8" lunar crater resolution...

Patrick Moore -[who clearly isnt one of my favorite authors] claims that an 8" telescope can resolve 1.1miles on the moon.
that is, a crater half filled with shadow. Too, he goes onto continue and sais the finest rille is 1/10 that resolution - linear.

He bases his claims on his 33" refractor observation of a 500 yard crater resolved - half filled with shadow.

what do you guys think of his claims?

Pete

Patrick Moore -[who clearly isnt one of my favorite authors] claims that an 8" telescope can resolve 1.1miles on the moon.
that is, a crater half filled with shadow. Too, he goes onto continue and sais the finest rille is 1/10 that resolution - linear.

He bases his claims on his 33" refractor observation of a 500 yard crater resolved - half filled with shadow.

what do you guys think of his claims?

Pete

From my own limited studies using the old LAC charts, I found Moore's estimates to be fairly accurate, although they might be a tad on the conservative side, especially for those doing high-contrast lunar imaging. Just using the formula d = 9/D, where d is the crater diameter in miles and D is the telescope aperture in inches tends to give results similar to those in Moore's table. Clear skies to you.

Going out on a bit of a limb, I've got an 8" Dobsonian with a pretty good mirror set and when I get good skies, I can count several craters in Plato's floor I've heard described as being a mile across. Linear features are tougher to estimate because you can pick out lines easier than dots, but it may be difficult to tell if the contrast is the same as with a crater. Still no flag or boot prints...

Going out on a bit of a limb, I've got an 8" Dobsonian with a pretty good mirror set and when I get good skies, I can count several craters in Plato's floor I've heard described as being a mile across. Linear features are tougher to estimate because you can pick out lines easier than dots, but it may be difficult to tell if the contrast is the same as with a crater. Still no flag or boot prints...

The central craterlet is 1.7 miles across, while two others are 1.5 miles across and another one is 1.3 miles in diameter (the "Big Four"). There is a smaller one near the western edge of the floor that is 1.2 miles across and another one near the eastern edge that is about 1 mile in diameter. After that, things get somewhat harder . Clear skies to you.

I have seen 8 Plato craterlets with my 10" dob, and seen craters about 2km across near the Straight Wall.

Going out on a bit of a limb, I've got an 8" Dobsonian with a pretty good mirror set and when I get good skies, I can count several craters in Plato's floor I've heard described as being a mile across. Linear features are tougher to estimate because you can pick out lines easier than dots, but it may be difficult to tell if the contrast is the same as with a crater. Still no flag or boot prints...

The central craterlet is 1.7 miles across, while two others are 1.5 miles across and another one is 1.3 miles in diameter (the "Big Four"). There is a smaller one near the western edge of the floor that is 1.2 miles across and another one near the eastern edge that is about 1 mile in diameter. After that, things get somewhat harder . Clear skies to you.

Hi Dave,

You know, that limit that describes 1.1 miles for an 8" aperture assumes a half filled crater -so REALLY - arent we just seeing HALF mile crrater at that point. Said another way, suppose we have a crater as wide as a half mile across but otally filled with shadow save for its rim walls. Than is could be said the smalled crater an 8" aperture can resolve is .55 miles across. True?

Im not trying to be funny Dave. Honest - if its only half filled, at that threshold level, we are only making out that half of the crater which forms that speck, or "pepper spot" if you will. Are we really seeing that other half of lit crater detail or does it just blend into everything leaving us that most minute speck of a shadow to call a crater?

I guess my upshot here is that perhaps if we observe close enough to the terminator where craters are virtually all black inside, we can actually reduce the actual size of the crater we call a "limit".

Pete
PS: Funny enough with plato - i find the full moon isn't such a bad time to go looking for those "famous four" as they appear like white specks.

Going out on a bit of a limb, I've got an 8" Dobsonian with a pretty good mirror set and when I get good skies, I can count several craters in Plato's floor I've heard described as being a mile across. Linear features are tougher to estimate because you can pick out lines easier than dots, but it may be difficult to tell if the contrast is the same as with a crater. Still no flag or boot prints...

The central craterlet is 1.7 miles across, while two others are 1.5 miles across and another one is 1.3 miles in diameter (the "Big Four"). There is a smaller one near the western edge of the floor that is 1.2 miles across and another one near the eastern edge that is about 1 mile in diameter. After that, things get somewhat harder . Clear skies to you.

Hi Dave,

You know, that limit that describes 1.1 miles for an 8" aperture assumes a half filled crater -so REALLY - arent we just seeing HALF mile crrater at that point. Said another way, suppose we have a crater as wide as a half mile across but otally filled with shadow save for its rim walls. Than is could be said the smalled crater an 8" aperture can resolve is .55 miles across. True?

Im not trying to be funny Dave. Honest - if its only half filled, at that threshold level, we are only making out that half of the crater which forms that speck, or "pepper spot" if you will. Are we really seeing that other half of lit crater detail or does it just blend into everything leaving us that most minute speck of a shadow to call a crater?

I guess my upshot here is that perhaps if we observe close enough to the terminator where craters are virtually all black inside, we can actually reduce the actual size of the crater we call a "limit".

