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Putting the "Rule of Thumb" to test

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#51 WRAK

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Posted 06 December 2012 - 04:46 PM

Fred, the following is kind of mysterious for me: Treanor states "The intensity of the third maximum is to that of the Airy disk as 415:100,000. The magnitude difference is thus 2.5log10 I1/I2 = 5.95 approximately." but this value would according to my information be valid for the sixth maximum and in the third maximum we have 1.5% of the total energy of the Airy disk and therefore the magnitude difference is 4.56. Maybe a little error of Treanor with whatever impact on his results or do I miss something here?
Wilfried

#52 fred1871

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Posted 06 December 2012 - 09:22 PM

Wilfried, I think part of the difficulty with brightness levels is that there is a difference between the total amount of light in a diffraction ring, and the maximum brightness of the ring, because the rings have a gradation of brightness across their width in the same way that the disc has a gradation of brightness across it.

So the total energy of the first ring, for example, is 7% of the total image light of a star, with 84% in the disc. That might suggest a ratio of 12:1 between disc and ring, but it's not that simple.

Although the disc has a gradation of brightness from centre to edge, the light is more concentrated in the disc, where the ring, being much larger, has its light spread out more.

Lewis (on page 374 of his article in "The Observatory") gives a table of illumination levels at a series of distances from the centre of the disc. The maximum illumination of the first bright ring is given as .017 (relative to 1.000 for the disc centre). That gives a ratio just short of 60:1, or near enough, 4 magnitudes instead of ~2.6 (12:1).

So in the case of Delta Cygni, where the secondary star is mag 6.3, it will be noticeably brighter than the brightest part of the first ring, which is equivalent to about mag 6.9. As well, the separation (2.6 arcseconds) will put the secondary's star image not on the brightest part of the bright ring, but towards the inner edge of that bright ring, where illumination is much less.

Rayleigh for 60mm is 2.3", and the brightest part of the first ring is around 3.0-3.1" from the disc centre. Where the secondary star is located, at 2.6", the illumination of the bright ring is about half the maximum, so closer to mag 7.6. Yes, I'm ignoring illumination fall-off in the secondary star disc, which makes the apparent size of the disc smaller, because that's a factor to be looked at later - though I suspect it makes not much difference overall, at least to the visibility of the star, placed where it is in diffraction terms.

The above may go some way towards explaining why a double such as Delta Cygni can be seen as a double with a 60mm refractor, when the telescope has good optics and seeing is very good, so it ceases to be a factor.

I'd expect that a similar delta-m and separation would be less readily observed with stars that are less bright. The light gathering capacity of 60mm has no difficulty with 3rd and 6th magnitude stars. At magnitudes of say 6.3 and 9.7 we'd be facing lack of light as a problem with a fairly close pair. In between magnitudes? - perhaps someone with a 60mm or similar scope might like to create a list of pairs around 2.5" separation, with delta-m of 3 to 3.5, but with the primary star at mags 4, 5 or 6, and see what's possible. Is Delta Cygni near a "sweet spot" for small telescopes? And are there some other bright pairs that show this pattern?

Hmmm... suspect I need some more thinking time on this... meanwhile, I'll hope the above ideas about brightness levels in the diffraction image might be in the right direction as part of explaining the sometimes surprising performance of small telescopes.

#53 WRAK

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Posted 07 December 2012 - 12:10 PM

Fred, do you have an online link to this article of Lewis?
Wilfried

#54 WRAK

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Posted 07 December 2012 - 04:42 PM

...Lewis (on page 374 of his article in "The Observatory") gives a table of illumination levels at a series of distances from the centre of the disc. The maximum illumination of the first bright ring is given as .017 (relative to 1.000 for the disc centre). That gives a ratio just short of 60:1, or near enough, 4 magnitudes instead of ~2.6 (12:1)...


