If Daphnis had 0 inclination, I wouldn't think it would pull ring material out of the plane. I would guess that it has a very slight inclination. If my math is correct, an inclination of .0042 degrees would place its center 10 km above (and below) the ring plane [sin(10/136,505) when maximally out of plane. Its diameter is listed in Wikipedia as 6-8 km. So at zero inclination it should stick up 3-4 km and throw an appropriate length shadow. If the shadow is longer than expected, then we can figure how much it can move above the ring plane and its inclination. I'll leave the trig analysis of pixels to someone with a better brain and more time than I.

What we are seeing is the gravitation wake of Daphnis in the Keeler gap. The wake has both an radial and angular (vertical) components.

Reference this link for some cool simulations of the wake http://www.cs.trinity.edu/~mlewis/Rings/KeelerGap2005/

and this for a more mathematical treatment http://oldenhuis.info/Reports%20and%20Arti...nis/daphnis.PDF

Cheers

Nice catch on the Daphnis wake shadows. I like the eensy little shadow that Daphnis itself makes on the rings as well. Seems like it should be possible to learn more about the size and even shape of Daphnis from looking at its shadow, but you'd have to know Daphnis' vertical position (if it deviates at all from being within the ring plane) and whether the ring itself had any warp at all to it.

I'm guessing it's not a coincidence that those shadows in the images we were originally discussing were located so close to Mimas' orbital position.

--Emily

The Looking Ahead Rev109: April 16-May 2 (posted previously by ngunn) indicates that many images of interest are being taken. Nothing has appeared at raw image page since April 14th, guess the image pipeline from Saturn is no better than from Mars at he moment.

April 17-Shadows of Mimas and Tethys on A & B rings
April 24-Daphnis
April 29-Shadow of Tethys on A & B rings
April 30/May 1-Daphnis & shadow of Mimas on A & B rings

I didn't want to say anything, but when I was out at Goldstone last month with Doug I tripped over a cable. It gave off a few sparks and I smelled a bit of smoke. I was afraid something like this would happen.

Figured it must have been something that someone from UMSF did that wiped out the image pipelines.
And an Admin person to boot.

chemman
The simulation of Daphnis' wake is totally awesome. I also enjoyed the manuscript, but the math is a bit beyond me. Thanks for posting these great links. Welcome to UMSF if someone hasn't welcomed you previously.

This picture, N00133715.jpg, was taken April 16 in the F-ring series. Is there a groove at the top of Prometheus, or is this a shadow of the F-ring on Prometheus?

Floyd, considering illumination from below, I tend to think is F-ring shadow.
Very interesting also the sequence of these two ringlets, with clear shadow projeced above.
Below, I made elaboration of both images, with subtracted "dark field" (horizontal weak bands) and improved contrast/sharpening.
Click to view attachment Click to view attachment

The recent images showing satellite shadows are interesting, e.g. this one:

http://saturn.jpl.nasa.gov/photos/raw/rawi...?imageID=190253

The "brightness reversal" within the shadow near the bottom is interesting. This is the unlit side of the rings.

A wide angle frame taken a bit earlier:

http://saturn.jpl.nasa.gov/photos/raw/rawi...?imageID=190230

Very interesting! I'm guessing the brightness reversal occurs because in this particular geometry, that part of the rings is illuminated more by Saturn than by the Sun (e.g., maybe the image has a forward-scattering geometry for Saturn light, and that part of the ring is particularly forward-scattering. Or maybe it's an opaque part of the ring and not much sunlight gets through from the lit side). So it's still lit by Saturn even in the shadow.

Looking forward to all sorts of even cooler effects as the equinox approaches...

John.

I notice that the edges of the umbral shadow become increasingly diffuse as they approach the apex of the cone. I swear that I also see the straight edge of the prenumbra as well, esp. on the left-hand side. Is this telling us something useful about the distribution of fine particles in this section of the rings, esp. that of any slightly above the ring plane?

It would be extremely interesting to catch a shadow across a spoke.

Wow...

http://saturn.jpl.nasa.gov/photos/raw/rawi...?imageID=190390

Discuss!

An even more pronounced brightness reversal than in the earlier image I noticed. We are looking at the unlit (northern) side of the rings and what John pointed out must be happening here: Saturnshine illumination and the brightness is providing a measure of optical depth. Where the brightness is not reduced within the shadow the rings must be completely opaque and illuminated by Saturnshine only. In the dark areas within the shadow the rings are tenuous and therefore do not reflect a lot of Saturnshine. However, sunlight filters through them from the lit side.