Pete
PS: Funny enough with plato - i find the full moon isn't such a bad time to go looking for those "famous four" as they appear like white specks.

What I see as a "resolved" craterlet is a tiny pit with both a bit of internal shadow and a clear form of visible rim (not a "single pixel" dot). This is where I use the 9/D formula and find it to be fairly accurate for giving a reasonable crater resolution minimum for a given aperture with the appearance constraint mentioned above. I can see the very tiny white dots of the "big four" Plato craterlets in my 90mm Mak-Cassegrain under a high sun angle, but I cannot resolve them into the true pits that they are. They simply aren't there when the sun is low, making Plato's floor look blank (I can sometimes see the central one as a light dot, probably from light reflected from the raised ramparts). In my 10 inch, under halfway decent seeing and low sun angle, I regularly resolve the "big four" and at least two more as pits depending on the shadow length near the east or west walls of Plato. My own personal record is around 10 or 11 craterlets visually, although images and some processing tend to bring out a few more that are difficult to see. Here is an older "map" of the craterlets of Plato:

A = 1.7 miles (2.7 km) B = 1.5 miles (2.4 km) C = 1.5 miles (2.4 km)
D = 1.3 miles (2.1 km) W (on west-northwest wall) = 2.0 miles (3.2 km)

e = 1.2 miles (1.9 km) f = 1.0 miles (1.6 km)
g = 0.94 miles (1.5 km) h = 1.4 x 0.8 miles (2.2 x 1.3 km)

i = 0.7 miles (1.2 km) j = 0.6 miles (1.0 km) k = 0.7 miles (1.3 km)
l = 0.6 miles (1.0 km) m = 0.7 miles (1.1 km) n = 0.7 miles (1.1 km)
o = 0.7 miles (1.1 km) (double craterlet) p = 0.7 miles (triple craterlet)
q = 0.6 miles (1.0 km) (double overlapping crater)

Hi David,
what would you say of a pic that overprocessed reveals the eastern wall even slightly?

How "real" a resolvement could this be said to be - or am I just seeing things on this?

I only found this feature out by overprocessing my previous pic as I was hinted by Brian Albin that this section of Plato was in the pic looking first like a tiny amount of snow on the wall of the crater Plato... See this thread for the original and the hint I was given (the original pic is in the 2nd set of thread and this link gets you directly to the beginning of the 3rd, so go back a bit from there if you want to see the original pic):

http://www.cloudynig...5/o/all/fpart/3

Please, note all that this pic in here is INTENTIONALLY OVERPROCESSED very hard to get out the detail Brian suggested!

Be well all!

You know it would be interesting to see progressive images - even in theoretical diagram of what would happen to a crater as it progressively passed the dawes limit. We know doublestars elongate [I think they just overlap], but craters have their own nifty way of fuzzing out. Itd be neat to see the progressive examples of this.

Pete

Dave whats that scope behind you in your pic? Looks like a 7" mak - am i right?

Pete

Patrick Moore ... bases his claims on his 33" refractor observation of a 500 yard crater...

Pete,

I'm curious to know where you found Patrick Moore's statement about being able to see a 500 yard (460 m) crater half filled with shadow using a 33 inch refractor? Did he mention the occasion, or which crater he is referring to? This sounds like it might be related to the table mentioned by David, which in turn sounds like it might be related to the one appearing in an Appendix to Wilkins and Moore, but which doesn't refer to observations by Wilkins or Moore. And, as Mardi has pointed out, despite claims of this sort, few of the detailed drawings in that book, including the many said to be made using the 33 in Meudon refractor in Paris show any reliable detail beyond about 2 km. That includes Wilkins and Moore's drawing of Plato , which shows no craterlets that can be identified with certainty beyond ~2.0 km diameter (David's "Big Four"). One possible exception is Wilkins' detailed (and almost incomprehensibly cluttered) plan drawing of Ptolemaeus which might, charitably, be supposed to show occasional real details at the 1.1-1.2 km level in small areas.

I don't know what Moore might personally be able to see with an 8" telescope, but as explained in some detail in the other thread, a skilled imager, like Bob Pilz, photographing with a blue filter, and using the latest image processing techniques on sequences obtained under conditions of good seeing can fairly consistently detect craterlets in smooth mare under favorable lighting conditions down to around 1.1 km. So that agrees with Moore's number, but implies reliably detecting something like 16-18 craterlets on the floor of Plato, which from David's comments is a bit unrealistic for a visual observer using the same aperture.

Correction: 1.1 km doesn't agree with Moore's number. I'm constantly getting confused in switching from miles to kilometers. Moore (following Whitaker) is giving a 1.1 mile or 1.77 kilometer visual limit for an 8" telescope, which corresponds to about 6 Plato craterlets. That indeed seems reasonable for an 8" aperture. 500 yards (0.5 km) for visual observations with a 33" probably is not, at least based on Wilkins and Moore's own much less impressive results: a 0.5 km limit would imply being able to reliably plot a couple of hundred Plato craterlets, something they certainly did not achieve.

