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Putting the "Rule of Thumb" to test

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#176 fred1871

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Posted 23 February 2013 - 08:23 AM

BU 100: Try as I might, I failed to split this double. I even cheated and looked up the Rho and Theta for the companion and still failed. I could, however, see a dim star about 6" arc south of BU 100. I have not looked up that star's magnitude just yet, but I am curious about it. I did spend a lot of time with this first double of the evening, because at mag 11 I really needed to be fully dark adapted to have a chance. Still, no success. At 3.2" sep, it sits very near my 4th diffraction ring (~3.6" arc.)

STT 145: Split. Companion easily seen near PA 340 just outside the first ring at 263x (UO 12mm HD Ortho, 1.6x Barlow.)

A2450: Split. Faint companion easily seen at ~3" arc sep near PA 120 to 130 (south east, anyway.) However, it's PA is listed at 053. I suspect this is incorrect, but I just don't know. If it's correct, then I failed to split it and simply observed another star near PA 130. But, my gut tells me the listing is incorrect. That pair just looked and felt like a double. Stellarium, ironically, shows the companion more south of PA 90, too.

STT 171. Split - maybe. ...


Wilfried and others, the above is quoted from Norme's observations reported 30 January 2013. As I've now caught up with a few of these I thought I'd provide my observing notes, done without benefit of checking what Norme wrote.

The folowing are with my 140mm refractor, seeing started at fairly good, becoming good-plus (7/10) for the more difficult ones. Unfortunately I didn't get to STT 171. These are in Gemini. Night of a 6 day moon recently. Nelm in the observed area was perhaps 4.5, despite moonlight.

For purposes of comparison, I started with STT 140, listed for a mere 117mm aperture - the mag 10.1 companion was seen at 160x, not very difficult; delta-m here is 3.2 mags. I compared it with A2450, same separation, delta-m 3.0, but fainter - mags 8.05 and 11.06. A2450 also showed as a double at 160x - however on the Gemini list it's got 140mm aperture indicated. It was nearly as easy as STT 140 - only the fainter magnitude of the companion made it less obvious.

BU 100 - mags 7.3 and 11.1 at 3.2" (listed for 144mm) was easier - the companion star showed at 100x. It was noticeably easier than A2450, and at 160x the companion was obvious.

STT 145 - mags 7.3 and 9.9 at 1.5" - listed for 147mm aperture. More difficult, but the companion was a just visible speck close to the primary at 160x, and more clear at 230x.

My feeling is that the model used for the Gemini doubles (since revised) was not entirely consistent in predictive capacity; and that exceeding it was not of high difficulty for at least some doubles.

I still have some other pairs, already observed, to provide notes for. And if the weather here ever stops being cloudy I can move on to Eridanus.

#177 WRAK

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Posted 24 February 2013 - 03:24 PM

... My feeling is that the model used for the Gemini doubles (since revised) was not entirely consistent in predictive capacity; and that exceeding it was not of high difficulty for at least some doubles...

Fred, you are probably right - it seems that at this stage I had too many underperforming observations in my data set (mostly from Lord's paper) resulting from the use of fixed apertures but meanwhile I have eliminated most of these. The Eridanus list should already do better.
Wilfried

#178 WRAK

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Posted 22 March 2013 - 06:13 AM

As I already posted in the thread "Star pattern for TML test with light pollution" I found a glitch in the last module of the RoT model checking the result against the for resolving of faint companions required telesocpe magnitude limit including the influences of light pollution for NEML below 3.5 as it seems that I have overestimated the influence of light pollution on TML.
I will certainly try to correct this but I have to sample more TML-observations depending on NEML.
As I have only a NEML range 2.5-3.5 available I would appreciate reports from other observers very much. As the advertised magnitudes for faint stars are often not very reliable I recommend the check with http://www.aavso.org...load-apass-data - when restricting the parameter "Radius" to 0.01 you will get most probably only one result and this should be the observed star.
Wilfried

#179 WRAK

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Posted 06 April 2013 - 05:50 AM

Foul weather for weeks made not only obervations impossible but stalled also other planned outdoor activities - so I had some time at hand to "play" with numbers.
Target was to gain some impressions how Lord's RoT works compared with the current version of my RoT model. As data set for this investigation I used the set of pairs of the Sissy Haas project and as additional tool I used the AstroPlanner implementation of Lord's algorithm giving not a number but a verbal rating from "UN" for unresolvable to "E" for easy for a given combination of avertised date for the double, telescope aperture, central obstruction size and seeing.

