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# Seeing Encke!

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### #1 EdZ

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Posted 02 March 2004 - 11:30 PM

Encke is assumed to have a width somewhat less than 1000km and possible as narrow as 500km. Some sources quote 350Km. Therefore, Encke has an angular measure of a maximum 0.18 arcseconds and may possibly be as small as 0.1 arcseconds. I do not calculate for the 350km value. For comparison the Cassini division is 4200km. Cassini, at the current distance to Saturn has an angular measure of 0.75 arcseconds.

In order to see small objects or features you must take into consideration several things; the size of the object or feature, the contrast with adjacent features or dark sky, the limitations of resolution of the instrument and the limitations of the eyes.

We'll leave atmospheric conditions out of this and make all assumptions that observations are being made under the best possible sky conditions.

We've identified the size of the feature. We'll use the most optimistic value and assume Encke measures 0.18 arcseconds. How about contrast? For Encke it's actually not very high, like Cassini. Unlike Cassini, which is bordered by the brightest features in the entire ring system and has one of the highest contrasts of any extended object, the Encke division has far less contrast being much more subdued in the less bright regions of the A ring. Contrast is not a big help for Encke.

How about resolution? It all depends on your optics. We can work various sizes down to see if they would be able to resolve Encke. Or we could work our way up using resolution criteria to determine what size scope might be able to see Encke. We'll do a little of both.

Resolution is calculated using Rayleigh criteria. Some will say we can use Dawes Limit, but that is an incorrect assumption. Dawes, based on being able to identify that a double has two components, does not provide for seeing a clear separation between to objects. Rayleigh criterion IS the formula for the Airy disk and is the basis for calculation of resolution in all optics. Rayleigh Limit = 138/Dmm or 5.45/Dinches.

Let's try an 8" scope. Resolution limit for an 8" scope is 5.45/8 = 0.68 arcseconds. That's not going to be good enough to see Encke, is it? Well there's a bit more to it.

Encke fits the classification of an extended linear feature, black on white (although without high contrast), and this gives the observer a benefit. It's much easier to see this particular kind of feature than any other type of extended feature. In fact, the benefit can be 3.5x to 5x greater than the resolution limit of the scope. An 8" scope can detect linear features as small as 0.68/3.5 = 0.19 arcseconds to 0.68/5 = 0.14 arcseconds wide.

Is the 8" enough to see Encke? We assume Encke measures between 1000km and 500km and has an angular measure of a maximum 0.18 arcseconds and may possibly be as small as 0.1 arcseconds. The 8" scope using the criteria R/3.5 or R/5, can see somewhere around 0.19 to 0.14 arcseconds at best.

If Encke truly is at the widest dimension suspected AND the 8" scope is seeing extended linear features to the maximum benefit, then the 8" IS just barely enough to see this feature. However every one of those assumptions are in the favor of making the claim it can be seen with 8".

Suppose any single one of those assumptions needs to go with B instead of A. For example, if Encke is only 500km wide (0.1 arcseconds) and the 8" scope is seeing extended linear features only 3.5x better (0.68/3.5 = 0.19 arcseconds), then an 8" wouldn't be anywhere near enough scope to see Encke. Even if the scope were seeing features at 1/5 the normal dimension of resolution, 8" still would not be enough.

If the scope is seeing features at 1/5th the normal dimension (0.68/5 = 0.14 arcseconds), it's still not enough if Encke is only 500km wide.

So, there are four possible combinations due to uncertainty, and in three of those conditions an 8" scope cannot see the Encke division. Only if you took every possible advantage and then had the best conditions (and a precise collimation) could an 8" scope see the Encke division.

Even a 10" scope will meet the conditions in only two out of the four possible combinations. If Encke is only 500km wide, neither of these scopes are enough scope under any conditions.

OK. Let's say, by whatever possibility, you met the slim conditions and your scope can see Encke. What will it take for your eyes to see it? This is acuity. Normal acuity for most people dictates that a feature must be enlarged to a dimension of about 2.5 to 3 arcmin before your eyes can see it. An exceptionally few people can see features when the apparent size of an object is magnified to only 2 arcmin. But, again that extended linear feature is going to help you. In fact, it would seem under excellent conditions, you may be able to see linear features if the feature crosses at least just two receptors in the eye. This may mean you might need to magnify it only to an apparent size of 1 arcmin or 60 arcseconds. So again, we will assume the most optimistic condition and allow that only enough magnification is needed to reach an apparent size of 60 arcseconds.