Fred, applied this to my small data set - does not help much as it increases the average error about 25% compared with my conservative approach concerning the delta-m between diffraction rings.
Wilfried

#55 fred1871

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Posted 07 December 2012 - 07:04 PM

Wilfried, the Lewis article is in The Observatory, for 1914, vol 37, pp372-379. The mention of it in Argyle (Observing and Measuring Visual Double Stars has the wrong volume number - in both 1st and 2nd editions).

I'm not suggesting my attempted analysis will be immediately applicable to an algorithm with predictive capacity. Rather, I was trying to explain why I thought a "special case" could occur. Generally, I'd expect placement neatly between the diffraction rings to be the best model; edging away from that gets into low probabilities of visibility. Delta Cygni seems to me a pair that
"sometimes" is visible with 60mm - that telescope, that observer, that night.

No algorithm is going to be completely accurate because of variable factors - observer eyesight, observer experience, interaction of telescope and seeing, are a few. I was reminded of this two nights ago when observing some difficult uneven pairs - even changing the eyepiece had an effect on the visibility of dim close companions, and the most difficult flickered in and out of visibility.

So, I was dealing with a matter - small telescopes, not medium or large - that did not fit the type of model I'd proposed for medium telescopes. And my feeling is that there are windows where the small telescope does better, comparatively, than medium telescopes. That would require a different algorithm, or predictive equation, and one with boundaries placed on it to allow for the modest light-gathering of small scopes.

I thought that my closer analysis of the diffraction pattern might be informative in the issue of Delta Cygni. I haven't yet got as far as applying it to medium-size scopes or other examples of doubles. But I have had the experience, not often, of having a "small scope" experience with my 140mm refractor, where I could definitely separate a double I'd expect to be somewhat beyond that aperture based on the RoT. I've not had that experience with somewhat larger telescopes such as my 235mm SCT, or a C14 (35cm) that I had access to in the past. With them, the ragged edge of visibility was pretty much where it was expected on the best nights. So I'm inclined to think something similar to the RoT has good predictive capacity within certain limitations. I agree it needs refining. And I'm beginning to see why Lewis didn't attempt an overall model, but gave a series of patterns (wry comment).

#56 WRAK

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Posted 08 December 2012 - 05:37 AM

Fred, this is going in small steps to a common ground I think:
- splitting doubles with small scopes is a separate game with own rules (I feel even no longer sure if Dawes is valid for small scopes as also his numbers are probably derived from observations with larger scopes)
- there is no one singular RoT but a set of rules like for example:
--- m1 < 6 and delta-m < 1 then Dawes
--- m1 < 6 and delta-m < 2.5 then Rayleigh
--- delta-m > 10 then TLM including NELM
--- inbetween maybe a rule derived from crude number crunching
- any serious RoT should not only provide one number for required separation or aperture but also the average error range
- this error range should allow deriving probabilities for splitting with a given aperture and the same time cover the vast number of side effects not taken into calculation

#57 WRAK

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Posted 11 December 2012 - 05:16 AM

Applied part of this step by step approach to Lord's data set for 3" and 6" refractor, but it did not bring much improvement - and once again I got the impression that this data set is not consistent on the "limit".
If for example 3" STF51 +6/12mag is a limit observation for a 150mm refractor how can then said the same of 3" A2225 +7.5/12mag and therefore 25% less delta-m?
Wilfried

#58 fred1871

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Posted 11 December 2012 - 06:59 PM

Wilfried, I think it's clear that Chris Lord's observations set does not have enough examples that are at or near the limits of the telescopes. If all his data is used, the range (from not difficult to very difficult) means there's no clear pattern. I think only his most difficult with each particular telescope examples are useful for establishing limits.

I've had a similar problem in going through my observing notes. I have observing records for thousands of double stars, hundreds of them difficult with the telescope I used in each case. The problem is determining which examples are the borderline cases, those where I was working near the limit of the telescope. All this would be much simpler if I'd had a diaphragm on the scopes I used, so I could stop down the aperture on the difficult pairs on the best nights, to see how much aperture reduction was possible without losing sight of the secondary star.