The explanation makes sense but what I can't get my head around is why the various opaque\not opaque ring bands then seem to be so similar in overall brightness outside of the shadow regions.

If it wasn't for the fact that the orbital mechanics make it impossible my first reaction would be that what we're seeing (especially in this image) is a shadow falling on a much lower ring region with the unshaded rings inhabiting an orbit that is substantially higher and thereby were outside of the shadow cone.

Yes this is a really neat image, as mentioned the shadow is sorting out the sunshine vs saturnshine components of the ring illumination. Really gives us a chance to understand what we're seeing in general with all the unusual ring illumination geometries. For me personally it gives a fuller appreciation of looking during past equinoxes to view the dark side of the rings through telescopes.

And I had thought that only the lit side of the rings had cool images. Here is a chronology of past encounters with links to some of the images and dates for future encounters. Dates are from Looking Ahead and Tour Dates 2009.

April 03 Titan encounter/Ring plane crossing north to south to sun-lit side
April 07 Mimas & Teths shadows
April 08 Closest Saturn
April 08 Mimas & Teths Shadow
April 10 Pan
April 11 Ring plane crossing south to north to unlit side
April 16 Furthest Saturn---------------------------------------Start Rev 109
April 17 Mimas and Teths shadows
April 19 Titan encounter/Ring plane crossing north to south to sun-lit side
April 23 Closest Saturn
April 24 Daphnis
April 26 Ring plane crossing south to north to unlit side
April 29 Teths shadow
April 29 Pan
April 30 Mimas shadows & Daphnis
May 02 Furtherst Saturn---------------------------------------Start Rev 110
May 02 Daphnis & Pan
May 05 Titan encounter/ Ring plane crossing north to south to sun-lit side
May 09 Closest Saturn
May 09 Mimas & Pandora shadows
May 09 Daphnis & Pan
May 10 Daphnis
May 11 Ring plane crossing south to north to unlit side
May 12 Mimas & Teths shadows
May 14 Pan
May 17 Furthest Saturn----------------------------------------Start Rev 111
May 21 Titan encounter/Ring plane crossing north to south to sun-lit side

And, of course, we now see a shadow of Pan on the rings:

Interestinger and interestinger...

--Bill

The little moon in the outer gap in that photo still casts no shadow, though.

Not sure that's a moon, Steve; looks like a CR hit to me.

Definitely a CR hit. Daphnis would have a wake around it, as do all the Daphnis images linked in the table. I've tried to pick out one of the best images for each moon shadow set. I'll add more links as images come in. Images of Pan and Daphnis can be found using the Cassini Search Raw Images with Camera: Narrow Angle, Target: Pan or Daphnis and Observation Time, Newest. To get the images of Mimas, Tethys or other moon's shadows, you can't search on the moon as it is not in the image. Instead use Camera: Narrow Angle, Target: Saturn-RINGS, and Observation Time: approximately day before to day after. You can use Newest, except you get a lot of images as Cassini has taken ring movies which show up as a few pages of images.

That very interesting observation prompted me to do some back of the envelope calculations. I obtained the following approximate results:

1. Surface brightness of the sunlit side of Saturn relative to the Sun = 1.2 x 10*-7.
2. Solid angle subtended at a typical ring particle by one hemisphere of Saturn relative to Sun = 5 x 10*5.
3. Present average cosine of illumination angle of saturnshine relative to sunshine crudely estimated to be 10.

1 x 2 x 3 = 0.6 or saturnshine 60% of sunshine.

These ring images remind me strongly of Bunsen's experiment to measure the luminosity of the sun which I have only last week repeated with my students.

(In this experiment a drop of oil is placed at the centre of a white filter paper, rendering that part of the paper more transparent. The filter paper is placed so that direct sunlight falls on one side, and light from a lamp on the other. The lamp is moved close in to the paper until the wet part appears the same brightness as the rest, from whichever side the paper is viewed. This occurs when the illumination is equal on both sides.)

Very interesting observations, ngunn!
Correct me if I'm wrong, the reason of equal luminosity observed by helvick is that, in such ring portions, scattered light from the sun has the same intensity of reflected light from Saturn...
(I didn't know the Bunsen experiment, looks pretty cool!)

That's a brilliant explanation ngunn - and I love the bunsen experiment comparison. I know there are plenty of other examples of shadowed lighting revealing details\characteristics that are otherwise hidden but I really love this one.