If Encke is 1000km wide (0.18 arcsec) then magnification required to see it is 60/0.18 = 333x. If Encke is only 500km wide then you need 60/0.1 = 600x magnification to see it.

The likely-hood that you could get every one of these conditions in your favor is extremely slim. In fact it is very unlikely.

So here is a set of very reasonable assumptions from all these facts and conditions:
It is not likely 8" is enough scope to see Encke. It's even a stretch, but it's possible, for a 10" scope to see Encke. It's not likely it would be seen by anyone, even someone with exceptional acuity, at anything less than about 350x. It's more likely that a magnification of around 450x might be required.

So the most likely combination to allow one to see the Encke division is a 10" scope at over 400x magnification. But donâ€™t let that stop you from trying!

edz

### #2 Scott Beith

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Posted 02 March 2004 - 11:54 PM

Thanks for the education Ed. I know I have never seen it. My largest scope is only 6". No chance at all. I have observed the Crepe ring at 400x with the CR150, but have never gotten even a hint of the Encke div.

Scott

### #3 Barry Fernelius

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Posted 03 March 2004 - 01:01 AM

I've seen it in my 12.5" -- exactly ONCE.

### #4 matt

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Posted 03 March 2004 - 03:01 AM

So you say I could not have seen it in my 8" at 250x ? (see my post from last night)
I'll try not to feel upset ; I understand what you say regarding resolution, and regarding observing linear features. What I don't understand is how acuity and magnification work when it comes to linear features.

BTW, do you have my opinion on what I thought was "ringshine"?

### #5 EdZ

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Posted 03 March 2004 - 05:59 AM

Well, I am saying it's not very likely. Both you and Jeff have claimed sightings of Encke with an 8" in the past week, With the question in my mind, I needed to do the math. Even if all conditions were met, it would have taken far greater magnification than ?254x to detect it. You may have seen albedo effect of the Encke minima, which might seem to make an appearance similar to a line feature. It may be possible for an 8" scope to see Encke, but it is not very likely. It is probaly not possible at all to see Encke below a magnification of about 350x.

A linear feature is not a single point source. It requires significantly more magnification to see separation between two point sources than it does to see a linear feature. The magnification that needs to be employed can be determined by the severity of the condition. Point sources need to be raised to an extreme minimum of 120 arcseconds and a more realistic minimum for most people of 150 to 180 arcseconds apparent size. Linear features, due to the fact that they cross a number of receptors in the eye, require less magnification.

Kenny Jones illustrated the fact recently by observing a guitar string at a distance with a binocular. By all indications of thickness and distance, the claim might seem ludicrous. However, when the math was used to do the calculations his guitar string in his binoculars was magnified to an apparent size of about one arcminute. The added benefit of daylight shimmer off the brass string helped even more. In this case the wire had light coming off it as if it were a line of point sources, making it somewhat easier.

See the thread in the binocular forum Resolving a Thin Wire, a very similar condition to resolving Encke, except for the reversal of black/white, which is even another condition.

edz

### #6 michaeloconnell

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Posted 03 March 2004 - 06:34 AM

Very interesting post Edz.

### #7 Special Ed

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Posted 03 March 2004 - 08:30 AM

Thanks for the educational post--it made for very interesting reading.

For more discussion of the Encke Division and the Encke Minima, people can go here: http://home.fiam.net/ericj/encke.html

It starts with a sketch done by Johann Encke

It also describes where to look for the Minima which is probably a more realistic feature to look for given aperture, seeing, and all the other variables that Edz described.

Regards

### #8 Bill Grass

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Posted 03 March 2004 - 09:52 AM

Interesting, Ed! I've never seen Encke either. My scope is hopelessly too small for that.