Even so, I'm gradually getting a list of pairs that do look close to the limit of the scope used. When that's finished, I'll see what pattern I can find from my own observing. Because I've been using mid-size amateur telescopes - 14cm to 35cm aperture - it fits Treanor's 15-inches or less, while avoiding the "small scope syndrome", most obvious around 60-80-100mm aperture refractors.

I'm also starting to go through the observations of others, similar to Lewis's data collection, but including some observers he didn't look at, notably some in the southern hemisphere, and some post-1914 northern observers (as his study was published in 1914).

#59 WRAK

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Posted 12 December 2012 - 12:21 PM

Applied the step by step approach now to my own data set (including 2 of your observations and some of the closest to limit from Lewis for 3" and 6" scopes) and feel stuck now - the best I could do so far is an average error in aperture of 20mm and this seems not this good as this the same value I got with more or less crude number crunching with a program for statistical analysis with hypothetical functions without much regard of optical theories.
I think I will take a recreational break with some reading on this topic and wait for opportunities for observation sessions to get some more data on limit observations in the range of 50-140mm aperture. Maybe some enlightment will come with time.
Wilfried

#60 fred1871

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Posted 12 December 2012 - 06:42 PM

Wilfried, I'm inclined to think that +/- 20mm isn't too bad related to a 140mm aperture - though I'd like to see it closer. Down at the 50mm aperture level that variation tells us nothing useful. It's proportional, as I'm sure you know.

I've had the experience of observing a double star that another experienced observer could not see, same time, same telescope, same eyepiece. The two of us looking alternately. To me the companion was fairly obvious; to him it was invisible, then after "look in this position" it was "maybe I can see it". So we have the observer factor as well. Some observers will need a bigger telescope, or higher power, or more practice on doubles.

I haven't mentioned another published paper on resolving doubles that I think you (and others) would find of interest. It was published in the (free, online) JDSO (Journal of Double Star Observations) - the particular item was in volume 4 no 4, Fall 2008 - by Tim Napier-Munn, "A mathematical model to predict the resolution of double stars by amateurs and their telescopes" .

It details a study based on observations by quite a few observers with telescopes from 80mm to 508mm on a variety of doubles to see what the limits were. And it deals with probability factors for predicting "splittability".

One thing I'd mention here is a graph that plots resolution against delta-m by aperture - for 80mm, 203mm, 356mm. There were 4x80mm, 1x203mm, 1x356mm scopes. The 80mm scopes did less well than I'd expect; the 203mm also less well; but the 356mm about what I'd expect from the RoT.

The paper discusses background - diffraction, Rayleigh, Peterson, etc etc - but the useful thing is the study based on new observations by 15 observers with 25 different telescopes. "315 valid observations were made". That's a reasonably significant total, despite the aperture spread being very large. There's no full data list, and the author does say that he rejected some observations for a variety of reasons, just as the USNO orbit catalog plots show some observations are well out of line with the pattern. Haas will have a similar experience - my impression is that one particular observer is already offering false positives on some doubles.

Last night I finally got a clear and dark and STEADY sky - able to take 400x with clear discs and neat diffraction rings - so I was able to try some difficult pairs again, and succeeded with some of them. Notes to follow after I've checked current WDS data etc.

#61 WRAK

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Posted 13 December 2012 - 03:31 PM

... +/- 20mm isn't too bad related to a 140mm aperture - though I'd like to see it closer. Down at the 50mm aperture level that variation tells us nothing useful. It's proportional, as I'm sure you know...

