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Anonymous
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While observing Moon and Mars couple days ago I started to wonder what is the resolution limit of a telescope on objects of this kind and how it can be defined.
It is easy to define resolution with double stars - they can be resolved, resolved partially or not resolved at all. Things get more complicated when components have different magnitudes, one or both are very dim or very bright, seeing is taken into account and so on, but still resolution is something that can be defined and observed.
How all that translates into planetary performance? In theory extended object is an infinite number of point sources of light but I am not sure how this definition can be applied to practical use.
I'd like to hear you opinion on the following Let's say that seeing is good, aperture is small and double star with equal components separated by 2" have been resolved well.
What would be the smallest apparent size at which planet will appear as definite disk instead of point of light?
What would be the smallest size at which high contrast feature like crater near terminator will be visible at all?
What would be the smallest size at which this well defined crater will actually look like a crater?
What would be the smallest size at which low-contrast feature on Jupiter can be just identified and when will its shape be visible?
Where is the limit of visibility of narrow, high contrast but long features visible on Moon?
When details on Mars begin to have shape instead of beeing just dark patches?
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sixela
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Posts: 13991
Loc: Boechout, Belgium
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Quote:
What would be the smallest apparent size at which planet will appear as definite disk instead of point of light?
With stupendous power and extremely good seeing, *nothing* looks like a point of light - even stars look like the Airy disc image formed by them...
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400mm f/4.46 self made Dobsonian on Tom Osypowski equatorial platform
Skywatcher 130mm f/5 BlackLine (finder, widefield scope and solar continuum scope)
Sumerian 250mm f/4.8 Alkaid (as travelscope without platform and on Tom O. platform above).
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 18806
Loc: Cumberland, R I , USA42N71.4W
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Dennis,
without taking each of your questions and answering it specifically, these posts will answer most if not all of your questions. All of these questions have been asked before and these papers were developed in answer. Since I keep a word file with access to all of them pasting them here in response was a simple matter of copy/paste/
What Does it take to see width in the Cassini Division
Nov, 2003
An expalnation of the difference in detecting and seeing a narrow division
What Does It Take To See Width In The Cassini Division?
Seeing Encke Division
Mar 2004
What’s required to see this extremely fine feature?
Seeing Encke
Resolving Jupiter’s Moons – seeing Jupiter’s moons as disks
Mar 2004
A development of extended object criteria for use in understand resolution of disks
Seeing Jupiter's Moons as Disks
Seeing Saturn’s Moons
Mar 2004
What’s the size and magnitude of the Saturnian moons
Seeing Saturn's Moons as Disks
Shadow Transits of Saturnian and Jovian Moons
Jan 2004
How does extended object resolution affect the ability to see shadow transits
Seeing Shadow Transit of Saturnian and Jovian Moons
Resolving a Thin Wire
Jan 2004
A thread discussion leading to what allows such fine resolution
Resolving a Thin Wire
The Flag on the Moon
Jan 2004
A little study in resolution
Seeing the Flag on the Moon
The Great wall of China
March 2004
Can it be seen from space?
Seeing the Great Wall of China from Outer Space
The last two are a bit of the lighter side of astronomy. I hope you find this information useful.
edz
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Scott Beith
SRF
Reged: 11/26/03
Posts: 42898
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Ed, Well done Sir.
--------------------
SLAP Observer --- TMB130SS, SV102V(LOMO Lens), SV80ED Deluxe
"The only thing necessary for the triumph of evil is for good men to do nothing." -- Edmund Burke.
"People sleep peaceably in their beds at night only because rough men stand ready to do violence on their behalf." -- George Orwell
"The measure of a man’s greatness is not determined by what he accomplishes for himself, but by what he accomplishes for others.” -- Some Bald Guy
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photonovore
Moonatic
Reged: 12/24/04
Posts: 2792
Loc: tacoma wa
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An alternative would be to crack a book dealing with the subject. I'd suggest "The Amateur Astronomer's Handbook" by John Sidgwick. It is a well-respected and very detailed reference; used copies are available for a couple of dollars.
As to the Lunar surface, as discussed here on the forum, there is a thread here that examines this issue in some detail.
-------------------- Mardi
4" achromat, ETX-70, 8"cat.
