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The paper seeks to explain why the central core of Saturn's F ring is so consistently shaped, even though various things are constantly acting to perturb it.

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In particular, Prometheus periodically plunges into the F ring, drawing out dramatic streamers and fans. In fact, Prometheus and Pandora, far from behaving as shepherds, actually act to stir up the motions of particles in most of the region near the F ring. Furthermore, there are other bodies that Cassini has spotted in the F ring region whose behavior is so chaotic that it's been hard to follow them; these things have "violent collisional interactions with the F ring core," so, all in all, it's really difficult to explain why the core of the F ring generally looks the same as it has ever since the Voyagers passed by.

Pretty much all of the structures in Saturn's rings that dynamicists can currently explain originate in orbital resonances, specifically mean motion resonances. Mean motion resonances are where two objects in orbit around a central body have orbit periods that are close to a ratio of two whole numbers -- like Pluto's orbital resonance with Neptune, or the orbital resonances of Ganymede, Europa, and Io. Although we think of orbital resonances using examples where objects are on stable orbits that are whole-number-ratio multiples of each other, it's actually more common for orbital resonances to be destabilizing, leaving gaps in ring systems and asteroid systems.

The largest gap in Saturn's ring system -- the Cassini division -- lies where particles have mean motion resonances with Mimas. Little Mimas exerts outsize control over the shapes of gaps and waves in Saturn's rings.

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The largest Cassini Division, between A and B rings, lies at the mean motion resonance with Mimas. This much I understood already, but there are other specific kinds of resonances that I've never understood and finally I asked for help on Twitter. Both Jeff Cuzzi's paper and the one I'll be looking at next featured Lindblad resonances, which are evoked to explain spiral arm structure in galaxies, but I couldn't figure out what they were.

Shepherd Moons: The Universe's Original Ring Forgers

Matt Hedman answered my call, for which I'm very grateful. He explained:. In the above simple case, the only thing that matters is where the moons are on their orbits. Things get more complicated if the orbits are eccentric or inclined, because now the moons are not just moving around the planet, they are also moving in and out and up and down. To give an example, Saturn's moon Mimas is on an eccentric, inclined orbit. It takes Mimas 0.

However, the time it takes Mimas to move in and out once is a bit longer, 0. This difference is why the point of Mimas' closest approach to Saturn steadily drifts or precesses around the planet. You know, I've been writing about space for a long time, and I had never heard this explanation of orbital precession: that the orbital period is not the same as the "in-and-out" period. I'm a geologist, not a physicist.

Shepherd moon

It's just a different way of framing the physics, but I had never thought of it that way before, and now a whole lot of stuff makes sense that didn't before. Thanks, Matt. He went on:. The fact that the moon's motion has multiple periods allows for different types of resonances. In particular, a Lindblad resonance is different from the resonance illustrated in the above cartoon because the perturbation on the moon's orbit does not always come when the moon is one the same side of the planet.

Instead, the moon always experiences the extra tug when it is at a particular point on its in-and-out motion.

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So: consider a moon and a ring particle orbiting Saturn. We don't care for the moment what the orbital periods of the moon and ring particles are; what we do care about is the "in-and-out" period of the ring particle in its orbit. You have a Lindblad resonance if, every time the moon passes by the ring particle, the ring particle happens to be on the same position in its in-and-out motion. Lindblad resonances generally tend to make orbits more eccentric make them move in and out more , and also tend to influence the position of the ring particle so that it's at either periapsis "innest" or apoapsis "outest" when the moon passes by.

Which one depends upon whether the particle is closer to Saturn than the moon, or farther, respectively. What Cuzzi and his coworkers figured out is that there is a peculiarity of the relationship between the orbital properties of Prometheus and particles in the F ring -- which they call an "antiresonance" -- where one shove from Prometheus nearly exactly cancels out the previous shove. This perfect balance is what holds the F ring particles in their orbits. Furthermore, these antiresonances are most effective in orbital positions that are not perturbed by Pandora, meaning that Pandora is not involved in shaping the F ring.

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They look at nearly nine years worth of Cassini astrometric observations to understand the motions and masses of the ringmoons. Cassini does these astrometric observations quite frequently, usually a few times per orbit.

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If you're a regular visitor to the Cassini raw images website , you'll see astrometric observations show up as a series of pairs of narrow-angle camera images of a dot near the rings. The two images of each moon are taken with different exposure times, helping analysts precisely locate the moon against background stars. Here is what the most recent astrometric observations of these moons look like:. There are all kinds of resonant interactions among these inner moons, many of which scientists have known about for a while.

For instance, there is the way that Janus and Epimetheus have a "horseshoe" orbital configuration: on average, they orbit at the same distance from Saturn, but at any given time either Epimetheus or Janus may be closer to Saturn; once every four years, they switch positions. There is a orbital resonance between Prometheus and Pandora, which causes their orbits to interact chaotically, making them drift in their orbits from the time of the Voyager flybys to the time of Hubble observations to the time of Cassini.

For the album by Enya, see Shepherd Moons. Retrieved Bibcode : Natur. Bibcode : Icar.. Reports on Progress in Physics. Bibcode : RPPh Planetary Ring System. Springer Praxis Books. Bibcode : Sci April Campo Categories : Celestial mechanics. Namespaces Article Talk.