The ringlets that share the same radial locations as small moons in the gaps follow horseshoe like orbits. An example is Pan orbiting inside the Encke Gap which has a number of associated co-orbital ringlets.

So typically librating about the L4 & L5 Lagrange points in the Saturn - moon three body problem. If you just look at the Saturn - moon systems and particles in the presence of these two bodies you can replicate the ringlet shapes which can exist for long periods of time.

I personally have not come across gaplets or endlets before though. However, in very dynamic rings like the F ring partial rings do exist. The rather destructive environment means there are spiral like rings and parts of the ring detached from the main core. These evolve on fairly fast time scales where as I presume the features you mention exist in areas of some kind of stable resonances? 

Terminology now:

Saturn's disk is made of rings and gaps, seen from small telescopes. Recent NASA photos, such as the one under study reveal ringlets and gaplets between the ringlets. These gaplets are not just darker, but are more rarified. We are reusing the term ringlets here to specifically refer to the repetitive structures such as those seen so clearly in the photo. The clearer ringlets on the left abut the less distinct ringlets on the right, at a discontinuity down the middle of the photo. .

Macroscale is poorly mimicked by microscale:

We are happy that a moon of Saturn sweeps up material to form and maintain a gap on the large scale. On the smaller scale, we need to explain the persistent, pervasive, regular, mathematical behaviour we see.

On the fine scale, there is no need to invoke explanations for the maintenance of the ringlet spacing which involve resonance with moons. However, explanations of more complex disturbances in other photos do involve resonances. It is not by accident that I chose this clean photo for the study.

Mechanism:

A gravity unevenness in Saturn temporarily perturbed part of the closest (formative, forming, formed) ringlet material, temporarily moving part of it (a small sector) inwards and then outwards from Saturn. This part of the ringlet being disturbed temporarily caused the next (formative/ forming / formed) ringlet outwards to also be perturbed temporarily inwards and outwards via their mutual gravity. This action caused the first gaplet to be cleared (only in that small sector). The temporary perturbation moves back a bit, and another part of the gaplet is cleared. so the process continues, small sector by small sector, first around a full orbit and then fastidiously repeated in endless cycles {of mindless domestic maintenance on a cosmic}.

The ringlet being perturbed sector-by-sector causes inner dust to be neatly swept up sector-by-sector by the next (formative, forming, formed) ringlet. Mutual gravity increases as more and more dust is picked up. Soon the whole process becomes self-sustaining. An outer ringlet, when perturbed in and out, has a domino effect on its inner ringlets, triggering each to do its own domestic work to sweep up its own narrow environment in its own small sector. In fact, if there is any lump in a ringlet, this action will spread it out evenly, explaining the uniformity we see vertically across the photo. {Not only is the gaplet clean of dust, it is also aesthetically neat!}

 [edited 2017-1-19]

So on the picture at the top I think what you refer to as ringlets are actually spiral density waves. Lindblad resonances caused by larger outer moons (not embedded in the ring itself) and relate to the radial oscillations of the moon and ring particles. The ringlets will be visible at different longitudinal locations but at the same radial location in the ring. 

The interaction between these spiral density waves and the moon can move the moon radially in location. This can occur where a net torque is applied to the moon from the spiral density waves. 

So there does not need to be what might be considered a nearby moonlet causing these structures, instead they could well be 1000 km's away.

Please download, zoom in and explain the above photo. The unprocessed photograph shows a white vertical bar down the centre. (Do not refer to the Wikipedia reproduction which has rotated our study picture 90 degrees. We work with the original NASA release.) Here the ringlets appear as vertical bars down the image. They are not circular in the image because the photo is a (very) close-up photo. Each light bar down the photo is a ringlet; each dark bar is a gaplet. The main endlet is composed of the two whitest bars down the centre of the photo. (And maybe the dark, double density feature right of the centre). 

The right half has density variations, which do not show up as well because, being more planar, they have no peaks to catch the sunlight. The left half has caught the sunlight.