Thank you for pointing out the obvious, I already got some blind spots here. The average error relative to aperture at this data status is 23% and this is certainly too much - but there is a focal point on fixed aperture observations (including the infamous 60mm observation of Delta Cyg) and these are almost always to some degree dubious.
I found the mentionded Napier-Munn article on the web and will study it with interest.
Wilfried

#62 WRAK

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Posted 16 December 2012 - 03:09 PM

I found the article of Napier-Munn "Model to Predict the Resolution of Double Stars" very interesting and I like the approach of statistical analysis of single observations. I modified the described algorithm of Napier-Munn giving the probability of splitting a specific double with a given aperture to providing the required aperture for reaching a 50% splitting probability for easier comparison with my other calculations - this did not give convincing results with my small data set (average error too huge to be mentioned here) and the behavior of the algorithm ist not gracious as for some parameter values it provides no solution for a 50% probability.
But the approach of statistical analysis of individual more or less "limit" observations encouraged me to resume my own efforts in this direction - I meanwhile got down to an average error in required aperture of 13mm (partly by eliminating 3 Lewis observations with statistically obvious deviation) and I am optimistic to get eventually to a single digit average error. My main problem remains the tiny data set available to me but I hope to solve this issue during the next year with a lot of limit observations with my iris diaphragm.
Wilfried

#63 astroneil

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Posted 17 December 2012 - 11:12 AM

Nae buttin' in like; but here's an 'infamous' quote fae Michael E. Bakich,(second in command at 'Astronomy' magazine.

"The Dawes limit is certainly only a guideline...Using this formula, my 4-inch f/15 Unitron should, at best, split a double star with a separation of 1.14 arcseconds. In May of 2,000, on a night where the seeing could only be described as "legendary," I was able to obtain a clean separation between a pair of double stars only 0.9 arcseconds apart. This observation was from my backyard in El Paso with six other people, three of whom were seasoned observers."

Source: The Cambridge Encylopedia of Amateur Astronomy, 2003. CUP, pp240.

Stick that in yer pipe and smoke it.

Eye. :)

#64 WRAK

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Posted 17 December 2012 - 02:17 PM

...Stick that in yer pipe and smoke it...

Thanks for your input - there are always amazing observation reports.
Some remarks:
1. "The Dawes limit is certainly only a guideline" ... this is certainly correct as the Dawes limit is an empirical value to be considered as 50% probability for a split in the form of an 8. The only fault here is the missing indication of a standard deviation range in the sense of a Gauss distribution
2. To obtain a clear split of a 0.9" double with a 4 inch refractor is according to the confirmed theory of diffraction pattern rather impossible as the spurious disks should overlap - may be it would be wise to recheck the advertised data on this double
3. I am disappointed that this observation was not done with a 60mm/f15 refractor
4. The above mentioned meaning of the Dawes limit as 50% chance for a split is valid for all so called limits for resolution - so a limit is no limit but a value with a 50% probability for a split according to the defined properties (for example a clean separation for Rayleigh) and can be taken seriously only with a given average error or standard deviation.
Wilfried

#65 fred1871

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Posted 17 December 2012 - 09:17 PM

Neil, interesting input, though I'm hesitant to credit it at face value - so my thoughts were pretty much in the direction Wilfried has offered. :grin:

Perhaps I'd have been more inclined to believe the claim if it were, as Wilfried suggests, a 60mm f/15 refractor :lol:
I hear those things are made by the Harry Potter telescope company, and even muggles can get the use of them - and they outperform anything else you can buy ..... :question:

More seriously, diffraction theory doesn't allow for what's claimed. And "theory" as you know is a strong word in science, though a dismissive term in common usage.

I'd certainly agree about getting elongation, perhaps notched, with a 4-inch f/15 refractor at 0.9". Of course, we'd need to know that the double in question was at 0.9" at the time of the observation - in case that was an old measure, and the pair had widened by the time of the observation.

Ne'ertheless, welcome to the discussion. I'm hoping a few more folk, from wherever, might be "buttin in".

So, feel free to offer more miraculous splits. I get the occasional one myself, and with no help from smoking anything nor from "a wee dram" as the Scots would have it. Though I find these miraculous observations more often happen with uneven pairs, where the rules are still uncertain. The even pairs are very law-abiding.