Whitepeak Lunar Observatory Website
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Anonymous
Unregistered
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Sixela,
I meant to say at what point I will be looking at the actual disk of a planet as opposite to the Airy disk representing a planet 
Ed,
Thank you for information, explanations are very clear and straight forward. I don't think I am quite ready yet to give a speech on a subject but definitely understand things much better now It turned out to be not that much different to double stars, just number of additional things needs to be taken into account. Also now I am inspired to examine moons of Jupiter more carefully, I did not realise that they can be resolved.
photonovore,
Just ordered it Would have done it before if was only aware of its existence!
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 18806
Loc: Cumberland, R I , USA42N71.4W
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Dennis,
one more article to complete the circle. this one more geared towards point source resolution than extended objects, but with some relevant information.
http://www.cloudynights.com/documents/resolution.pdf
Mardi,
I take it you picked up a copy of Sidgwick, or was that the one you had. Do I recall not long ago a request for technical Astronomy book recommendations? and thisone (out of print) is certainly one of the best.
edz
-------------------- Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
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photonovore
Moonatic
Reged: 12/24/04
Posts: 2792
Loc: tacoma wa
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Ed, Sidgwick's is still in print--at least amazon offers new copies on it's website (for 13$) as well as used, albeit it hasn't been updated since the 80's 3rd edition. That doesn't seem that great of an issue to me, however, as much of what it contains re; telescope optics is rather immutable in any case.
-------------------- Mardi
4" achromat, ETX-70, 8"cat.
Whitepeak Lunar Observatory Website
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 18806
Loc: Cumberland, R I , USA42N71.4W
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New or Old, it is one cetainly well worth having.
edz
-------------------- Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
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Anonymous
Unregistered
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Ed,
Very interesting article, I think I am quite comfortable now about resolution of both point and extended objects. There is one thing, though, which I still don't quite understand - 'partial resolution' which is mentioned in your reply on Jupiter's moons.
Point sources of light cannot be resolved and form an Airy disk. If we take two stars of same color and magnitude they will produce Airy disks of same size and we will not be able to make any judgments about their real angular size.
If we look at Jupiter through 4" telescope we will see actual disk of a planet which we can measure.
Now let's look at Io. It cannot be resolved in 4" telescope so we will see just an Airy disk, not a real disk of a satellite. Since Io is extended object an Airy disk will be different (bigger?) to that of a point source of same color/magnitude. So if we can spot this difference we can make a judgment that observed body is an extended object. Does it mean that there is a certain range below resolution limit where we can notice a difference between point source and extended object, similar to Dawes limit where we can't split a star but still can see its double nature or case with Cassini division which we can easily see in small aprture but cannot resolve? Also is it correct that there is no clear boundary between point source and extended object, it sits somewhere below resolution limit and depends on all those parameters which usually not taken into account to make things simpler - seeing, quality of optics, aperture, abilities of observer and so on?
Dennis
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EdZ
Professor EdZ
Reged: 02/15/02
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If we look at Jupiter through 4" telescope we will see actual disk of a planet which we can measure.
Probably Not. Since it is an extended object, the light on the disk forms an infinite number of Airy disks. Even the light at the very edges forms Airy disks. So any attempt to measure the diameter of the planet disk with a precise instrument would probably show a wider diameter than actual due to edges of Airy disks extending very slightly beyond the true diameter of the planet disk.
Now let's look at Io. It cannot be resolved in 4" telescope so we will see just an Airy disk, not a real disk of a satellite. Since Io is extended object an Airy disk will be different (bigger?) to that of a point source of same color/magnitude.
I don't think so. Any bright object on a black background smaller than the resolution limit of the objective is seen as a point source, meaning the image formed by the objective will be formed to the diameter of the Airy disk.
or case with Cassini division which we can easily see in small aprture but cannot resolve?
this is a very special case and there is a great deal written about it. A linear black feature on a white background can be seen far below the resolution limit of a scope. This is detection, not resolution.