Your suggestion that the increased amount of shadow at low sun might enhance the detectability of small craters is an intriguing one. Some of the Apollo images certainly give that impression. Tiny fresh pits can also be seen with higher sensitivity at very high sun because of their brightness, but it's impossible to tell, in that case, which of the tiny dots are craters and which are dusted hills. As you say, it's not clear the best angle for detecting small craters has been studied in a quantitative way. Things aren't always as we assume (or as they appear to be).

-- Jim

Edit: correct 1.1 miles --> 1.77 km

David,

Inspired by the fine work of you, Mardi and Chuck Wood in preparing crater sequence charts like this, I posted some new measurements of the Plato craterlets on the-Moon Wiki. The main diagram gives the kilometer-diameters of all the circular craterlets to a diameter of 0.9 km, while a text file gives the positions and diameters of 111 Plato craterlets, ranked by size, including all larger than about 0.7 km.

Regarding "Moore's table" and his "d = 9/D" formula, in which of his many books does this appear? As I mentioned to Pete, it sounds very closely related to the formulas and table appearing in an Appendix to Wilkins and Moore. But the latter is not the work of Moore or Wilkins, but rather that of Ewen Whitaker, who contributed that Appendix on Lunar Photography. Despite the title, at least as it appears in their 1961 edition, the table expresses Whitaker's own very definite views on the limits of visual observations (which he apparently thought of as the ultimate goal which photographs might someday approach, but not exceed), which I think are based on his own experience, rather than Moore's.

The table is simply a listing based on the following principles which Whitaker says he established experimentally for visual lunar observations through telescopes having an aperture of D [inches]:

(1) The diameter of the first dark ring of the Airy pattern = 10.9/D arc-sec.
(2) The apparent diameter of the central disk is 0.8 of this diameter (one doesn't see quite to the ring) = 8.7/D arc-sec
(3) The lunar image can be thought of as a myriad of tiny detail elements. These elements are 3/8 the diameter of the dark ring = 4.1/D arc-sec.
(4) The true diameter of the smallest crater that can be detected as such (by juxtaposed light and shadow) is 9/10 of the Airy disk diameter = 7.8/D arc-sec.
(5) The true size of the smallest "line of shade" that can be detected is 1/20 the Airy disk diameter = 0.44/D arc-sec; but as seen in the telescope it will appear up to 8 times larger than this.

Moore's claim of a detecting a 500 yard crater (0.25 arc-sec at the Moon's average distance) crater with a D = 33 inch refractor is quite consistent with Whitaker's formulas (7.8/33 = 0.24 arc-sec); but one might wonder how Moore knew that the actual size of this marginally-resolved crater was 500 yards? He wouldn't have had any higher resolution photos to go by. His assertion that an 8-inch telescope will resolve less than that in the proportion 8/33 (i.e., 1.1 miles) is also in agreement with Whitaker's principles (and matches the value listed in Whitaker's Table), although Moore's claim (cited by Pete) about a 10X advantage in detecting rilles is less optimistic than Whitaker's (who estimates an 18X advantage).

Whitaker's table begins with a listing of a 9 mile crater threshold for a 1" telescope, which would seem to be the basis of Moore's formula (although Pete says it is based on observations with a 33" telescope).

Unfortunately Whitaker doesn't explain what sort of experiments he conducted. He might possibly have looked at the Moon through very small apertures and noted the appearance of objects whose true dimensions he knew from observations with larger instruments. Alternatively he might have looked at terrestrial targets of know size (e.g., threads or lunar photos) through a variety of apertures.

Whatever experiments were conducted, the table extends the results to visual observations with apertures as large as the 200-inch Palomar telescope (the largest of that day) on the assumption that the resolution will improve in inverse proportion to the aperture. But there is no disclosure as to whether any attempt was made to verify the results given in the table for any of the larger apertures listed there (and, as noted above, in the absence of high resolution space photos it would have been exceedingly difficult to know what size features were actually being detected and missed).

-- Jim

Moores books is titled: The Amateur Astronomer published by Norton. Below is the paragraph above the table where he makes his claim:

"The following table [based upon the work by E.A. Whitaker ]gives the approximate diamters of the smallest crater half filled with shadow and the narrowest black line certainly distinguishable. Obviously different observers will have different results but using the Meudon refractor in Paris during the pre apollo period, when i was engaged in moon mapping, I recorded a craterlet at the summit of a mountain near BEER that was only about 500 yards across"
-Patrick Moore ©1990

There you go - now to find that mountain peak! It seems plausible as the same ratio applied to an 8" yields that 1.1 mile crater .

You raise good questions about how he could know the size of the crater he observed at that point in time. I dont think he could. BUT - the numers seem right in theory. For all we know he observed a crater a good 2/3's of a mile across.



Pete

Jim,

Doesnt this all scream for someone to do some definitive test to settle this once and for all. For the life of me I thought about doing some land based kind of resolution grid with circles and strings and bars etc. But' itd never work. Even if the dots were say 1/4" and smaller, its still so far away that the turbulence over land would blot out all attempts of really getting to the bottom of anything.
Its a nice idea that for now seems pretty impossible to really achieve - for the moment.