And I'm still hunting for the fabled SW Burnham 0.2" double seen with a 6-inch telescope. I'm working my way through his General Catalogue of Doubles (the 1900 version - only his own discoveries). So far, no definite find, though plenty of tough examples. Does anyone know which double it was that keeps being mentioned - without identification? as the 0.2" pair found with the 6-inch....

I have found several cases where Burnham writes along the lines of "thought it was likely double with the 6-inch, but it was single with 18.5-inch and/or 36-inch" - and the star in question is not listed as a double these days in the WDS. Which suggests it was a false impression - indeed, Burnham remarks on this view himself, saying it was the likely explanation in several cases where follow-up observations found no sign of a second star. Working at the limits is tricky.

#66 astroneil

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Posted 18 December 2012 - 03:32 AM

Neil, interesting input, though I'm hesitant to credit it at face value - so my thoughts were pretty much in the direction Wilfried has offered. :grin:

Perhaps I'd have been more inclined to believe the claim if it were, as Wilfried suggests, a 60mm f/15 refractor :lol:
I hear those things are made by the Harry Potter telescope company, and even muggles can get the use of them - and they outperform anything else you can buy ..... :question:

More seriously, diffraction theory doesn't allow for what's claimed. And "theory" as you know is a strong word in science, though a dismissive term in common usage.

I'd certainly agree about getting elongation, perhaps notched, with a 4-inch f/15 refractor at 0.9". Of course, we'd need to know that the double in question was at 0.9" at the time of the observation - in case that was an old measure, and the pair had widened by the time of the observation.

Ne'ertheless, welcome to the discussion. I'm hoping a few more folk, from wherever, might be "buttin in".

So, feel free to offer more miraculous splits. I get the occasional one myself, and with no help from smoking anything nor from "a wee dram" as the Scots would have it. Though I find these miraculous observations more often happen with uneven pairs, where the rules are still uncertain. The even pairs are very law-abiding.

And I'm still hunting for the fabled SW Burnham 0.2" double seen with a 6-inch telescope. I'm working my way through his General Catalogue of Doubles (the 1900 version - only his own discoveries). So far, no definite find, though plenty of tough examples. Does anyone know which double it was that keeps being mentioned - without identification? as the 0.2" pair found with the 6-inch....

I have found several cases where Burnham writes along the lines of "thought it was likely double with the 6-inch, but it was single with 18.5-inch and/or 36-inch" - and the star in question is not listed as a double these days in the WDS. Which suggests it was a false impression - indeed, Burnham remarks on this view himself, saying it was the likely explanation in several cases where follow-up observations found no sign of a second star. Working at the limits is tricky.


"And you shall not bear false witness against your neighbour." Exodus 20:16

Take the matter up with him and not me. He's got a physics background so I'm sure his reply will be interesting.

Merry Christmas to you and yours.
Nelly

#67 WRAK

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Posted 18 December 2012 - 02:53 PM

"If yer quote another one you have taken own responsibility" WRAK 18:12
Best wishes
Wilfried

#68 7331Peg

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Posted 19 December 2012 - 12:13 AM

Here's a little something to spice up the conversation -- using stars that are closely matched in magnitude:

Using a 3.8" Dolland refractor, which by the good Reverend's own forumula results in a Dawes limit of 1.20", that same Reverend Dawes measured the separation of Xi Librae(magnitudes are 5.2 and 4.9)in 1831 at 1.15" at a magnification of 295x.

He included this comment: "Occasionally divided. Fine night. Measures very good."

He measured it again in 1834 at 1.17".

For comparision, the senior Struve came up with these figures:

1825: 1.15"
1832: 1.22"


Using the same refractor to measure Zeta Cancri (magnitudes of 5.3 and 6.3), Dawes recorded a separation in 1831 of 1.09" at a magnification of 226x and included this comment: "Discs just separated when steady. Decidedly elongated with 140."