Assuming perfect seeing and zero central obstruction when using the algorithm of Lord's RoT results in a required separation for a split and when you use this result in AstroPlanner you always get a "D" for difficult - I interpret this as comparable with my model approach of a 50% probability for a split meaning a fair chance.
Applied to the Sissy Haas set of doubles and "translated" from separation into aperture you get a set of apertures required for a 50% split probability.

Comparing these results with the results when applying my current RoT model to the same set of doubles gives some interesting insights:
- Lord's RoT is rather conservative when the separation is small - with only few exceptions my RoT requires far smaller apertures with the exception of fainter doubles as the aspect of faintness is not part of Lord's model (a +4/6mag pair gets the rame rating as a +8/10mag one - this I consider a main weakness of Lord's RoT)
- For separations somewhat larger beginning with 3" Lord's RoT is consistenly below the values delivered by my RoT model: The main reason for this is probably the fact that as far as I know Lord had no observation reports available for scopes with apertures smaller than 75mm so his results for larger separations are projections from the other observations with larger apertures and such an approach is prone for desaster. As I have meanwhile with the help of an iris diaphragm a lot of limit observations below 75mm aperture I am quite confident in the numbers of my model
- The combination of somewhat larger separations with not this large difference in brightness of the double star components poses also a problem for the Sissy Haas project because nobody uses scopes with apertures smaller than 50mm so observation reports in this range without the use of aperture masks or iris diaphragm are of no value for the project
- Using the results of my RoT model for the aperture in the AstroPlanner implementation of Lord's RoT gives for separations below 3" separation most of the time "VD" for very difficult oder "ED" for extremely difficult - this may be the other side of the coin regarding available observations: Lord had a lot of observations with apertures above 140mm in his data set while I have only a very limited data set in this range available and especially no own observations. But here I have some plans (see below)
- Things get again very interesting when using the AstroPlanner implementation of Lord's RoT to determine the aperture required for an "XD" (exceedingly difficult) rating - Lord's RoT delivers here extremely optimistic values with in average about 42% smaller apertures as required for a "D" rating. This indicates an extreme wide variation is his data set of observations most probably due to the use of fixed apertures with only a few observations really at the limit and most above. This would also explain the rather pessimistic results for the average "D" rating of Lord's RoT
- In average Lord's "XD" rating corresponds very well with the double standard deviation of 14% for my RoT model meaning reducing the for a 50% chance split required aperture by 28% resulting in a probability of about 3% for a split means once in a while under the very best conditions.

Today I have received the delivery of an iris diaphragm with an inner diameter of 225mm for use with my C925 SCT which means I can then cover the range of 170-225mm (and 235mm without iris) with own limit observations. Below 170mm will not be very useful as then the CO would exceed 50%. But the small gap between 140 to 170mm should pose no serious problem for the validity of the statistical analysis. I can only hope for a good performance of the C925 I did not use so far for double star observing as I do not like the handling, feeling and image quality in terms of crisp spurious disks of this scope this much.
Hope for more clear skies for the rest of the year then.
Wilfried

#180 WRAK

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Posted 22 April 2013 - 04:47 PM

The hope for good performance of the C925 did so far not realize - the secondary mirror has somehow gained some freedom for rotation and shifting and therefore collimation is non existent and the star test showed severe distortions of the diffraction pattern. Has to be corrected.
Second mishap was a not this perfect iris diaphragm - changing the aperture required too much force to be useful on a telescope so I had to return it for exchange.
As I do not like the problems with dew on the schmidt plate of the C925 I ordered a Mewlon 210 to have another option - will arrive in a few weeks.
Wilfried

#181 fred1871

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Posted 22 April 2013 - 07:49 PM

Wilfried, the rotating secondary on some SCTs is a common issue. Mine did the same - fairly easily solved, as it's just the result of the secondary moving, and rotating in its housing. I re-centered the housing and screwed it tighter; then could re-collimate the secondary, being careful to hold the housing while turning the screws to avoid any slight new rotation.

Nice to be able to afford a Mewlon 210 as an additional telescope. :)

Dewing? - can be overcome,anyway. The diaphragm, when you get one that works properly, will I expect only be useful for testing limiting magnitudes. Unless your interest is in the effects of enhanced central obstruction, as the CO factor becomes bigger rather quickly as you close the diaphragm. As you've noted, ou can get from the normal 36% obstruction of the C9.25 to 50%, which is very destructive of visual image quality, by stopping down from 235mm to 170mm aperture. I doubt this will be helpful for exceedingly difficult or even very difficult uneven pairs. Indeed, even merely "difficult" uneven pairs may be promoted to "exceedingly difficult" (or impossible) from the enlarged CO.