Pete

Well, there is so much noise in the over-processed image that it is difficult to see much, but overall, I would say no, there does not seem to be much in the way of any Plato craterlets in the image. The somewhat milder original image does seem to show a central brightening which corresponds to the ejecta blanket and craterlet in the middle of Plato (my "A" craterlet), but it is not resolved as a definite relief feature. Clear skies to you.

Dave whats that scope behind you in your pic? Looks like a 7" mak - am i right?

Pete

It is the NexStar 9.25GPS (9.25 inch f/10 Schmidt-Cassegrain) which I reviewed for Cloudynights (and which I purchased after I got done reviewing it). It is a fine performer, especially on the moon with my binoviewer. Indeed, it was the addition of my binoviewer which really turned me back into a "Lunie". Clear skies to you.

Jim Mosher posted:

Inspired by the fine work of you, Mardi and Chuck Wood in preparing crater sequence charts like this, I posted some new measurements of the Plato craterlets on the-Moon Wiki. The main diagram gives the kilometer-diameters of all the circular craterlets to a diameter of 0.9 km, while a text file gives the positions and diameters of 111 Plato craterlets, ranked by size, including all larger than about 0.7 km.

All I had was the Lunar Orbiter images from the Digital Lunar Orbiter Photographic Atlas of the Moon:

http://www.lpi.usra..../lunar_orbiter/

plus a few take by Maurizio Di Scuillo using a CCD camera on a ten inch Newtonian optimized for high resolution planetary work (which showed between 25 and 30 possible craterlets). At the time I did this, I had to just assume an east-to-west rim-to-rim diameter of 60 miles for Plato (a commonly-quoted figure) and go from there. Without a highly accurate scale on the Lunar Orbiter images, it was difficult to obtain any precise figures for the craterlets, which is why in my earlier postings on the subject, I give an error bar of +/- 0.2 miles (+/-0.32 km). There were a few high-resolution images take of sections of Plato by the Clementine probe, but I have had difficulty in getting scale figures for those either. Linne (2.4 km across) has always been (at least to me) slightly easier to resolve than the central craterlet "A", so I don't know what that says about the diameter of the "A" craterlet (might have to do with the lack of foreshortening with Linne as well as its bright ejecta blanket which would help with the contrast). In any case, I think that figures for the craterlets on the Wiki should be stated *only* to +/- 0.1 km, as going finer than that is probably stretching any measuring accuracy a bit too much.

Regarding "Moore's table" and his "d = 9/D" formula, in which of his many books does this appear? As I mentioned to Pete, it sounds very closely related to the formulas and table appearing in an Appendix to Wilkins and Moore. But the latter is not the work of Moore or Wilkins, but rather that of Ewen Whitaker, who contributed that Appendix on Lunar Photography. Despite the title, at least as it appears in their 1961 edition, the table expresses Whitaker's own very definite views on the limits of visual observations (which he apparently thought of as the ultimate goal which photographs might someday approach, but not exceed), which I think are based on his own experience, rather than Moore's.

The 9/D formula is one I derived Patrick Moore's book AMATEUR ASTRONOMY (c. 1968 W.W. Norton & Co.) from a table (Appendix XI) on page 224. The first few entries are:


1 inch aperture: smallest crater: 9 miles...Narrowest cleft: 0.5 mile

2 inch aperture: smallest crater: 4.5 miles...Narrowest cleft: 0.25 miles.

3 inch aperture: smallest crater 3 miles...Narrowest cleft: 0.16 miles.

This goes on to where he hits 10 inches and a 0.9 mile crater diameter figure, then going on to 12, 15, and 18 inches of aperture. This sequence of aperture diameter vs. crater diameter is where the "9/D" formula basically comes from. Under the table, Moore states:

"The smallest craterlet that I personally have recorded is probably that on the summit of a mountain peak near the crater Beer. The instrument used was the Meudon 33-inch, and the diameter of the summit depression cannot have been much more than 500 yards."

As a youngster (in the autumn of 1969), I was given an early version of the LAC-76 chart of the Raphaeus Mountain Region by my uncle who got it from a cartographer he had hosted on board the carrier USS Enterprise. It showed craterlets down to just under one mile across, and from using my 8 inch on that region of the moon, I found that with difficulty, I could get close to one mile resolution. This was consistent enough with Moore's table that I was satisfied that the 9/D formula probably was a realistic one. Clear skies to you.

When i was interested in this subject, during sessions i would examine a given area for the smallest features that i could identify as craterlets and made detailed locational notes and/or sketches then used those to locate the features on the Bowker & Hughes LO images and measured them. I also used B&H at the eyepiece on numerous occasions to ID such features and measure them as i went along.

Using a 5" f/9 achomat with binocular viewer under seeing that was sufficient to reveal it's diffraction limit (1>1.5" and even this an utter rarity at my location), i found the threshold to be at ~2km. On an inch/mile relationship this works out to between 6-6.5/D.

However, if an 8" were to be considered as operating at its diffraction limit, this would require noticably better than 1" arc median seeing, taking into consideration the seeing's moment to moment variability to a better figure (those transitory good seeing moments).