Again, for comparison, the elder Struve measured the separation at 1.05", also in 1831.

Data for Dawe's measurements comes from pages 82 (Zeta Cancri)and 87 (Xi Librae) of "Micrometrical Measurements of the Positions and Distances of 121 Double Stars, taken at Ormskirk, during the years 1830, 1831, 1832, and 1833", which was published in Volume 8 of the Royal Astronomical Society's journal, Philosophical Transactions, which can be found HERE, starting on page 61.

So it would appear that the good Reverend Dawes beat his own limit at least a couple of times.

Cheers,

John

:refractor:

#69 WRAK

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Posted 19 December 2012 - 03:13 AM

John, thanks for the comments and especially for the link - very interesting.
"So it would appear that the good Reverend Dawes beat his own limit at least a couple of times" - this has to be necessarily so because his "limit" is calculated as average value derived from many observations so about 50% of his own observations have to be below his "limit". To know the average error would be of high interest - this way we could calculate the probability of a resolution of for example 10% below Dawes limit.
Wilfried

#70 7331Peg

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Posted 19 December 2012 - 02:47 PM

At this late date, I'm afraid it would be a bit difficult to determine the average error -- but I certainly understand your point. That was part of the reason I included Struve's measurements -- they at least provide a reference point as well as a basis for comparison.


John :refractor:

#71 astroneil

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Posted 20 December 2012 - 06:51 AM

John,

In an age where men are sending space probes to Mars and uncovering the deepest secrets of the Universe, amateur astronomers on the cutting edge of double star research are looking to Dawes for answers.

Isn't it ironic that it's not the Apo or Newtonian, Maksutov or SCT that is setting the standards, but a humble, early 19th century spy glass, built with a token nod to optical theory.

Regards,

Neil. ;)

#72 WRAK

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Posted 20 December 2012 - 05:59 PM

I don't think anybody is looking for answers from Dawes - diffraction theory is the base of the discussion here and the Dawes limit is a potential starting point for any usable Rule of Thumb for splitting of double stars with unequal brightness and doubles with a primary fainter as +6mag.
Some errors are certainly not avoidable here as the Dawes limit is derived from observations with fixed aperture size and with advertised data for doubles less then perfectly exact corresponding to the available methods then - both factors together let expect an error range of 10% or more but even this is good enough for a starting point.
I think I am now at an interesting point of investigation with a multi step approach giving an average error of less than 10mm in required aperture but my data set is still far too small to take this seriously. Most interestingly statistical analysis of limit observations does not suggest any exponential effect of magnitude differences (especially not 2.512 as base as one would expect) but the effect of decreasing separation is exponential as one would expect.
I asked Napier-Munn for use of his raw data to counter check these results but so far without positive response.
Wilfried

#73 fred1871

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Posted 21 December 2012 - 12:06 AM

My reply is much the same as Wilfried's, first off - Dawes is a starting point but not a final answer. Dawes already had Airy's work on diffraction available by the time he came up with what we call the Dawes Limit, long after his early observations that John mentioned above. And I find it interesting Dawes does better than predicted using a smallish telescope - later he used larger scopes more typically around 6- to 8-inch aperture. And didn't do quite as well per aperture?

Wilfried, is the mentioned 10mm average error in aperture consistent over a range of apertures, or does it apply at some particular point? 10mm on 60mm is much bigger than 10mm on 150mm. Sorry to keep harping on this...

Re the data used by Tim Napier-Munn - no doubt some of the results in the raw data will be of use, but I find most interesting his graph for the 356mm aperture, which fits fairly well with my old suggestion of the RoT for significantly obstructed reflectors. The graph for 80mm and 203mm indicate under-performance for their sizes compared to the RoT and compared to my own experience.