Bear in mind also that this is a close-up photo, and that the spacings we see between ringlets (the gaplets) are really very fine scale phenomena. 

I prefer not to refer to ring particles. This nomenclature can create a stumbling block in us modelling and trying to understand the very fine-scale features in photos such as this. 

Dirty ice lumps make ringlet sectors; ringlet sectors make ringlets; ringlets and gaplets make make rings; rings and gaps make the disc. This is a new hierarchy for future modelling and simulation, now that we have  such photos.

[edited 2017-6-19]

Please go to the project at https://www.researchgate.net/project/What-is-the-mechanism-of-ringlets-gaplets-and-endlets-in-Saturn-2

https://www.researchgate.net/project/What-is-the-mechanism-of-ringlets-gaplets-and-endlets-in-Saturn-2

As Phil said, that picture looks like a spiral density wave caused by an inner Linblad resonance. If you had the radial location, you could probably look up exactly what resonance with what moon you are looking at. Similar structures can also appear in certain lighting conditions from bending waves. These are caused by resonances with slightly inclined moons that lead to waves that only appear in the vertical structure and have basically no impact on particle density.

If you had a much higher resolution image of this, you would likely also see gravity wakes at the scale of ~50m. If this is in the A ring, that will almost certainly be true. It is less likely if this is in the B ring. The gravity wakes also change structure into what is called "straw" in the peak areas of strong density waves. I believe that is the result of coherent motions similar to what was seen in my 2005 Icarus paper looking at Pan wakes.

Most density waves are in the A ring region, with fewer observed down in the B ring for a variety of reasons. However, there are ringlet-like features in the B ring that aren't well explained, but the leading option if viscous overstability. Going further in, you have the C ring plateaus, regions of high optical depth with sharp edges. Those are very poorly understood as they appear to have the same surface density as the surrounding low optical depth areas, so the cause has to almost certainly be related to the particle size distribution.

@Mark. Thanks! I think that the left half is (pure) bending; the right half (pure) density, based on the directions of ringlets becoming closer.

The centre of the photo is more intriguing. The photo appears to be centred on the interesting discontinuity where the bending meets the density.

(A general view is that bending and density may come in pairs.)

This is a very high resolution (1024x1024 pixel) image, taken with the narrow-view camera. (The initial letter of the file name is N, not W.) What is surprising is the vertical uniformity of the "bars" in the photo. This may partially be due to motion smear, but it is still remarkable.

The clear ringlets (and their gaplets) on the left are self-maintained by nothing else than their mutual gravity. There is no straw-like structure visible as in some other photos, which surprised me. I expected to see visible corkscrewing. Certainly the photo being studied shows other discontinuities which might be explained by anti- and clockwise corkscrewing ringlets being adjacent and interacting.

Why do simulations build up by simulating particles, but never simulating ringlet sectors. E.g., 1 degree arcs of a possibly corkscrewing ringlet and its swept gaplet?

[edited 2017-6-19]

Can you define what you mean by moonlet instead of moon? If you mean a small body embedded in the rings that doesn't form a gap, they can't sustain eccentricity or inclination as frequent collisions would damp both out very quickly.

Once again though, without knowing the radial location of this photo it is hard to say much more.

@Mark. Thanks. It is a matter of scale. [definitions deleted]

As the ringlets associated with the gaplet are not inclined or elliptical in their orbit, they are self-sustaining. The most closely spaced ringlets will have the least agitation and be the darkest.

According to the uploader, the photo is of part of the D-Ring. https://commons.wikimedia.org/wiki/File:N00282108_rotated_edited_-_Saturn%27s_rings_from_the_inside.jpg 

Is D reasonable?

[edited 2017-6-19]

The definitions you are using differ from the standard definitions. By your definitions, many things that are commonly called moons become moonlets, even outside of the rings. Note that neither Pan nor Daphnis, which both open gaps, are spherical, nor are they visible from Earth. Both are called moons though normally. The term moonlet is generally used for larger bodies in the rings that are too small to open a gap.