The paucity of sub arc second seeing at the vast majority of amateur home observing sites, combined with a lack of serious useage of smaller aperture refractors (which reach diffraction limited performance in much less optimal seeing conditions) of the serious lunar observers of this era (mid 20th century--they always favored the largest aperture they could lay hands on as a sort of policy it seems) who authored these tables, would probably account for the more conservative 9/D craterlet resolution figure, IMO. IOW, 9/D is a number one would expect using larger apertures (8-12inches) which are nearly always actually used short of their diffraction limit due to persistent seeing limitations.

If, however, these larger apertures *were* used in seeing conditions which allow their diffraction limits to be actually reached on this sort of target, a 6-7/D figure would be more accurate IMO.

However, seeing being limited to about 1/2second of arc at the best sites in the world, one can easily see the aperture limitation for diffraction limited visual observation lies at about 12" of aperture. Past this point in aperture, optical contrast will increase (which can mimicor imply a resolution increase), but the finest resolution will remain limited to that allowed by the prevailing seeing. Only by using a different imager than the eye (digital & related post processing) can the effective seeing be reduced further, thus allowing the further increases in resolution we see in the best digital images. Even digital imaging (amateur) seems to top out at about 0.25"arc resolution or 500meters ground resolution. That I have seen to date, the best professional digital imaging has achieved (using fully adaptive optics plus digital imaging & post-processing) is 130m ground resolution on craterlets using ESO's VLT telescope. Note that *if* resolution were not limited by seeing, a 78" refelctor would offer the same visual resolution. Yet, as was discussed in yet another thread about lunar resolution, Kuiper, using a 61" reflector in an optimal observing location vis a vis seeing, found it difficult to break even the 1km threshold while observing visually.

So, i'd agree with David that Whitaker/Moore's 9/D represents a reasonable formula to use with apertures 8-12", but that for apertures =<6" a somewhat more liberal figure of 6-7/D, reflecting actual diffraction limtied resolution values, would be appropriate as these resolutions are more frequently allowed by the seeing most amateurs deal with.

David (and Pete),

Thanks for clearing this up.

1. Moore's tables in Amateur Astronomy (1968) and The Amateur Astronomer (1990) sound like reprints of Ewen Whitaker's table from Wilkins and Moore's The Moon (1955/1961 - I haven't seen the 1955 edition, so I don't know if it had Whitaker's Appendix). The lines David quotes from the table are identical to those in the 1961 book (although Whitaker originally included at the end of the rows his values for the "Apparent Size of Smallest Cleft" as seen in the eyepiece, which he estimated to be 8 times the "actual" size). In view of where these numbers come from, it would seem to me that the "9 miles/D[inches]" threshold rule for visual observations should be referred to as "Whitaker's formula" (rather than Moore's). As previously mentioned, Whitaker's exact formula (which he presumably used to generate his original table) is "8.7 arc-sec/D[inches]". At an "average" lunar distance of 384,400 km (238,860 mi) that translates to 10.1 mi/D[inches], so Whitaker seems to have assumed a shorter distance -- something closer to 213,000 mi (343,000 km) -- for his table. That is, he seems to be trying to give the size of the smallest craterlet he thinks will be detectable when the Moon is at its closest approach to Earth.

2. The region around Beer was thoroughly photographed by Apollo 15 (1971), but if Moore made his statement about detecting a 500 yard (0.46 km) craterlet there as early as 1968, then I'm guessing he means that there is something on one of his drawings from the 1950's which, when checked against a Lunar Orbiter IV photo (1966) proved to be a 0.46 km crater. The problem with claims of this sort is, as Mardi has pointed out, there are numerous examples of Wilkins and Moore's drawings made with the 33" Meudon refractor in their 1961 book. But unlike the work of their more conservative predecessors, these drawings are invariably peppered with totally imaginary features. Little they show below about 2 km (actual size) has any obvious connection with reality. So Moore may indeed have drawn a hill with a 500 yard pit, but it's very hard to assess the significance of that since (absent the drawing) one has to assume he drew many others of that size that didn't exist. Last week I copied most of the drawings from the library's copy of Wilkins and Moore, but somehow missed Moore's drawing of Beer. As example of Moore's work with the 33" refractor, his drawing of Grove shows only what he records as a 0.5 km pit on the crater's north rim. This turns out to be non-existent, while he completely missed prominent 2, 3 and 4 km craters on the floor, as well as a 3-km diameter central peak. The drawing of J. Herschel, also attributed to him, is all but incomprehensible when compared to photos from space.

3. David, your Plato scale sounds correct to me. Plato looks like it initially had a nearly perfect circular form, now scalloped by slumping. 100 km (59 miles) seems a good estimate for the present inner rim diameter. An exact east-west rim-to-rim diameter, measured from what you've labeled the "west rim bow-in" to the opposite side is 99.5 km (58.9 miles). Features like the "mass of faulted rock" (once known as Plato Zeta) labeled in your illustration look like they've moved the rim-crest out by 5-7 km in places (of course, even the sections that look undisturbed may already have been moved out by collapses whose debris is now hidden under the floor). A sort of least-squares fit through the present rim scallops would probably give a "diameter" of around 104 km.