### #9 jmoore

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Posted 03 March 2004 - 10:34 AM

Ed...you were out to get me!

seriously, I really appreciated the info in your post. Very intersting. As I mentioned days ago (in my claim of seeing Encke), I was less than certain that I'd seen it, especially since I'd read similar "requirements" before and thus knew that an 8" scope was marginally small to detect this feature. But, I figured since seeing was excellent, and I was up at 417x, that maybe my perceived glimpses of the gap were real. And I do think my visual acuity is pretty good.

Indeed, it sounds like it was possible, provided that Encke is on the wider end of statistical estimates, but improbable.

I know that when I was viewing at 333x, I definitely could not see it.

cheers,
jeff

### #10 michaeloconnell

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Posted 03 March 2004 - 11:51 AM

I also thought I saw it once but shortly afterwards I read about the Encke Minima. SInce then, I'm not so sure it was the division I saw. As the division is more difficult to detect, if it is indeed visible then the minima should be adjacent to it. Perhaps that's a handy and conclusive way of confirming what we see for future observations.

### #11 EdZ

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Posted 03 March 2004 - 01:46 PM

Gents,

Up front I'll say that I think these attempts to see Encke, with any instrument, are well worthwhile.

You guys have seen enough of my stuff to know, I'm a "show me the numbers" guy. I was so curious about the possibilities that I had a calculator out as I wrote. I honestly did not know what results would show. No, I'm not out to get anybody. But I am out to keep people on the path or reason and knowledge.

Mike Rosalina's link to Eric Jamison's article is interesting. I remember reading that article several years ago. He points out that Encke may have been seen several times with 6.25" and 6.75" refractors. He also notes that magnification required to see it is on the order of 45x per inch or 400x for scopes smaller than 10".

As I mentioned to Jeff a few days ago, these attempts, wether they result in real or suspected acomplishments, should not be left to go by the wayside. This is the kind of stuff you need to be recording in a log. You need to sketch what you see or even what you think you see. Note it as such. if you think you see it, say so in your log. if your sketch looks lousy, sketch it again, draw a bigger sketch, draw a partail sketch, label it and note it. Write down all the pertinent info about scope, eyepiece, NELM, conditions, time, how high in the sky. If I had a suspected observation of Encke it would cover a full page in my log! Not necessarily neat, just full of notes.

Hopefully, you all know a lot more, not only about Encke, but also what things affect your instruments and your ability to see. If so, than this was worth it.

edz

### #12 matt

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Posted 03 March 2004 - 03:56 PM

Thanks for the educational post--it made for very interesting reading.

For more discussion of the Encke Division and the Encke Minima, people can go here: =http://home.fiam.net/ericj/encke.html

OK
With all the astroreading I'm doing, I had not realized that the Encke Minimum and the Encke Division (which I hope is the same as the Gap!) were two distinct features.

The feature I've seen many times at the middle of the A ring and thought was an illusion is obviously the Minimum.

Now I wonder if seeing the gap was an illusion or not; could the outline between the dark minimum and the brighter outside create the illusion of seeing a line?

I also wonder how Kater saw it with a 6" scope.

What is funny that when I saw the gap I did not notice the minimum. Maybe I was not paying attention to it I can't check now, tonight anything above 100x is useless.

To put things into perspective, seeing Encke or not does not matter from an aesthetical perspective (which is why I do astronomy). When I look at saturn, the smooth bands on the disk, and most of all the darkening on the inside of the A ring are the most pleasing.

### #13 StarWars

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Posted 04 March 2004 - 03:02 AM

EDz

How would the Meade ETX 125 perform with regard to see the moons around Saturn..??

### #14 EdZ

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Posted 04 March 2004 - 10:04 AM

Ap

see separate post titled Seeing Saturn's Moons

edz

### #15 EdZ

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Posted 02 February 2005 - 08:03 AM

Some recent discussion on the Encke division was brought up in the "Lowest power to see the Cassini division" thread. It is worth posting and linking to here. I had commented over there when asked about seeing the Encke division.

There are posts by people who claimed to have seen Encke with a 6" or 7" scope at 250x to 300x! I have doubted this, but the standard answer is usually "I know what I saw." The real explanation might lie in just exactly what it is that was seen. You just can't say what it is that someone else sees, but you can say what they should be able to see.