With my own C9.25 I can get quite good spurious discs, and often get a near match on uneven pairs for what I see with my 140mm refractor. Certainly the refractor gives neater star images - smaller aperture is less seeing-affected, no CO means no detrimental interaction with seeing (as per Couder et Danjon), and no enhancement of diffraction rings - plus the refractor optics are of better quality. So 235mm with CO is similar to 140 without CO, though with a brightness advantage to 235 that does show with fainter secondary stars. The extra ~1.0 magnitude is useful.

It'll be interesting to see what results you get, with the two obstructed telescopes as well as with the diaphragm usage. Problem with the diaphragm on scopes with CO is that you then have two issues - aperture reduction means CO increase, where with the refractor it's simple aperture reduction.

#182 WRAK

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Posted 24 April 2013 - 01:53 AM

I have not yet directly compared the C925 with my 140mm refractor regarding resolving doubles but would expect closer splits and fainter companions with the C925. But may be this is not only a question of reflector with CO vs. reflector but also a question of reflector construction - at least some MAKs seem to do very well with for example Questar 7 comparable with a 6" refractor. Also the Dall-Kirkham design seems to be a candidate for good results - and may be the Schmidt-Cassegrains design is reasonable good for Deep Sky Objects but not this performing with double stars. I think I will let fix my C925 by a profesional and not try to challenge my own limited mechanical ability and then I will see.
Wilfried

#183 WRAK

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Posted 01 May 2013 - 03:10 PM

After a few good nights in the last weeks I could expand my data set by about 40 new limit observations between 50 and 140mm. I think this aperture range is now very good covered and with the existing RoT model also quite good defined - the correlation coefficient is still above 0.95. But it is time now to cover also somewhat larger apertures.
Got today the message that my C925 is fixed (secondary mirror secured within the Schmidt plate, Schmidt plate cleaned from the inside, collimation done) and got again (after an inital test after purchase) the very good optical quality of this scope confirmed.
The less than perfect 225mm inner diameter iris diaphragm is returned to the source and I got my money (minus double transport) back but no new iris so far. I hope now again for some clear skies to try the C925 with double stars and will substitute the missing iris with cardboard aperture masks if I have the impression that the C925 is doing a good double star job.
Wilfried

#184 WRAK

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Posted 01 July 2013 - 05:44 AM

Paul Rodman has released version 2.1 of his AstroPlanner with an implementation of my current algorithm as one of the new functions. AstroPlanner now offers two additional collumns for double stars:
- One for "Splittable with the selected telescope and location" with content "Yes" for pA (calculated proposed Aperture for a 50% chance for resolving) less or equal the aperture of the selected telescope, "???" for pA larger than telescope aperture but within the standard deviation and "No" for pA above. This is a slightly conservative approach, as a "No" can still mean a small chance for a split if pA is within the 2x standard deviation range
- Second for "Splittable with mm" giving the calculated pA for this double.

The pA algorithm can also be used in the "Select from Catalogue" function with "Splittable with the selected telescope and the selected location" as one of several criterias like mag1, mag2, separation, delta-m, ...

This latter implementation shows drastically how important the topic of TML is in this context as a huge part of the doubles included in the WDS catalogue is very faint and at the same time very wide - so the usual paramters like separation and delta-m are completely to neglect for resolving the companion but only the telescope magnitude limit counts. This works currently good enough for locations with NEML +3.5mag or better but for NEML values significantly worse I have made the error of overestimating the influence of light pollution as already mentioned several times.

Next steps will be the elimination of this TML plunder and the increase of the number of limit observations for apertures > 150mm to get a better statistical significance for this aperture range.

My C925 seems to be in good shape now and the iris diaphragm is already operable.

Wilfried
PS: The selection of the location is necessary for the parameter "average brightness of the sky" resp. NEML
PPS: My relation with AstroPlanner is strictly only as private user contributing some input for additional functions for double star observers like myself

#185 Nucleophile

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Posted 01 July 2013 - 06:20 AM

That is outstanding, Wilfried! The calculator works really well with my 8 inch--I think it is a very useful tool for those of us who like to observe near the edge.

#186 WRAK

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Posted 08 July 2013 - 07:39 AM

The limit observation results of my recent experiments with an iris diaphragm on the C925 and the resulting very high CO values made me aware that the effects of reduced clear aperture and reduced light energy in the Airy disk need to be taken into account at least for CO >0.3.
One example is the observation of Eps Boo/Izar with a limit aperture of 40mm with zero CO and 120mm with CO 0.75.
The latter corresponds with a clear aperture of ~80mm and taking the reduced light enery in the smaller Airy disk into account gives an equivalent clear aperture of ~40mm.
The calculated pA of the RoT model with 0.75 CO and NEML 3.5 gives 56mm and this is clearly nonsense compared with the effective needed 120mm.
Currently the algorithm calculates only the effects of the reduced size of the Airy disk especially for the separation of more or less equal bright doubles and the negative effects of the changed diffraction pattern for rather unequal doubles.