May 9th images down. I'll post some links when I get back from Star Trek
Pan
Daphnis
Mimas Shadow

Star Trek was great!! No shadows of the Enterprise on the rings, but flying out of Titan's atmosphere was cool.

Ooooo!!!! Ahhhhh!!!! Seriously!

That Daphnis shot is particularly wild; some of the wake knots look like they're casting little shadows of their own, while the moon isn't!

Which moon is casting that shadow on your last pic, Floyd? Mimas? I don't see any of the ring rocks anywhere nearby.

nprev, I think its Mimas. Updated my previous post.

Quick animation of 6 of today's raws, showing the shadow of one of the moons (dunno which one) sweeping across the rings...

http://cumbriansky.files.wordpress.com/200.../animation1.gif

Propeller:

http://saturn.jpl.nasa.gov/multimedia/imag...0/N00136051.jpg
http://saturn.jpl.nasa.gov/multimedia/imag...0/N00136052.jpg

Good eye! I would never have noticed that. It's looking like most of the disturbances in the ring are 3-D, not just 2-D.

John

April 03 Titan encounter/Ring plane crossing north to south to sun-lit side
April 07 Mimas & Teths shadows
April 08 Closest Saturn
April 08 Mimas & Teths Shadow
April 10 Pan
April 11 Ring plane crossing south to north to unlit side
April 16 Furthest Saturn--------------------------------------------------------------------------------------------------Start Rev 109
April 17 Mimas & Teths shadows
April 19 Titan encounter/Ring plane crossing north to south to sun-lit side
April 23 Closest Saturn
April 24 Daphnis
April 26 Ring plane crossing south to north to unlit side
April 29 Teths shadow
April 29 Pan
April 30 Mimas shadows & Daphnis
May 02 Furtherst Saturn--------------------------------------------------------------------------------------------------Start Rev 110
May 02 Daphnis & Pan
May 05 Titan encounter/ Ring plane crossing north to south to sun-lit side
May 09 Closest Saturn
May 09 Mimas & Pandora shadows
May 09 Daphnis & Pan
May 10 Daphnis, Daphnis, Mimas & Mimas -
May 11 Ring plane crossing south to north to unlit side
May 12 Mimas & Teths shadows (I didn't find them?)
May 14 Pan
May 17 Furthest Saturn---------------------------------------------------------------------------------------------------Start Rev 111
May 21 Titan encounter/Ring plane crossing north to south to sun-lit side
May 24 Pan & Daphnis
May 25 Closest to Saturn/periapse
May 25 A-Ring images of Encke and Keeler gaps-looking for topology
May 26 Ring plane crossing south to north to unlit side
May 27 Moon shadows Pan & Mimas
May 27 Daphnis in Saturn's shadow
May 30 Moon shadows Mimas, Pan & Prometheus
June 01 Moon shadows Pandora, Pan & Mimas
June 02 Furthest from Saturn/apoapse---------------------------------------------------------------------------------Start Rev 112
This is an update with several more links plus Rev 111 image plan

Great image of Daphnis shadows. Link Thirty images of Pan and shadow. Link
Someone more skilled than I could make a great movie. [The Cassini links and images seem to come and go.]

Here even with my eyes it's remarkable how the 3-D aspects of the perturbations are there for us to see.

I wonder if Daphnis bobs up and down relative to the ring plane. It would be interesting to watch its shadow on the rings to see if the length oscillates.

Daphnis' orbit might be ever so slightly inclined relative to the rings. If one could image it in its orbit from 45 degrees before closest approach to sun to 45 degrees past, Daphnis could (if you are lucky in how the axis of inclination lined up with the direction of the sun) move from maximally above or below ring plane to zero, of zero to maximally above or below. I don't think there is any mechanism that would allow it to bob up and down quicker than one orbit, which just equals an inclined orbit.

Not sure about that - what about the gravitational field of the rings themselves? The disturbed wake material looks as if it's bobbing up and down.

Or Daphnis gravity field isn't spherical nor aligned with the rings. Depending on which side of the moon the particles approach to, they would end above or under the plane.

I agree that the ring material is bobbing up and down. Don't know about Daphnis. It would be important to know the mass of Daphnis vs the mass of the particle bunches we see bobbing.

How sure are we that the perturbation is purely gravitational? Could the ring particles be colliding as a result of Daphnis's passage?

Why would that be critical in this context? Ring particles and Daphnis alike are in free fall. Shouldn't they respond the same way to whatever field is present?

Yes there must be either collisions or viscous drag of some kind to damp out the bobbing in the case of the ring particles, but not Daphnis in its gap.