The article above, in the first post in this thread, is purely theoretical and is based on an assumption that Encke may be as wide as 1000km. The most important thing, it's basis is grounded in accepted theory. I do present some what if it is really narrower. Info currently published on NASA website has Encke listed at 350km. The Cassini division is about 4,500km wide. Encke division is about 350km wide. So the more stringent limits must be held in the original article.

I believe David Knisely has performed an actual field exercise on observing Encke. His article can be found here
Seeing The Ring Divisions of Saturn

This photo by Wes Higgins shows what people might be seeing in the vicinity of Encke. I'm not sure that what you see here is the Encke Division. Could this be the darkening caused by diffraction effects in the ring structure in the vicinity of Encke due to the inabilty to resolve or separate features too close and without a high enough contrast gradient to see a distinction, as David's explanation describes?
Saturn by Wes Higgins

However this excellent photo, also by Wes Higgins clearly shows he detected the Encke division with his 18" Starmaster. But, if you enlarge this photo and measure, you will find that Encke in this picture is considerably fattened. As fine as I could measure on a full screen shot, when compared to the known width of the cassini division, the dark line as seen in this image is 6 times wider than Encke. Is Encke only seen with some adjacent ring structure forming part of the image? Or is this just simply beyond the capabilities of the image processing software?
Wes Higgins Satrurn/Encke 12-2-04 18" Starmaster

Seeing Encke is much more dependant than Cassini on how much scope you have. You need enough scope to provide the resolution. Minimum magnification is up in the 300x to 400x range. But there is more to it than just how much scope you have. Diffraction effects sometimes cause us to see things differently than they really are. Actually, better you just read David K's explanation for this. See David's explanation here Why it might be so hard to see the Encke division and then read further down in this thread for more of David's commentary.

Another very good reference article is
Eric Jamison's History of the Discovery of Encke Division but carefully read and compare some of this documentation of historical observations to verify what might be correct and what might not. Then read Bill Ferris' comments further down in this thread pertaining to some of the sketches.

Here is a link to Nasa pictures from the Cassini-Huygens space probe.
NASA JPL Cassini-Huygens photos

Saturn's Rings

edz

### #16 Scott Beith

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Posted 02 February 2005 - 09:35 AM

Ed,
I have had my CR150 at 400x on Saturn and I haven't even seen a hint of Encke - Division or Minima. Cassini is wide enough to drive a truck through, but no hint of Encke for me.

### #17 BillFerris

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Posted 02 February 2005 - 11:53 AM

Hi Ed,

Thanks for the posting and links. To those links, I'll add one for a monograph written by Jeff Medkeff and posted to S.A.A. in September 1998: Official IAU Ring Gap Names.

On a personal note, I share your skepticism of reported observations of the Encke division made at magnifications of less than about 300X. I would contend that seeing conditions need to be such that a moderate aperture instrument is able to perform at very high magnifications with no discernible seeing for extended periods. Under such conditions, any aperture capable of discerning the Encke division is easily capable of 300X or more. A good 10-inch aperture will produce a rock solid image at 400X to 500X under excellent seeing. If the seeing limits the useable magnification to less than 300X, in my book the conditions simply aren't good enough to make a reliable detection of the Encke division.

With respect to historical observations of the Encke division, I'm skeptical it was seen prior to the 1850s. My reasoning is based on the fact that the C or crepe ring is an obvious feature in my 10-inch Newtonian, even under average seeing conditions. The C ring should be an obvious feature in moderate to large aperture under conditions that would allow a legitimate detection of the Encke division. Yet, this ring was not discovered until the 1850s.

To me--and this is just a personal observation--I can't resolve an observation of the Encke division that does not include an observation of the C ring. Also, looking at the historical sketches on Eric Jamison's site that purportedly include observations of Encke's division, I'm struck by those that show symetrical patterns of divisions within the A ring. Kater's 1825 sketch, and Coolidge's 1854 and 1855 sketches show divisions where none exist. That they saw and reported nonexistent features, leaves me skeptical that they actually detected a real ring division that would only have been visible at the threshold.

My approach is to treat an observation of the Encke division as an extraordinary accomplishment requiring extraoridnary evidence to support general acceptance of the claim. Some may argue such a standard is too restrictive. But it's the only one I'm comfortable with where threshold observations are concerned. Keeler's 1888 observation with the Lick 36-inch is the only one of the group that, to me, presents an accurate rendering of the ring system, including the Encke division.