Does it mean that there is a certain range below resolution limit where we can notice a difference between point source and extended object
If the object is a light disk on a black ground, smaller than the resolution limit, then I would say no. However, If the object is a feature on a much larger disk, say the moon or Jupiter or Saturn for instance, and the feature has shape, such as linear dimension but has width insufficient to exceed resolution limit, or a circular crater smaller than resolution limit but creating a black spot, or a shadow disk projected on a planet disk, then if these conditions meet or exceed special criteria, they may be be noticed as extended objects even though dimensions do not exceed resolution limit.
edz
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Anonymous
Unregistered
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Reading over some of the notes with great images of Mars I am beginning to see a little misunderstanding or at least errors in interpretation of what observers believe they are seeing on these images. First, a review of HST images of Mars over the past decade will give you some idea of what has been revealed by these magnificent up-close images, but how the surface details become clearer and more distinct as Earth approaches Mars closer and closer. In 2001 HST image of Mars we saw what appeared to be features that could only be interpreted at craters and volcanoes. In 2003 the two planets were even closer and images from HST revealed even more features that appeared as craters and volcanoes. However, is this evidence that we are actually seeing topography or even relief? I should caution those who may jump to these conclusions that many times an observer interprets visual sensations that may be illusions and even trained cartographers will at times interpret features on Mars with a different opinion.
Another problem I have seen is that bright desert regions on Mars may appear like a dust cloud to some and a dull haze area to others. These features are difficult to detect at best, but when alerted by someone that a dust cloud has been identified in a certain region -- this only heightens the excitement for some observers and the game of illusion begins. It spreads until it becomes quite obvious no dust exists. Dust cloud are bright in red light, they move and obscure stuff on Mars. You will certainly see how bright red they are the first time you see one, and when they cover up a dark feature they really leave it looking weird. In other words, you will know a dust cloud when you see one.
While I will not proclaim that everyone has accepted their visions of what appears as topography in these images never the less I read much excitement on Internet that many have believed they are actually seeing true relief on Mars in their images. For what it is worth I would like to leave yawl with the quote below, by repeating a letter to S&T by Cornell's Jim Bell wrote to Roger Sinnott in 2003:
"While I acknowledge that there can be moments of incredible clarity (some would even say clairvoyance) at the telescope, I have never seen any convincing evidence for the observation of craters on Mars based on their topography. It's not hard to be skeptical: the elevation differences are quite small and the phase angles are not ever really that large. However, I find it easy to believe that observers have seen craters on Mars in the past, not based on their topography but instead on their albedo variations.
A good example can be seen in the June 26, 2001 Hubble Space Telescope image, which is among the highest resolution images of Mars ever obtained from Earth. One can easily see a number of large and even smallish craters in the Meridiani and Arabia regions, but they are resolved because they are just shallow holes in the ground filled with dark sand scattered amidst a "sea" of bright dust. The craters in this area (and many others) are natural sinks for coarser-grained and thus darker particles, leading to these large albedo contrasts. Even the keenest observer could mistake the dark inter-crater deposits for shadows, especially for cases where the deposits fortuitously appear biased towards the direction that one might expect for shadows."
Now that everyone is mad, please stop and think about what Jim and, now, I have said. Interpretation is in the eye of the beholder.
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David Knisely
Postmaster
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Posts: 13646
Loc: southeastern Nebraska
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Jeff, while many of the claims in amateur images of crater imaging may remain somewhat questionable (mostly, people are imaging the darker patch *in and across* Huygens and claiming they imaged the crater itself), HST *did* image both craters and other non-albedo features. The ACS image of Mars taken in 2003 *clearly* shows the interior walls and floors of *many* impact craters. They do *not* show much in the way of shadowing due to the sun angle, but like those craters visible on the moon at high sun angle, they are there, and most workers agree that they have been conclusively imaged. In addition, that ACS image *clearly* shows the brighter walls of various portions of the Valles Marineris canyon system, and the color WFPC 2 camera shows not only a few craters but the Tharsis volcanoes. A few of the better amateur images taken earlier this apparition also appear to show relief in the form of the shadowed (terminator) side of Olympus Mons, so in this case, I might be willing to give them the benefit of the doubt as far as topography is concerned, especially considering what Damian Peach is doing (which is totally amazing). Clear skies to you.
-------------------- David W. Knisely . . . . . . "If you aren't having fun in this hobby, you aren't doing it right."
Hyde Memorial Observatory
http://www.hydeobservatory.info
Prairie Astronomy Club
http://www.prairieastronomyclub.org
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Anonymous
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The Tharsis volcanoes and Olympus Mons - at least their shadows - have been captured by countless people on this forum and elsewhere with telescopes ranging from 5" in aperture and upwards.
