Saturn's rings do the wave

By Phil Plait | June 11, 2009 5:12 pm


Holy Haleakala!

The thing is, it’s not just another gorgeous picture. This image — from Cassini, of course — is truly remarkable.

The first thing you should know is that Saturn’s rings are incredibly flat. If you scaled them down to the size of a piece of paper, they’d actually be far thinner than a single sheet of that paper. In fact, even though they’re about 200,000 kilometers across, they are only at most a few dozen meters thick!

But not everywhere.

Daphnis is a teeny tiny moon, just 8 km (5 miles) across. It orbits Saturn inside the broad A ring, and it’s carved a gap in the rings called the Keeler Gap. The gap is about 45 km (25 miles) across. As it happens, Daphnis has an orbit that is not perfectly circular, so sometimes it’s in the middle of the gap, and sometimes near the inner edge. Not only that, but the orbit of the little moon is tipped a bit, so sometimes it’s a bit above the ring plane, sometimes a bit below.

When it’s near the inner edge and also above the ring plane, it pulls the nearby ring particles up out of the ring plane with it. When it’s below the plane it pulls the particles down. When the elliptical motion of the moon is combined with the tilt, the gravitational interaction on the ring particles produces vertical ripples in the ring. These ripples have been predicted in the past, but now Cassini has clearly imaged them for the first time.

Here’s a closer view.

[You can get an even tighter zoom at the Cassini CICLOPS site.]

Right now, Saturn’s tilt is such that the rings are almost edge-on to the Sun (I’ve explained this in more detail in an earlier post). If you stand outside at sunset in a flat area, you can see your shadow stretching for a long way… and the same is true at Saturn. The rings are flat, and the Sun shining almost parallel to them, so any deviation from flatness is obvious by the shadows.

And that’s what you’re seeing in those images. Daphnis is the obvious white lump in the image with the long, black, triangular shadow stretching beyond it. And you can clearly see the ripples it causes in the rings, too! To the left of Daphnis the waves are on the edge of the rings outside the Keeler Gap, and on the right they are on the inside of the Gap. This may seem weird — it threw me for a moment — but remember the rings are made of particles that are traveling at almost but not quite the same speed as the moon itself. The particles in the ring outside the moon’s orbit (farther from Saturn) move a bit slower, and inside the moon’s orbit (closer to Saturn) move a bit faster. So it’s like cars on a racetrack, catching up and passing each other. When Daphnis passes the outer edge particles it pulls on them, and as the particles on the inside edge pass Daphnis they get pulled too. The combined motions are pretty complicated, but add together to produce the effect you see here.

And what an effect: those ripples are big, from 0.5 to 1.5 kilometers (1/3 to 1 mile) high. Even then they’re dwarfed by the immensity of the rings, though, which only rams home the scale of these images.


Saturn’s empire of moons and rings is an amazingly complex interacting system. But the mathematics of it is predictable, since the important factors are basically gravity and the fact that the particles can collide with each other and exchange momentum. Sophisticated computer models can be made which do predict these interactions, and that has been done. These ripples were not only modeled, but predicted to occur with this size before they were observed! John Weiss — Cassini astronomer and a friend– was the lead author on a paper about this:

We thought that this vertical structure was pretty neat when we first saw it in our simulations, but it’s a million times cooler to have your theory supported by such gorgeous images. It makes you suspect you might be doing something right.

True. But of course, that’s the essence of science. Predictions aren’t terribly useful unless they’re borne out by observations, and I agree strongly with John: it’s even better when images this spectacular have your back.

Science! Pleasing to the eye and the brain.

Comments (63)

  1. the Saturn system never ceases to amaze

  2. JoeSmithCA

    Does this mean Daphnis is gaining mass as it travels through the rings or is it getting erroded by collisions with the particles in the rings or non of the above?

  3. Bill Nettles

    A beautiful demonstration of Kepler’s 3rd law. I make my Earth & Space students explain those “front and back” ripples on a test.

  4. Lawdog

    I wonder what those rings would sound like if someone made a phonograph of them.

  5. dhtroy

    Wow. Just … Wow.

  6. Joe

    Lawdog– it would sound like Led Zepelin.