That said, I acknowledge that this is a debatable topic and that there are knowledgeable folks who disagree with me regarding Kater's and other historical observations.

Regards,

Bill in Flagstaff

### #18 David Knisely

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Posted 02 February 2005 - 04:19 PM

Well, the thread EdZ mentioned is really more on why the division is so hard to see rather than what might be mistaken for the Encke division. One problem is that an albedo feature causes a contrast effect which can mimic the presence of a true division. The brightness of the A-ring shows a peak intensity just outside the Cassini division in a sort of brighter "ringlet". Farther out, the brightness shows a marked fall off, beginning about halfway out from the inner edge of the A-ring and continuing to its outer edge. This brightness fall-off combined with the brighter inner "ringlet" can give the impression that there is a diffuse division in or near the middle of the A-ring, especially at moderate powers where the image scale is not extremely high. Some amateurs have referred to this illusionary "feature" as, "the Encke Minimum", although this name is not official. Many observers prior to the Voyager probes (including Encke himself) apparently mistook the brightness falloff/contrast effect as a division and repeatedly reported it nearly in the middle of the A-ring (a few even drew 2 divisions there!). Others have had seeing cause doubling effects which can make ring edges look like additional divisions. The Voyager and HST images show one significant but narrow division in the A-ring near its outer edge *not* near the middle of that ring. That narrow gap has since been "offically" named the Encke Division by the IAU. Keeler's 1888 drawing (done with the 36 inch refractor at Lick Observatory) appears to be the most reliable early observation of the gap we now call Encke (the others being somewhat questionable for various reasons).

At mean opposition, the Encke Division is only 0.5 arc seconds away from the dark outer edge of the A-ring. The division and the edge of the A-ring have a diffraction structure, and thus need to have a minimum separation to be resolved in a given instrument. Using Dawes Limit for that separation, this would imply a minimum of a 9.12 inch aperture to resolve the two. However, Sidgewick (AMATEUR ASTRONOMER'S HANDBOOK, p. 50) indicates that two parallel lines need a separation of between 1.1 and 1.4 times Dawes Limit to be resolved (otherwise, they would merge into a diffuse band). If we consider the Encke Division and the dark outer edge of the A-ring to be parallel lines at the ansa (the "bend") of the ring , then the aperture required to resolve them jumps into the 10 to 12.8 inch range. Again, I have some real doubts that telescopes much smaller than 10 inches will show the true Encke Division. I flat out don't believe claims of seeing the division at powers significantly less than 300x, as the image scale has to be very high to overcome the eye's own resolution problems. Clear skies to you.

### #19 EdZ

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Posted 02 February 2005 - 04:34 PM

Thanks David for reposting that info here. Also, I edited the above to "Why".

edz

### #20 Guest_**DONOTDELETE**_*

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Posted 03 February 2005 - 12:57 AM

I think this is a great season to try and make an all out effort to see the Encke, as the rings are shifting away from us, meaning it will become more difficult to see in the coming years.

### #21 matt

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Posted 03 February 2005 - 02:20 AM

I understand my past tribulations a little better now, but why would "The division and the edge of the A-ring have a diffraction structure"? Is it because they are so close?

As for the doubling effect, I've noticed it often, but I to me it is plainly visible as an optical illusion/aberration, not an actual structure.

### #22 David Knisely

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Posted 03 February 2005 - 03:27 AM

I understand my past tribulations a little better now, but why would "The division and the edge of the A-ring have a diffraction structure"? Is it because they are so close?

As for the doubling effect, I've noticed it often, but I to me it is plainly visible as an optical illusion/aberration, not an actual structure.

Any feature at high enough power will show some sort of diffraction structure or may show a less than sharp appearance due to diffraction effects. A point source like a star will show the familiar disk and ring diffraction structure, but a thin line which is thinner than the resolution limit of the instrument at a high enough power will show a diffuse band like appearance rather than just a thin sharp line, as if one took the diffraction disk of a star, and stretched it out in one direction. This is due to the wave-nature of light. The interference of light waves blurrs geometric detail which might theoretically appear sharp otherwise. A dark line will appear as almost a "negative" stretched out diffraction disk which is dark instead of light. At high enough power, features which at low power appear to have sharp edges will seem somewhat soft, and this is due to diffraction effects. A line at high enough power will start to show soft edges. If you put two such lines too close together, their fuzzyness will tend to merge them into a broader diffuse band-like structure instead of two discreet lines. This is what often happens with the Encke division at an aperture which is not capable of clearly separating them. Clear skies to you.