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Anonymous
Unregistered
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Dave, Robert,
I am sure you realize that posting something that may not ring true with many observers is hazardous to one’s health and also using only one reference by a professional source may have been a little cheap. However, by now you probably realize that Jim Bell’s letter to S&T in 2003 is but one of many references stating similar to Jim’s and my views on identifying topographic features Vs albedo featrues on Mars. Read Jim’s letter again and then read what Richard McKim has to say in his message: http://groups.yahoo.com/group/marsobservers/message/6004.
While working with Chick Capen, Leonard Martin, Jim Bell, et al for several decades on the HST imaging team, such amateur dudes such as me and Don Parker, to drop a few names, it was not in our interest to get into get into any semantically charged arguments with people who believed everything they read or thought they saw on those images in question. I realize too that few amateur astronomers had the opportunity to work with professional planetary cartographers and researchers as we have over he past 40 years, so we have generally not said much. I just cannot keep quite now, especially after getting phone calls and e-mails from close friends and associates who are yukking it up over an article in a recent S&T.
You say “The ACS image of Mars taken in 2003 *clearly* shows the interior walls and floors of *many* impact craters.” Well, it may be beneficial for you to research and post the definition for identifying topographic features on other Solar System bodies. It is not as straight foreword as one may think and because one “clearly” see what they think is craters or shadows from volcanoes on Mars may not be a shadow or whatever they state. I have written that IMHO the images of such features appear to me at least as craters and mountains – but most professionals in know disagree. Their discussion seems more valid that my first assumptions, so there is where I stand. Also, letters have been or are in the process of being written, to S&T disputing every aspect of that particular article and the assumptions as you make in your message – I will wait until the dust settles to respond, so to speak (no dust devils now). BTW, you might want to ask Damian Peach what he thinks too, since he works closely with Richard McKim, and he is not too keen on identifying Mars craters and volcanoes in telescopes. Remember, that Olympus Mons may not cast the typical shadow, owing to its shallow slope angle. The dark zone to the terminator side of this feature is quite likely due to albedo and the lack of direct sunlight – at least that is what the pros have to say about it. If S&T publishes some of the letters, months from now, then maybe this discussion may be re-run or re-ran, perhaps returned to. 
At any rate, this non-scientific subject must stir some interest in me since I sent far too long in replying to yawls’ messages, and I have to run and catch flying debris from another feeder band from Rita!
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Anonymous
Unregistered
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Ed, I think I've got it now. Extended object can be either resolved or unresolved, there is no such thing as partial resolution. In case of special circumstances unresolved object can be detected as an extended object but otherwise once the size of an object gets below resolution limit it just becomes a point source (provided it is a bright object on a dark background). Things are very complicated with planetary details due to complex shapes and various levels of contrast but in general when we look at high contrast areas it is a bright areas which actually form an image so it is always a 'bright object on a dark background' even if we are looking at small dark area on a large bright planet. Dark areas will appear a bit smaller and bright areas a bit bigger than they really are. And when we observe a bright feature on a bright backround things get even more complicated as both will participate to image generation and this is where telescope's ability to provide high contrast image becomes vital. It can be a situation when telescope resolves an object but difference in brightness between object and a background is so low that we just can't see it. Dennis
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sixela
Postmaster
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Posts: 13991
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Quote:
it is a bright areas which actually form an image
Well -- ever heard of electron holes?
Quote:
so it is always a 'bright object on a dark background' even if we are looking at small dark area on a large bright planet. Dark areas will appear a bit smaller and bright areas a bit bigger than they really are.
They won't. Convolve an circular object with an Airy disc and it becomes both "larger" and "smaller" - the edge is blurred, which, if you use a low cutoff light intensity value to determine where there's an object, actually does make it larger. But the inside has gotten a bit darker, too, as points close to the ege will have redistributed energy outside of the "real" unconvoluted shape.
So if you take the negative of this - a dark spot on bright background *also* becomes larger if you take a *high* cutoff value to determine where the intensity of the bright background is diminished enough to perceive that "there's something there".
The background and the dark spot both become larger - they bleed into one another.
--------------------
400mm f/4.46 self made Dobsonian on Tom Osypowski equatorial platform
Skywatcher 130mm f/5 BlackLine (finder, widefield scope and solar continuum scope)
Sumerian 250mm f/4.8 Alkaid (as travelscope without platform and on Tom O. platform above).