4. Regarding the accuracy (or lack thereof) of the craterlet diameters I posted on Chuck Wood's the-Moon Wiki, the high resolution USGS scans of the Lunar Orbiter images that have become available in the last few years are a considerable improvement over the LPI's scans from Bowker and Hughes. Also, using the LTVT circle drawing tool removes almost all uncertainty about the scale. By knowing the geometry in which the images were photographed, and by identifying the pixel locations of distant points at known lunar longitude/latitude, the scale is known to a fraction of 1%, and the circle tool permits a sort of visual least-squares-fit to the rim crest. Unfortunately, the definition of the rim-crest position (the transition from light to dark) is not always as sharply defined as one might hope, so there is a certain arbitrariness in how the circle is set that can be affected by magnification, contrast and room lighting. Plus there is my inherent sloppiness and human error. So your guess of +/-0.1 km accuracy is probably not unreasonable, although I feel they are a bit better than that. As a test, the diameters I posted on the Wiki were recorded on LO-IV-127H. Since it takes only a few minutes to do so, I just now re-measured the "Big Four" on LO-IV-127H, and then measured them for a first time on LO-IV-134H and on LO-IV-128H (much less sharp). The scale/geometry of each of these images was independently determined some months ago. Here the results (without editing or fudging -- my memory is too poor to remember the numbers from one photo to the next):

Re-measured Craterlet Diameters [km]

# Wiki 127H 134H 128H Aver SD
- ---- ---- ---- ---- ---- ----
A 2.44 2.47 2.49 2.47 2.47 0.02
B 2.09 2.05 1.99 2.09 2.06 0.05
C 2.22 2.29 2.23 2.23 2.24 0.03
D 1.98 2.05 1.99 1.91 1.98 0.06

The final two columns give the average and the standard deviation (scatter). It looks to me like +/-0.04 km would be a slightly better estimate of the actual experimental scatter in this particular image set. The difference in size between "B" and "C" looks significant to me. That between "B" and "D" may not be.

I didn't think to try to verify these numbers with the Clementine images. In general, their standard resolution is inferior to Lunar Orbiter IV, but if they took some in their Hi-Res mode they would be interesting to evaluate. As best I can measure them on the new (standard resolution) USGS Warped Clementine basemap (where there should be no doubt about the scale), the rim-crest diameters are: A=2.60, B=2.06, C=2.24, D=1.94 km. The diameter for "A" may be an overestimate because the Clementine lighting is from south to north and I'm including what looks like a possible image glitch (it looks like a double image in the mosaic) on the north rim.

It will be interesting to see what diameters Kaguya and Chang'e-1 obtain, but I doubt they'll be much different from these.

5. If one believes the list posted on the Wiki, Maurizio's 25-30 craterlets photographed with a 10" aperture corresponds to a detection threshold of 0.90 km. That can be compared with Bob Pilz' 18 possible craterlets (16 real), or 0.98 km, photographed with an 8" aperture. The rather modest gain (0.98 --> 0.90 km) in going from 8" to 10" seems in keeping with my earlier observation that the craterlet resolution threshold seems to improve only as the square root of the aperture, but Bob may have had some advantage from using a blue filter (shorter wavelengths give less diffraction) and newer image processing software. Even though the individual craterlet diameters given in the list may, as you say, be in error by up to +/-0.1 km, these are, for the most part, random errors; so the general trend expressed there (of numbers of craterlets in various size classes) should, I believe, still be valid. In other words, if, all else being equal and the performance of the telescopes being limited only by diffraction, an 8" scope can detect 16 craterlets ("0.97 km" in the list), we would expect a 10" scope to get to (8/10)*(0.98) = "0.78 km" in the list. "0.98 km" is between numbers 16 and 17 on the list, and "0.78 km" is between numbers 45 and 46. That implies that with "equal" performance, if one can detect 16 craterlets with 8" then it should be possible to detect 45 craterlets with 10", whether the individual craterlets listed were accurately ranked or not.

6. As to how the detectability of Linné compares to Plato craterlet "A", the rim-to-rim diameter of the bowl of Linné appears to me to be 2.23 +/-0.03 km. This was measured on the new medium resolution scan of Apollo AS15-M-0580 from Arizona State University registered to LTO-42A4. On lower resolution scans of AS15-M-0406 and AS15-M-0409 from the LPI, I get 2.28 and 2.24 km; and on LO-IV-097H and on LO-IV-098H I get 2.24 and 2.25 km. These are all independent measures on independently calibrated images. 2.4 km seems too large. My best guess is 2.24 km, which is significantly smaller than the 2.47 km (average) reported above for Plato craterlet "A", and about the same as Plato "C". If this is not convincing, the attachment shows Linné and Plato craterlet "A" in overhead views at the identical scale.

Since Plato "A" is 51.6° north of the Moon's equator versus 27.8° for Linné, there is a significant difference in foreshortening (the apparent north-south dimension of Plato "A" is compressed by a factor of 0.62 vs. 0.88 for Linné), so there would definitely be less total area of shadow to see in Plato "A". However, the east-west foreshortening which affects the separation of the bright-dark components (and therefore, one might think, is more important to the detectability) is not much different. Plato "A" is 9.1° west of the central meridian (on average) and Linné is 11.8° to the east.