Note that propellers aren't moonlets. They are structures formed by the wakes of moonlets. The moonlet is solid and small. The propellers are made of normal ring particles and span up hundreds or thousands of kilometers.

That image being in the D ring changes everything. It isn't cause by any moon or moonlet. The D ring is the one closest to Saturn. It has a very low density, and is so deep in the Roche zone that I'd be surprised if any icy body in the 100m-1km size scale could survive. On the other hand, the features in the D ring appear to be generated by features internal to Saturn. Matt Hedman is an author on most of the papers that look at these types of features. They are really cool in that they are able to tell us things about the interior structure of Saturn that none of our spacecraft instruments could directly measure.

Thanks for your clear definition: a "moonlet is [a term] generally used for larger bodies in the rings that are too small to open a gap". 

So, is opinion currently that propellers are built in situ?

Is the logic of creation: Moonlet settles down, gap gets formed, wake encourages prototype propeller to start, this grows to an extensive propeller (by accretion)?

"Cool", but not icy! :-) Hedman refers to "...or asymmetries in the planet’s internal structure" so there may be an off-centre gravitational anomaly in Saturn's body which explains the long term, smooth nature of the ringlets in the photo?

How you get moonlets is still very much up in the air. There are two potential mechanisms. One is that they are "primoridial" in that they are the same age as the rings and they just happen to be larger chunks that never got disrupted. In that case, their numbers should decrease over time as comets and whatnot run into them and break them up on timescales of millions of years. The other option is that under occasional, and rare, conditions, particles in the rings can aggregate. It is very unclear how this would happen, but especially in the A ring is seems feasible. I did some simulations where we saw spontaneous moonlet formation, http://www.cs.trinity.edu/~mlewis/Rings/FormMoonlet/. The large cell simulation is by far the coolest one. But these were very idealized particles. They were perfect spheres of a uniform size. They were also frictionless. The moonlet formation mechanism shown here required the uniform size so they could form a lattice, but non-spherical particles with friction might also be far more likely to lead to particles clumping together in semi-stable ways.

The features down in the D ring would likely be formed by long-living, non-spherical anomalies in the interior structure of Saturn. They can even tell the m-number of those anomalies and their internal speed based on the details of the features they create.

So does this photo prove that the ring is made up of short nested spirals?

Does it show that it is not ONE spiral (or even a series of concentric circles)?

Counting leftwards from the bright central bar, there is a bundle of 10 mathematically spaced bars, followed by an endlet or discontinuity, a bundle of of 4 mathematically spaced bars, followed by another endlet, followed by another bundle of 7 bars, ... etc. Each bundle is one multi-turn spiral! The number of rounds per spiral, b is 9, 4, 7, ... respectively. The "purpose" of an in-between endlet is then to provide a transition space to the next spiral. {celestial glue!}

@Thierry De Mees -- 

A motion of masses is not necessary to create a gravitational force or field, unlike the motion of charged electrons. F=GMm/d^2 contains no velocity term.

In our work, we have not yet had to invoke Saturn's magnetic field or electrostatic fields for explaining spiralets. All is explicable in terms of Newton and Kepler.

We are content to admit that there may be non-uniformities in Saturn's gravity which we may have to invoke.

However, we also do not subscribe to theories of gravitational dipoles. https://www.physicsforums.com/threads/explanation-of-why-there-cant-be-dipole-gravitational-radiation.164013/ 

Nor do we subscribe to the concept of “induction gravity”, as this term is only found in Google Scholar with an internal comma.

We are currently struggling to explain the central "chrome bar" in the image.

N00282123 and N00282124 show adjacent (tilted) views which apparently also contain our N00282108 study chrome bar, but positioned this time on the top right and bottom left respectively.