That the magnitude differences don't follow a log scale (as per magnitude 2.512) is perhaps surprising but I'd come to a similar conclusion. Separation, however, I'd agree does appear to follow a model that's beyond linear - I'm wondering how much effect here is increased difficulty from seeing, as well as light spread, diffraction ring interference, and approaching the (diffraction) limits of the particular aperture.

Seeing in particular can make a huge difference. There are pairs I can't see one night in apparently steady conditions, and another night, looking similar on seeing, the pair is obvious. SW Burnham commented on the same experience. It does make finding the limits more difficult, because seeing appears to affect uneven pairs much more than even ones.

#74 WRAK

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Posted 21 December 2012 - 04:25 AM

Fred, the average error in relation to the calculated required aperture is 10,85%. You are right, seeing is all important but how you handle this depends on the intended use of the RoT model - I see it as tool for selecting doubles for sessions and then you have given the advertised data for the doubles, your scope and light pollution on your site. Seeing and possible other factors should therefore covered by the indicated average error.
The proposed model for small telescopes means refractors from 60mm to 150mm (work clearly still in progress) works as follows: Required aperture rA for a split is
1. If sep larger 10" then rA = derived from TLM modified by light pollution (this part is not yet implemented)
2. Else base is Dawes limit (116/sep) - this covers the beaten path of equal bright pairs up to +6mag
3. If delta-m >1 or m1 > 6 then rA = Dawes + f(delta-m) = 7.82302995069649*(m2-m1)/sep^0.814655479470003 else zero - this covers delta-m
4. If m1 > 6 then rA = Dawes + f(delta-m) + f(m1) = 8.28247140956849E-02*(m1+31.0737334876114)/sep^-0.999405092970208 else zero - this covers faintness of primary above +6mag
5. If m2 > 9 then rA = Dawes + f(delta-m) + f(m1) + f(m2) = 19.7728649102522*(m2-8.84688581507273) else zero - this covers increasing faintness of the secondary
6. If NELM < 6.5 then rA = Dawes + f(delta-m) +f(m1) + f(m2) + f(NELM) = 2.33967425240235*(6,5-NELM)^2/6,5 else zero - this covers light pollution.
The resulting rA is to be interpreted as 67% chance to split a spedific double within a 11% range of this value.
The unwieldy numbers are the result of a statistical analysis - different runs produce slightly different values with similar final result so there is no theoretical optical background for this numbers.

Some examples for NELM of 3 means rather heavy light pollution:
23 Aql 3,2" +5,3/8,3mag -> 68mm with error compared to obervation of 2mm
STT216 2,2" +7,38/10,28mag -> 133mm with error 13mm
STF2482 1,6" +9/10,2mag -> 123mm with error 17mm

Some examples for NELM of 6 means no light pollution (advertised data from Lord's paper mentioned earlier):
STT279 2,2" +7/9mag -> 77mm with error 2mm
STT140 2,8" +7/9,5mag -> 87mm with error 12mm
HO161 2,9" +7/11mag -> 155mm with error 5mm.

These examples were selected by chance and 4 of 6 values are within the expected range and therefore within the expected probability range.
Wilfried

#75 astroneil

astroneil

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Posted 21 December 2012 - 05:13 PM

More seriously, diffraction theory doesn't allow for what's claimed. And "theory" as you know is a strong word in science, though a dismissive term in common usage.


That's tosh as well.
There's a whole bunch of reasons why this project is downright silly. But here's one specific objection for ya.
Angular resolution (in radians) is approximated by Lamda/D. For the Dawes limit Lamda is set at 562nm. But an average human eye can detect radiations as low as 390nm. Doing the math (which I'll leave for you to do) shows that you can resolve stars down to a smidgen lower than 0.8".
Sticking a blue or violet filter on an eyepiece would easily allow a 0.9" split in a 4-incher and compounded still more if the stars are already bluish. :grin:

I believe Mike Bakich; it was something about the way he said it, unambiguously and plainly. And with several witnesses.

Far too suspicious you lot. :lol:






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