I agree with you that the easier visual detectability of the bowl of Linné (if true – photographers may have the opposite experience) would be due to a combination of the larger visible shadow area (by a factor of about 1.3x from foreshortening alone, without even counting the greater hiding of the shadowed floor by the rim in the more northerly craterlet) and the greater contrast of the black shadow with the surrounding bright ejecta blanket.

-- Jim

Mardi and Jim,

I dont have experience with scopes over 10" of my own. Sure Ive looked through enough to think I even "adopted" and 18" dob, but really, I cant comment on whether or not seeing allows diffraction limited results for tele's greater than 12". I can say without pause that on good nights I see it with out a doubt on double stars. These nights are for me, say, one in a dozen. Maybe I can do it more often. Fact is I need to see a certain steadiness before I look at .5 doubles - wether or not lesser seeing will let it happen.

Mardi, the optimist in me wants to say you're wrong and that the diffraction limit is there for everyone regardless of aperture, you just have to be willing to put in your time to access it. I'm sorry, I see a politically correct sky LOL. I simply cant argue your point Mardi but everything in me wants to - like i said though my biggest scope was 10" so it'd be pure conjecture - which fills a lot of message boards as it is. It is a wise point though in that the scopes available to amateurs that often have the huge aperture also carry a huge central obstruction to say nothing of the fast f/ration coma distortions. Before they even start thats some things that a 12" f/7 for example just doesnt have to deal with.

JIM...

You wrote a terrific post but Mardi sapped my energy so Ill reread it tommorow!!

Pete

Pete, seeing's effect upon resolution varies by target. The effect upon a point sources (like double stars) is much abridged compared to the effect upon extended targets (planets & Moon) as these are much more complex images comprised of a multitude of "points" of varying contrast relationships vs. two single points of 100% contrast coefficient with their background. So seeing has a great effect upon fine complex detail such as even a craterlet represents. This means that although a larger amateur telescope will not be able to visually obtain it's theoretical limit of resolution on an extended target, it can on simple point source targets.

One can see the dramatic effect of seeing upon lunar (extended, complex) detail in real time. A good place to see this (with a 5-8" telescope) is by observing the little "astronaut craters" (Armstrong Aldrin & Collins) over the course of a night or several evenings. Usually the seeing median (the several second average of sub-second fluctuations) will vary throughout the night and certainly day-to-day. One would expect if seeing determined the visibility of small detail that such variances would affect the visibility of the smaller of these three craterlets-- common values for diameter are Armstrong; 4.6 km diameter, Aldrin; 3.4 km and Collins; 2.4 km. Observation bears this out--some nights only Armstrong will be visible...some nights only Collins will be invisible...some nights you will see all three. I have watched during one session Collins as steadily resolved, then begin to pop in and out of visibility then disappear altogether as seeing deteriorated. If you realize that there is always some atmospheric disturbance affecting astronomical images and that larger telescopes have theoretical resolutions that *exceed* this threshold (which lies at about 1/2 second arc) you should be able to deduce that such high theoretical resolutions will be effectively blocked by the even higher value of even the best seeing.

The difference between seeing's effect upon stellar (point) resolution and extended can also be observed directly. For example, on a night when the Moon is high and partial phase with what you consider good seeing from your locale, locate a more-or-less equal double pair that lies at or a bit above the Rayleigh resolution for your scope. It should be split nicely. Then observe the Moon and ascertain the finest craterlets you can see as having a discernable light & dark side (and thus determine that the feature is a depression not a positive feature) that represents the lowest threshold of 'resolution' of a craterlet. Go back and forth over the course of the evening on both targets--you will often see that although the close double star will remain separable, those lunar craterlets lying on the edge of resolution will fade in and out through the night and perhaps altogether disappear. The difference can be quite dramatic--i have had productive nights of observing close doubles while the Moon was basically a swimming jumble at higher magnifications.

One other item that bears repeating is that a craterlet seen as an undifferentiated spot, with no shadow and highlighted areas distinct, cannot be considered "resolved" as without the reference of the light and shadow parts there is no way to tell if the spot is a positive or negative elevation feature--IOW a craterlet or a hill.

This distinction is fuzzy these days because today, thanks to the high quality lunar images available, we _know_ what spot is a craterlet and what spot is not. This has given rise to many observers reporting seeing this or that (many) small craterlet(s) and which were seen resolved or as a spot one never really knows as it is seldom reported (typical of contemporary Plato observations). This has introduced much confusion as to the limits of craterlet resolution as it is well-proven that spots can be discerned at far higher resolutions--even less than the Dawes limit implies-- than resolved craterforms. This again goes to the realtive complexity of a spot (simple) vs a resolved craterform (complex). Seeing's delitorious effect increases in direct proportion to the increasing complexity of any given image.