N00282123 is particularly interesting as it reveals another "chrome bar", which is more fuzzy. So our study "chrome bar" is not unique.

Our current ideas are the "chrome bars" are "chrome rings" at Linblad resonances.

Our speculation is that the "chrome rings" are perfectly circular, not tight spirals, as seen elsewhere in the images.

Their eccentricity will be zero, as will be their inclination. They are speculated to be true ringlets, and not spiralets.

They might well be the end point / starting point of the adjacent spiralets. After all, every spiralet must have a start and a finish (the "wrapping up worry"). We have thought that the "chrome rings" may serve the "purpose" of a transition zone or buffer zone between meeting spiralets. Our tentative term for the transition zone is "endlet". We decided against choosing "startlet" or "terminalet" or ringlet.

Why endlets are so bright is unknown. Also why they exhibit a darker stripe is uncertain. Perhaps it is older, darker material, and each "chrome bar" has unequally collected new material from the adjacent spiralets.

{The differing positions of the darker stripes in the two "chrome bars" of N00282123 prevent conspiracy theories that they really are chrome bars as the lighting conditions are so similar!}

Then, are the gaplets similarily just dark intervening material between the spiralets? Or (as we are inclined to advocate) are gaplets simply the largely unpopulated shear areas between the two edges of adjacent spiralets caused by their differential rotation speeds?

We are referring to Kepler shear, not a Kepler orbit.

I am very happy to accept that some spiralets themselves may be twisting like barley sugar. This will help to distribute the material evenly the way the images show. This twisting is not visible in our part of the Saturnian Ring under study, but there are hints in other images...

Classically, the ringlets were expected to be in circular orbits, but measurements on opposite sides of Saturn have shown shifts in radial distance! Hence we break away from the previous terminology and refer to spiralets.

Dear Thierry,

No. The gaplets fall radially where the spiralets are 180 degrees away! So a spiralet is not a closed orbit! Admittedly 180 degree comparisons have not been done for all cases, but the door is now wide open for all ringlets now to be regarded as spiralets.

The disk is very thin because elliptical orbits and inclined orbits quickly die down to circular orbits in the equatorial plane having no eccentricity or inclination. It is only when a passing comet comes by it can provide disturbing forces.

I think that the one trap we keep on falling into is in continuing to call the ringlets rings. They are not closed elliptical or circular rings. They are visible spiralets that become more tightly wound away from their origin, (which may be towards or away from Saturn). Also we have to break away from regarding the disc as being solid like a Compact Disk, or even a cut-out rotating spiral or a solid Catherine Wheel firework. The spiralets and their associated gaplets are _visible waves_ of regions of more concentrated matter or temporarily out-of-plane matter (or both).

The pictures you have posted here are interesting. They give us, I believe, snapshots of how the spiralets can start to form.

Yes, because the spiralets are so tightly wound, the Kepler shear at a gaplet is a low force because the relative orbital velocities of two adjacent spiralets differ only marginally. There are even images which possibly show the exchange of material across a gaplet from one spiralet to an adjacent spiralet. To complicate the pattern, there may be multiple arms forming a bundle of spiralets.

Radial Wave velocity or radial particle velocity? I assume you mean radial particle velocity.

There is some Doppler work by nicholson2005radar on Rings A-C. However, they do not have Doppler measurements of spiralets or ring particles.

Since the spiralets are so closely wound, a spiralet will look _almost_ like a perfectly circular, non-inclined _solid_ ringlet (bangle). The mass ratio of two adjacent ringlets (bangles) will then be the inverse ratio of their radii from the centre of the planet, or equal to the inverse ratio of their orbital velocities. The mass ratio can be proxied from their brightness (or ringlet width) or "optical depth", giving an estimate of their velocity ratio. However, the spiralets on the left of our study image have their widths get _less_ leftwards, showing that a concentric solid ringlet model is inappropriate (i.e., wrong). See my graph of pixel row 511. If we are mistaken that Saturn is on the right of the image, then the same argument relates to the fuzzier spiralets on the right of the image.