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 18806
Loc: Cumberland, R I , USA42N71.4W
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Dennis,
all that you siad there makes sense.
edz
-------------------- Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
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David Knisely
Postmaster
Reged: 04/19/04
Posts: 13646
Loc: southeastern Nebraska
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JDB wrote:
Quote:
You say “The ACS image of Mars taken in 2003 *clearly* shows the interior walls and floors of *many* impact craters.” Well, it may be beneficial for you to research and post the definition for identifying topographic features on other Solar System bodies. It is not as straight foreword as one may think and because one “clearly” see what they think is craters or shadows from volcanoes on Mars may not be a shadow or whatever they state. I have written that IMHO the images of such features appear to me at least as craters and mountains – but most professionals in know disagree. Their discussion seems more valid that my first assumptions, so there is where I stand. Also, letters have been or are in the process of being written, to S&T disputing every aspect of that particular article and the assumptions as you make in your message – I will wait until the dust settles to respond, so to speak (no dust devils now). BTW, you might want to ask Damian Peach what he thinks too, since he works closely with Richard McKim, and he is not too keen on identifying Mars craters and volcanoes in telescopes. Remember, that Olympus Mons may not cast the typical shadow, owing to its shallow slope angle. The dark zone to the terminator side of this feature is quite likely due to albedo and the lack of direct sunlight – at least that is what the pros have to say about it. If S&T publishes some of the letters, months from now, then maybe this discussion may be re-run or re-ran, perhaps returned to.
Well, I did run Celestia with the vantage point from Earth looking at Mars using the topographic model enabled (allows features of known heights to cast shadows depending on the sun angle). I recreated David Moore's August 4th image viewing situation and guess what? The darker shadowed portion of Olympus Mons stood out quite nicely in almost exactly the same form as was shown in his image on p. 66 of the November Sky and Tel (although of course, at a much higher level of detail). Now, if the topography relief was exagerated in the Celestia model, this might yield some shadowing discrepancy from reality, so I used Vistapro and the MGS Digital Elevation Map data with a scale of one (i.e. no surface relief exageration) and did some playing with lighting using a neutral color map (i.e., no overlay of the MGS images, just the elevation topography). What I found was that even at a sun elevation angle of up to 40 degrees above the martian horizon, the terminator side of Olympus Mons was somewhat darker than the sunward side, with the darkening becoming more pronounced as the sun elevation angle decreased. Indeed, at sun angles of less than 20 degrees, the darkening became considerably more pronounced, and by 5 degrees, a complete shadow covered the *entire* terminator side (half) of the mountain and began extending slightly onto the surrounding plain. As far as I am concerned, these two exercises have convinced me that in the quality large-scale amateur images taken at the proper time, what is being shown is indeed shadowing effects generated by the topography of the volcano, and *not* purely albedo effects. Clear skies to you.
-------------------- David W. Knisely . . . . . . "If you aren't having fun in this hobby, you aren't doing it right."
Hyde Memorial Observatory
http://www.hydeobservatory.info
Prairie Astronomy Club
http://www.prairieastronomyclub.org
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Anonymous
Unregistered
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Well Dave, I will not belabor the point but after receiving a nice e-mail from Steve O’Meara, who has measured the exact locations of both Dave’s and Ed Grafton’s great Sept 04 image of Mars showing the exact same albedo feature his detailed finding us that, paraphrasing you, “the darker shadowed portion of Olympus Mons” is just that, darker material at the center of Olympus Mons. He furthers explains to me that “the fact is, the dark spot is not the shadow of Olympus Mons but it is the central massive of Olympus Mons. The bright spot is part of its skirt. In fact, you can see two oblique arcs of the skirt in Grafton's magnified image.” After Steve overlaid Ed’s image onto a HST image and adjusted the CM’s to the same aspect angles, Steve goes on to say that “the dark spot is where the center of Olympus Mons should be. No long sloping shadow here.”
Of course, other experienced observers and students of Barsoom, that will remain nameless herein, have similar explanations for this feature -- many of which are showing up on so many images. But, since this takes me away from my research, the atmosphere of Barsoom, and is not of any scientific interest to me I will accept that you believe what you believe and are still having fun observing the same reddish spot in the sky that I do. Even Steve thinks similar thoughts. At any rate, by the time rebuttal letters, if they are indeed published, arrive in future issues of S&T about the subject I am sure my nimble mind will have altogether forgotten it. 
I can almost believe that some of these images will show some relief on Mars, but visually seeing them is another story.
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