Now the pre-spaceflight observers had no such advantage--no one knew what the finest features on the Moon actually were--so they were recorded and drawn as the observer suspected them to be--as spots, as hillocks, as craterforms-- to the best of their ability and to the limits of their optics. As they left good records, it is possible today to compare what they thought they saw with the reality revealed by the orbiter images--and from that we can deduce the limits of their accurate resolution. Their limits must also be our own--as eyesight has not improved over the last century nor has the optical quality of telescopes re; resolution ability. IOW, there are no variables extant which would suggest the possibility of better resolution today by a visual observer than that obtained by a highly skilled observer using a long german made 10inch refractor in the 19th century--like Krieger.

So perhaps you can see now that there really is nothing "PC" about seeing setting a real threshold upon possible lunar resolution--it is rather a conclusion based entirely upon reasoned argument and observational evidence.

I might add that there is little to be gained from obsessing too much about what the possible resolution of one's scope may or may not be--one will always see what one believes one sees after all. What is far more important, i think, is recognizing whatever level of resolution one actually *gets* and then being able to see those identifiable landforms in the context of the geological evolutionary processes the Moon has faithfully recorded over billions of years. This is what makes the Moon so unique--it is possible to actually *see* the passage of time on the Moon's surface (at virtually any telescopic reesolution) --where one can only *imagine* it when viewing some featureless & static fuzzy object representing the equivalent passage of time in deep space.

The next time you look at the crater Kepler, recall that you are looking at something that was created at the same time that flowering plants proliferated upon the Earth during the Cretaceous --for the very first time in all of history. Kepler and the birth of flowers...imagine that!

Mardi,

thats all heavy stuff -and something I'm going to reread again to be sure - lol - and print out. Something I've been meaning to ask the lunar crowd here - I want to observe those three craterlets at the apollo eleven sight unde rtthe same EXCACT lighting/moon phase conditons they had at the time of landing, and , well, bouncing about the surface.
Imagine that Mardi - it is preserved - atleast to our level of resolution so the lighting would seemingly anyway be an exact duplicte of that amazing evening. But how would i know what night and phase and time was that of the Apollo 11 landing our wonderful year of 2008?

Thaks again Mardi for the info!

Pete

Hi Pete,
if I made everything correctly, this pic should show the Moon phase on the moment of Apollo 11 landing (21th of July 1969, at 02.56.20 UT, location on Mare Tranquillitatis at 00.674 Nortern latitude, 23.472 Eastern longitude, angular diameter of the Moon was 1829.3 arc-seconds and 35.94 per cent of the Moon was illuminated).

Jim Moshers Lunar Terminator Visualization Tool predicts (for my location), that the similar conditions would occur on the 11th of May 2008 at 23.17.01 UT, on the 10th of June 2008 at 10.34.24 UT, on the 4th of December 2008 at 11.36.17 UT and on the 1st of February 2009 at 16.45.28 UT (to pick out just the next few of these...)

Attached please find a map from Jim Moshers Lunar Terminator Visualization Tool (the center of the blue cirle is on the landing site and the circle has a diameter of 100 km, and terminator is visible on the lines)

Sorry desertstars, could not have this file into 60 K without losing the text...

Mardi,

I cant thank you enough. Before the age of the computer and the internet - wher ethe heck would I have gotten that info.
If the seeings good, for the novelty of it I want to sketch the area and see how "far down" I can go . I know theory says roughly 1.1 mile or so. Still it'd be wild to do.

Thank again. I still have a problem with seeing resolution on extended objects like the moon and planets as that of "points" or many of them as opposed to te descrete contrast of stars. Seems more like rays than points. Or am I misunderstanding it?

Aain, thanks Mardi. I'll be sure to let you know when I blast off.

Pete

Hi Pete,
re; "that of "points" or many of them" Sidgwick puts it this way: "The (extended) image is composed of the overlapping diffraction patterns formed by light emanating from every point in the object."

Compare this with a star, which since it has no measurable diameter itself, you get just one source of light and therefore just one diffraction pattern.

One can simplify this by visualizing an extended image as being composed of overlapping pixels shaped like diffraction patterns...

There is also a form similarity to those shown when sprinkling many pebbles into a still pool of water--the larger and smaller of which forming overlapping concentric wave patterns of varying sizes --which roughly correlates to varying brightnesses when such wave patterns are expressed by light rather than water.

There is also a structural similarity between an extended image and the stellar centers of dense globular clusters (M13 or 15 for example) that are unresolved into individual stars. This is because the center of an unresolved globular is likewise composed of an virtual infinity of separate but individually unresolvable points, the diffraction patterns of which therefore heavily overlap and together form what appears to be an unresolved but nonetheless still "textured" appearing core. In this way such a target could be considered both stellar and effectively extended in image form.

I might mention that "form" is an important term as to its relative nature when talking of "stellar" and "extended" images as well--for example although the sun is definately a star and therefore "stellar" it is actually an extended object as it is close enough to us to see a great deal of actual surface detail; oppositely, although Saturn's moons are planetary objects, i.e. also containing a wealth of detail, they are nonetheless classed as "stellar" in appearance by us earthbound observers since they are too far away for us to effectively resolve their discs.

I hope these examples furthered rather than confused your understanding of this and my apologies if the latter is the case--sometimes i don't know when to stop explaining things... :o