  7. JoeSmithCA:

    No, sadly. Daphnis (and all of the ring moons: Pan, Atlas, Prometheus, and Pandora) seems to be at *just* the right density so that the net force at the surface is zero. (This is a combination of tides, moon’s gravity, and rotation of the moon.) So no accretion for these moons. At least, not anymore…

    Actually, the A and B rings appears to be more like *one* dozen meters thick, based on results for a broad range of Cassini’s instruments. (Oddly, we should have expected that, as mind-blowing as it is. Numerical models predict it.) The thickness is mostly a struggle between gravitational interactions that tend to scatter particles out of the plane and collisions that damp the motions.

  8. It is so cool to think that I am taller than Saturn’s rings.


  9. PeteG

    I wonder what the view would be like from the surface of Daphnis, looking out across the rings?

  10. Arlo

    Thanks for all of the explaianatory science posts lately, Phil.

  11. jamerz3294

    Woosh! This stuff *never* gets boring, thanx for sharing! :)

  12. Steve

    Hey, Phil – how about a post on Betelgeuse possibly going supernova soon?

  13. Sundance

    Phil, I really hope the imbecile you mentioned a few posts ago (about asking the Moon’s permission before crashing Kaguya into it) sees this. I feel like grabbing her and saying “See? SEE?! Left-brain sciencey-stuff shows us things about the Universe that are infinitely cooler than your new age mumbo-jumbo!”

    Yet again, the Universe has given me reason to gasp at how unbelievably cool it is. And our own solar system is only such a miniscule part of it. How much more is out there for our left brains to discover admire the elegance and complexity of, and our right brains to admire the beauty of?

  14. That’s just amazing. You made my day with these images and your explanations of the science.

  15. @Liz D

    So, I’d estimate that you’re between 40 and 120 feet tall.

  16. Phil:
    Actually, predictions -ARE- terribly useful when they’re not borne out by observations. This is when you learn that you’ve been wrong in your assumptions and need to rethink things.
    But you knew that. ;^)

  17. Liz D @ 8, the link to your blog should have a dash in it, rather than an underscore. It took me an extra 30 seconds for find your blog!

  18. Stone Age Scientist

    This is what I love about Phil’s blog. It takes me out of my stone-aginess.

    Phil, do you also write sci-articles for Discover?

  19. SpriteSuzi

    Absolutely beautiful and awe inspiring – thank you Phil!

  20. Maugrim

    I swear, the best thing about this blog is Phil’s contagious enthusiasm. I was all set to swing right by this post in my feed reader, thinking exactly what he wrote as his first line. But he sucked me in, and I’m glad he did.

  21. Kristin Carlsson

    Daphnis wins +10 solar system points for awesomeness.

  22. markogts

    Is this picture taken upside-down, i.e. from the south pole? It looks like the moon is traveling to the right, but aren’t all the rotations in the solar system counterclockwise?

  23. Stone Age Scientist

    Not only was I surprised that a moon could be that small, but that this thing (Daphnis), according to this Wikipedia article, actually travels around Saturn in just 14.257915 hours!! Your metaphor of racetrack cars is spot on.

    By Jove!! Some of these satellites orbit around Saturn fast, and I mean FAST!!!

  24. markogts: Short answer: Yes, this is a lit-face (southern face) image.

    Teach-a-man-to-fish answer: if you got the CICLOPS site and look at the caption for the image (or any image), it’ll include the geometric information about the image.

  25. timmy

    Great article Phil and thanks to John Weiss for his contributions, it made for a thought provoking read. One thought that it provoked is, has anyone ever modeled a right angle (to the rings) meteor strike? In all the photos of the rings, I haven’t seen any distortions that might come from such an event. It’s a huge target. There would be some degree of “healing” in the disruption over time but that would take a long time. Any thoughts?

  26. Small meteors wouldn’t leave much of a mark, the rings would flow back into the hole pretty fast. A bigger hole wouldn’t take very long, either. It’d sheer out due to the differential orbital speeds and disappear within a few orbits, I suspect. You probably need some what to keep the hole open in order for it to persist beyond that.