Straightforward application of Kepler's third law would tell us how fast that ring edge is drifting past Daphnis. That combined with the observed wavelength of the wake perturbations should yield the number of bobs per orbit (or orbits per bob?). Anybody fancy the maths? I can't - I've got a busy day.

Ngunn & Gsnorgathon, I think the above simulation and paper are very relevant to this discussion. Ngunn, I mentioned mass, because that of Daphnis is big enough to kick up a wake that bounces ring particles both radially and angularly (up and down) without the particles having enough mass/gravity to perturb/bounce Daphnis. It would sure be nice if one of the authors of the PDF could comment--or anyone else who is an expert in orbital mechanics--which I'm not.

There is the very simple consideration that when two objects are perturbing each other, the more massive one will move less and the less massive one will move more. It makes sense to me that the rings could try to pull Daphnis bobbing up and down if they are massive enough. Perhaps a relatively simple model could show this?

As an analogy I believe that we (with the Sun) bob up and down in the plane of the Milky Way galaxy.

Yes. The rings must have an effect on Daphnis, though, by adding a restoring force toward the ring plane. If the resonant period of the resulting vertical motion is close to the orbital period (or a multiple or a sub-multiple) this might even maintain the non-zero eccentricity and inclination of Daphnis which otherwise you might expect to get damped out eventually. The particles at the gap edges would, I now realise, experience a bigger restoring force than Daphnis itself because the very nearest part of the rings would contribute a significant fraction of the total and for Daphnis that nearest part is missing (most of the time - I think its eccentricity takes it quite close sometimes).

I realise that the reality of all this is much too complex for my kind of handwaving analysis, but I enjoy trying to build my own first order approximate understanding of what is going on whenever possible. Thanks for the links. See also this, from Ciclops:
http://ciclops.org/view_media/5598/Discove...f_the_Wavemaker

This sounds like one to read - pity I don't have access to it.
http://www.iop.org/EJ/article/0004-637X/68...9/73975.web.pdf

Aha! Here it is in poster format:
http://gemelli.spacescience.org/~hahnjm/co...2007/poster.pdf

Floyd - thanks for the link to the simulation. I'm mortified to admit I'd previously seen those, but just watched the vids in "ooh-aah" mode. That oughta teach me.

ngunn: nice abstract. Do I understand correctly that in the long term for Pan and Daphnis, e and i are damped to 0 and therefore they have stable orbits. The ripples we see (with shadows) are a more short term effect than described in the abstract?
scalbers: you are of course correct that there are always reciprocal effects. Big mass little effect--Little mass big effect.
ngunn: Daphnis may therefore bob a little relative to its mass vs ring particles. However, the induced motion of the ring edges seems to be both up and down--as well as in and out radially. Could it be that the complex sinusoidal shape created has a net zero vertical and radial gravitational effect on Daphnis?

I hesitate to comment further, given the complexity of the situation, the sophistication of the published analysis and my almost total ignorance, but here's how it seems to me reading the Hahn poster.

There are Daphnis-ring interactions working both ways. Some mechanisms pump up the inclination and eccentricity while others damp them. The ultimate cut-off for the eccentricity seems to be the point at which the moon collides with the ring edge. At this point damping is enormously increased, presumably for both e and i. So we could be looking at a system which varies in an irregular way, mostly within narrow limits but with a safety barrier in place to chop off any sudden spikes in the orbital parameters.

One theme runs through this: there are undoubtedly dissipative processes involved, so there must also be an energy source. I haven't a clue what form that takes. Gradual widening of the gap? It's slow migration, along with Daphnis, either inward or outward? Angular momentum somehow transferred from one of the larger moons via resonance? I stand in awe of this whole mid-boggling circus and of the efforts of those who have the daunting task of sorting out its workings. I wish them luck! For me, it's back to the sofa with a glass of home brew.

Clarification relating to your last question: I never meant to suggest that the vertical waves in the wake have a significant reciprocal effect on Daphnis, only that the rings as a whole acting as a planar mass must have - a very simplistic point.

A whole new series of images of Daphnis taken on May 25th. N00136503-N00136509 plus a few more where only ripples are visable.
N00136503;N00136504;N00136505;N00136506;N00136507;N00136508;N00136509
Click to view attachment

Also a new propeller N00136512-N00136519. It comes in from the left just outside (below) the Encke gap in image 12 and goes out the right side of image 19.
N0013612;N0013613;N0013614;N0013615;N0013616;N0013617;N0013618;N0013619
Click to view attachment