For those people following this thread, there is now a good explanation of the mechanism available at

https://en.m.wikipedia.org/wiki/Orbital_resonance

Question:

What is the mechanism of ringlets, gaplets and endlets in Saturn?

this is a very important issue that requires scientific research.

Dear Ian Kennedy, Thank you very much for making very important inquiries on the Research Gate portal and inspiring important discussions on particularly important issues.

The topics that are the subject of discussion are particularly important and scientifically important and in the context of human life.

I wish you all good and best regards

The above discussion inspired me to the following considerations:

Will the new generation of astronomical instruments ever reach the farthest corners of the universe, reach the edge of the universe and explain the essence of the boundlessness of what is possibly beyond the known Universe?

Perhaps someday in the future, thanks to the huge telescopes, we will discover the details of the distant planets in other planetary systems in other galaxies, i.e. exoplanets.

According to astronomers' forecasts, it will be technically possible to build such large telescopes in a few dozen years.

Astronomers have so far discovered a small part of the planets in our Andromeda Galaxy.

Billions of exoplanets existing in other constellations are still unknown.

However, even these known exoplanets are studied to a very limited extent.

In the case of the majority of exoplanets learned, apart from the knowledge of size and mass, little is known about them.

More and more perfect astronomical tools are being built, more and more telescopes provide new knowledge.

Thanks to more perfect astronomical instruments, we know more and more about the cosmos, but on the other hand we know that we still do not know more and more about the vastness of the Universe.

Will we ever know the answer to the question: Are there other forms of life somewhere in the universe and how does life look like?

Will the new generation of astronomical instruments ever reach the farthest corners of the universe, reach the edge of the universe and explain the essence of the boundlessness of what is possibly beyond the known Universe?

In view of the above, the current question is: Will the new generation of astronomical instruments ever reach the farthest corners of the universe, reach the edge of the universe and explain the essence of the boundlessness of what is possibly beyond the known Universe?

I invite you to the discussion.

Saturn Spiralet Electrostatics Ian Kennedy Open for comments please. It should be recalled that the Cassini images show dense and less dense regions and periodic transgressions above and below the orbital plane. These waves are here called spiralets and gaplets. This paper proposes that adjacent spiralets of Saturn work in mutually grooming pairs, and they are composed of windings of opposite electrostatic polarities. (+) (-) (+) (-) (+) (-) The overall charge of a ring from a distance is thus neutral. There are outstanding problems in explaining how Saturn's rings are stable and long-lived. This paper applies not just a knowledge of the science of Statics and Dynamics, but also a knowledge of Electrostatics to the problem. After all, aurorae cannot be explained through only a knowledge of Statics and Dynamics. This paper theorizes that adjacent spiralets turns of Saturn's rings are composed alternately of lumps of oppositely charged material. • This theory will ensure that adjacent spiralets would not coalesce through mutual gravity forces. • It will also permit mutual grooming of adjacent rings of each other. As one lump is moving in a slightly larger spiral path, lumps on the adjacent inner turn (winding) are moving more slowly according to the laws of Dynamics. This passing has the effect of the outer turn (winding), ironing out non-uniformities in the inner turn and vice versa. This is via the passing application and removal of electrostatic repulsion. Any loose, foreign bodies falling in the gaplets will be attracted to the turn of opposite charge. If the body has no charge, then the dynamics of gravity will dictate which turn (winding) it will join. The joining will then determine its inherited, shared and ultimate electrostatic charge. • This explains the uniform nature of the spiralets, and the lack of intervening material in the gaplets. The above theory applies to both types of spiralet pairs, be they seen as changes in the rarefaction of the lumps (density wave) or be they seen as waves in and out of the orbital plane, casting heavy shadows (bending waves). The above theory might be extended to other astronomical phenomena such as spiral galaxies which always have an even number of proton-rich arms paired with electron-rich arms.