    There is evidence that a comet went through the D ring in the mid-80s. The evidence is in vertical distortions in the ring that are winding up with time. See

  27. Phil Hibbs

    I bet those slightly brighter lines that we see all across the surface are actually spiral, and the thick white wavy line near the dot is the leading edge of the spiral being formed. Maybe the rings are a huge Disaster Area record, and the dot is Hotblack Desiato’s recording ship!

  28. I follow the Cassini twitter as well as BA, and I found it amusing the Dr. Plait twittered about this before the Cassini. :)

  29. Off Topic: Dr. Plait: Whooping cough taking hold in my little neck of the woods:

  30. Lawyer

    What would be really cool is if Cassini folk guide Cassini to PUNCTURE the Inner portion of the Rings of Saturn in this shape using the structure of Cassini itself:

    (up/down is orthogonal to radius)

    __SS___ SS
    __SS___ SS
    __SS___ SS

    That way we have a symbol of PI circling around the rings for eternity (or the next mission ABR) around the perfect symbol for PI, the near perfect circular rings of Saturn.

  31. Gary Ansorge

    ,,,and here’s an aside about detecting life on exo-solar planets,,,

    The James Webb Space Telescope(launch in 2014???) may actually be able to detect life markers.

    ,,,and a short poem about Saturn,,,

    Free Range Artists

    Imagine poets running rampant
    in the asteroid belt,
    musicians playing the
    rings of Saturn like a
    painters and sculpters
    playing with materials
    made of star stuff
    unseen on planet earth,
    writers telling the stories
    of our mutant offspring
    as they trip the universal light.

    A million years of evolution
    is just around the corner,
    ten thousand new species
    may be born to carry on,
    if we can just
    love them enough to
    let them be
    artists of the universe
    ranging free.


  32. Greg in Austin

    It looks like the NASA/Hollywood stage directors are finally getting better at faking the images. All the shadows appear to be in parallel. ;)


  33. Gary Ansorge

    13. Sundance

    This poem is for you,,,

    The right brain listens
    to the butterflies wings,
    whipping up an
    Adriatic storm,
    then sings a song of rainbows
    for the noisy mind to see,
    that both may share in wonder
    and be pleased.



  34. Gary Ansorge

    ,,,and as ANOTHER aside, I wonder if Daphnis is accreting material from the rings? Study of this may give us some additional insight into planetary formation,,,

    GAry 7

  35. mike burkhart

    As I said before I would like to see a close up view of the rock and ice particles that make up the rings Saturn not just to see if the movies portry them right but it could answer a lot of questions about the rings and advance our undersatnding of how the particles are aranged in the rings and the sizes of the particles

  36. It really makes you wonder how old such a small moon as Daphnis is and whether or not -as it cleared its path in the A ring- it accumulated any mass or if it was whittled down in size to its present scale. Either way, this is a fantastic observation!

  37. MJKelleher

    Paging Niven & Pournelle — Are the Fithp on their way?

    Amazing photo, great explanation to get my head wrapped around. Thank you!

  38. Pseudacris

    Wow that is cool!
    Even cooler that it was predicted before we ever even saw it.

    Have you heard about the boy in Germany that was just hit by a meteorite Phil? Just a little one, no major injuries, but interesting!

    Here is the url for the story on yahoo news.

  39. Sylvan:
    We’re pretty sure that Daphnis grew from a smaller, denser core. We published a paper in Science in December of 2007 (look for Porco, Thomas, Weiss, and Richardson) where we explained how the densities and shapes of these moons are most consistent with a dense core accreting less dense material until it was at the point where no more material would accrete.

    Gary Ansorge:
    See comment 7 and this comment, above. :)

    It’d be cool, but it wouldn’t persist. Thanks to the racetrack effect Phil mentioned, material at different radii move at different speeds and any pattern you could make would be erased pretty fast. (That’s quite apart from collisions between ring particles filling in the holes, which is also a pretty fast process.) Ah, well. The laws of physics be a harsh mistress! (With a nod to Bender Bending Rodriguez.)

  40. John Weiss – Thank you! I’ll definitely look for that paper!

  41. Gary Ansorge

    John: So, how do those dense cores form in the first darn place? The implication here is that the Jovians must have first accreted a large, dense core, in order to then accumulate the lighter/less dense material. Or am I missing something?

