptical they could not possibly be stable.”

My friends disagreed. Now, I only have an intuative (at best) grasp of celestial mechanics, but something still tells me that I must have been right. Can anybody shed any light of this topic?

[Q.E.D]

Are the rings circular? Nope:

Another challenge scientists face in understanding the rings is that even general dimensions do not seem to remain true at all positions around Saturn: The distance of the B-ring;s outer edge, near a 2:1 resonance with Mimas, varies by at least 140 kilometers (90 miles) and probably by as much as 200 kilometers (120 miles). Furthermore, the elliptical shape of the outer edge does not follow a Keplerian orbit, since Saturn is at the center of the ellipse, rather than at one focus. The gravitational effects of Mimas are most likely responsible for the elliptical shape, as well as for the variable width of the Huygens Gap between the B-ring and the Cassini Division.

[Padeye]

I think you may be arguing a matter of degree. After all what does an ellipse become as the foci are close to being the same point? I’ll go even one better. I’m pretty certain that all the particles make up the rings don’t all orbit in the same plane. I don’t think the variation is very much but any particle at the “top” face of the ring at one point is going to be at the bottom point on the other side. A few geosyncronous satellites deviate this way and appear to have a N-S cylical motion that takes 24 hours to repeat. No doubt particles bump but as for stability how long have you been watching it?

[Polycarp]

If you draw a whole bunch of “shallow” ellipses – ellipses not terribly far off from perfect circularity, but definitely elliptical – the net result is an area that is effectively annular (ring shaped) – a locus occupying the area between two circles. That’s essentially the effect of the elliptical orbits of the particles in Saturn’s rings – and of the stars in the galaxy.

[Gaius.Cornelius]

@Polycarp

If you draw a whole bunch of “shallow” ellipses – ellipses not terribly far off from perfect circularity, but definitely elliptical – the net result is an area that is effectively annular (ring shaped) – a locus occupying the area between two circles. That’s essentially the effect of the elliptical orbits of the particles in Saturn’s rings – and of the stars in the galaxy.

I don’t think that is necessary for every particle to have an exactly circular orbit, only that it would be very nearly the case. In any event, what you describe is perfectly circular rings. Similarly, I can see that the rings have a finite thickness, so I can see that individual particles will go up and down as they orbit.

Clearly there are many concentric rings. I am really thinking of those that are close together not any outer rings that might be exceptional in some way. It still seems to my fuzzy head that if the rings were more than very, very slightly eliptical, they could not be stable.

[mitchythekid]

Uniformed,yes.With all of the variables that could inter-act with the rings shape,impossible.Sorry