### #23 cildarith

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Posted 03 February 2005 - 11:28 AM

Scratching some quick equations on the back of the proverbial envelope...

According to Sidgwick (p.50) the Cassini division has a width of 0.5". If this corresponds to a width of 4,500 km as mentioned above, then the Enke division at 350 km has an apparent width of only about 0.04". Sidgwick (pg. 50) also states that the visibility of a "single dark line on light ground" (with Cassini as an example of such), is on average 1/5 of the Dawes limit (R'), with values quoted up to 1/15 of R' in the case of exceptional observers and/or equipment.

At 1/5 R', a scope in excess of 20 inches aperture would be required to see the division.

At 1/15 R', a scope of nearly 8 inches would be required to see the division.

Interesting discussion.

### #24 Starman1

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Posted 03 February 2005 - 01:49 PM

Ed,
I have seen Saturn through a 7" f/12 refractor on a night of sub 0.1 arc-second seeing. Magnification was over 1000X, Saturn was on the meridian.
The rings appeared "grooved" as if made of countless small ringlets. "Spokes", or radial dark area were visible at several places. Cassini's division went completely around the planet. Color differences between and within the rings were easily seen, and the C ring extended to the ball.
Multiple ring shadows were seen superimposed on the planet, and many bands, ovals, storm, swirls (all in various colors) were visible on the planet.
The A ring definitely had variations in brightness across its width.
Yet no one could see the Encke Minima for sure, and CERTAINLY no one could see the Encke Division.
So I will empirically verify your supposition about conditions required to see the Minima, let alone the Gap/Division, which I think requires a lot more scope.
Nice analysis, but VERY optimisitic.
The general rule of thumb I go by is that the minimum scope necessary to see something is probably at least 1/2 the width of the discovery scope (lots of exceptions to this rule, I know).
Didn't this gap get identified by Keeler in a 36" refractor? That would mean an exceptional 18" might see it.
I have never met anyone who has seen the Division, though several acquaintances have seen the Minima.

### #25 EdZ

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Posted 03 February 2005 - 02:13 PM

Scratching some quick equations on the back of the proverbial envelope...

According to Sidgwick (p.50) the Cassini division has a width of 0.5". If this corresponds to a width of 4,500 km as mentioned above, then the Enke division at 350 km has an apparent width of only about 0.04". Sidgwick (pg. 50) also states that the visibility of a "single dark line on light ground" (with Cassini as an example of such), is on average 1/5 of the Raleigh limit (R'), with values quoted up to 1/15 of R' in the case of exceptional observers and/or equipment.

At 1/5 R', a scope in excess of 20 inches aperture would be required to see the division.

At 1/15 R', a scope of nearly 8 inches would be required to see the division.

Interesting discussion.

There is some incorrect info here.

Yes, Cassini is approx 4500 km, comfirmed by NASA data. No, it is not 0.5 arcseconds as stated in Sidwick. At the distance of 8AU a 4500km division calculates to 0.75 arcseconds. Therefore, by relation a 350km division measures 0.06 arcseconds. I believe when Sidwick's book was written, the actual width of the Cassini division had not been verified.

And there is reason for using one value and not the other.

The relation of R/5 is used here. The values Sidwick reports for R/14 and R/15 are for daylight observation, a much different condition.

A 10" scope has a Rayleigh Limit = 138/254 = 0.54". Seeing an object 0.6 arcseconds would be the equivalent of 0.54/0.06 = 9 or R/9.

Due to the nature of the location of Encke in dark regions of the A ring, very much different than Cassini which is bordered on both sides by the brightest features in the ring division, it is difficult to determine just what the width of the dark area seen really is. It is a minimum of 350km, but incorporating even small portions of the adjacent rings into what is seen, it could easily be somewhat greater.

edz

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