    GAry 7

  42. Gary:
    Probably? Shards left from whatever body formed the rings.


  43. Gary Ansorge

    Jovians: BIG planets,ie, gas giants,,,

    So, we’re still left with a chicken/egg scenario. Even the sun becomes a problem. How could it accumulate light/less dense material w/o a dense core, which had to have already been accumulated by something else? I know, we have good models of the solar accumulation via shock wave interaction with a nebula, but again, the source of the shock wave must come from some other bodies explosion.
    I wonder if we’re missing something( a gravitational point source) that would provide the initial impetus, such as cosmic strings or dark matter? Then the initial impetus is quite understandable.

    ( I’m thinking that dark matter is nothing more than the gravitational effect of regular old matter on a neighboring brane. Hey, that works in string theory.)

    GAry 7

  44. Leave it to Daphnis to make waves…

  45. Lawyer

    Weiss: Thanks for your answer! I forgot further out material would be spinning slower, than its inward neighbor (as Sun’s Mercury is to our Earth)

    How dare I suggest defacing the rings? It appears they have a defense mechanism – the darn laws of physics!

  46. The Sun formed (we think) from the collapse of a cloud of gas. There is no solid core in the Sun (although the core is *dense* thanks to pressure). The collapse may have been caused by a nearby supernova (there’s reason to think it was).

    The planets form out of the gas (mostly) disk that forms around the protostar. (Material doesn’t fall in directly since it has some angular momentum.) The planets… now that gets more interesting. It’s *generally* believed that they form from the bottom up: small bits of solids stick together, which form bigger solids. Eventually, they get big enough to be aided by their gravity, so they grow even faster. The biggest stuff (out past the point where it was cold enough for hydrogen compounds to freeze into ices) eventually have enough mass to hold on to the hydrogen and helium and become giant planets.

    There is a dissenting view, though. It is still possible, within current data, for the planets to *also* be the results of collapse of the gas in the disk. Each little collapse would form a planet. Solid material would differentiate to the middle, so if the gravity weren’t strong enough to hold the case, you’d get a sold body.

    As far as the rings go, the parent body may have been a moon that formed a bit further out. The rings can’t accrete without a denser core because Saturn’s tidal forces frustrate that process. But a moon farther away can accrete just fine. If it then is broken up, perhaps by a large collision, it it would leave some dense pieces.

  47. Gary Ansorge

    AH yes. I completely forgot about the tidal interaction.

    Tanks for clarifying that.

    GAry 7

  48. Lawyer

    Is it just me or does it seem a little bizarre that gas can collapse on itself to form ANYTHING, let along planets or solar systems??

    I mean just due to Brownian motion (now we are going back to high school for me), aren’t all gaseous particles kind of flowing around randomly to increase the Entropy gods? I would think in space gas particles (like before our solar system formed) would be more spread out and so it would be almost impossible for gravity which decreases with the square inverse to find attraction to another far away (even 1 cm is far in gaseous terms) gaseous particle.

    I guess (with absolutely no relevant background whatsoever), that gas can only collapse when to black holes KISS or something. What else would cause the gravitation (can GAS just on its own do so)?

  49. Gary Ansorge

    56. Lawyer

    All matter exerts a gravitational attraction on all other matter(yeah, even Dark MAtter).

    Gas clouds collapse all the time. We call some parts of that stars, some planets. There are a number of mechanisms that can initiate collapse besides just the gravitational attraction of gas molecules to each other, such as compression of a gas cloud by shock waves from a nova(which forces gas molecules closer together and thereby accelerates gravitational collapse), possible cosmic strings, or the gravitational interactions of Dark Matter/normal matter or a wandering large object, neutron star, planet, etc. but these all just speed up a process that would eventually occur anyway. Gravitational collapse is entropy in action, ie, stuff falling to the lowest stable energy state possible, which is, eventually, a black hole.

    GAry 7

  50. Torbjörn Larsson, OM

    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 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.

  51. Brian Foley

    What a great prediction/discovery!

    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?


  52. Brian Foley:

    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: 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.

  53. Oh, sorry, I promise to watch which direction I aim that thing next time


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