I will correct this in the next version.
Please notice that this weakness does not show noticeable impact for scopes with CO <0.3 (Newtons and Maks) while values for scopes with CO >0.3 (especially SCTs) might be a bit on the optimistic side but still within the standard deviaton range.
So as practically nobody is using scopes with CO >0.4 for double star observing the results of the pA calculator should still be of good use.
Wilfried

#187 Nucleophile

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Posted 08 July 2013 - 10:55 AM

I like that you keep refining your formula with newer observations.
Keep up the good work! :grin:

#188 WRAK

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Posted 11 July 2013 - 10:12 AM

My recent experiments with cental obstructions larger than 0.4 show a drastic effect regarding resolving unequal doubles - the energy transfer from the Airy disk to the diffraction rings of the primary rises progressive and at the same time the energy loss in the Airy Disk of the secondary does the same. So the secondary gets quickly lost in the otherwise optical impressive diffraction pattern of the primary. A first look at the numbers suggest that the resolving power of scopes with CO correspond to that of scopes without CO calculated according corresponding to the reduced surface for wide doubles where the resolving power corresponds with the telescope magnitude limit and for close doubles with less than ~10" separation also reduced energy in the Airy disk relative to the by CO reduced size of the Airy disk.
Examples:
- Already mentioned Izar with an equivalent of 40mm refractor to 120mm reflector with CO 0.75
- STF2011 2" +7.93/10.23mag with an equivalent of 90mm refractor to 160mm reflector with CO 0.56
- STF2029 6.2" +7.95/9.62mag with an equivalent of 65mm refractor to 130mm reflector with CO 0.69.

But this approach seems only valid for really large CO's as the same calculation would give for a 235mm SCT with CO 0,38 an equivalent of a 213mm refractor but this is certainly far too optimistic. For CO less 0.4 seems the equivalent diameter calculated only with the energy loss without relation to the size of the airy disk more appropriate. This would give for the C925 an equivalent of 185mm - for my feeling still a tad too optimistic.
What I still think is that reflectors with CO significantly smaller than 0.3 (Newtons and Maks) have an advantage for resolving equal bright doubles and not this much troubles with moderate delta-m's.
Further investigation needed.
Wilfried
PS: Spreadsheet with simple algorithm for calculating equivalent apertures for download available (based on numerical approximation for size of Airy disk and energy loss depending on size of CO)

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#189 Nucleophile

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Posted 12 July 2013 - 07:22 PM

PS: Spreadsheet with simple algorithm for calculating equivalent apertures for download available (based on numerical approximation for size of Airy disk and energy loss depending on size of CO)


Thanks, Wilfried.

I am putting the finishing touches on a calculator I have developed for my 15"---will post the results to this forum as soon as I refine a few parameters.

#190 WRAK

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Posted 16 July 2013 - 03:55 AM

My current RoT model includes a final step checking the magnitude of the secondary against the (with the most simple approach 2.7+5*LOG10(D_mm) calculated) TML of a scope with the proposed aperture pA of the calculator including the effects of light pollution (calculation somewhat more complicated).

I thought this a clever approach to avoid crass errors with unrealistic pAs especially for wide doubles with very faint companions.
As I made some plunder here with overestimating the effect of light pollution on TML I looked for ways to do a better job but progress was slow. For example a small project for getting TML observations with different amounts of light pollution got stuck due to the lack of for this purpose usable open clusters currently in my field of view - but I am still interested in this question and will continue to investigate this topic.

My research for other approaches in this field resulted in the insight that the topic TML itself is more complex than I anticipated - even very sophisticated models like this calculator http://www.cruxis.co...ngmagnitude.htm based on the work of Bradley Schaefer http://adsabs.harvar...PASP..102..212S deliver results with errors too large for my requirements thus creating huge erratic pA values I wanted to avoid from the very beginning.

So I decided to change my approach - I will simply add fictive bogus double in to my data set of limit observations with large separations above 10" and faint companions with magnitudes at the observed TML values of different aperture sizes and let do the program for statistical analysis do the final work while I concentrate on the structure of the RoT model.
Maybe there will be then with specific parameters occasionally an unrealistic small pA with a TML below the magnitude of the secondary but I will try to make the probability for such a result very low.

After some more research and consideration I came to the conclusion that the concept of checking the for light pollution corrected telescope magnitude limit of the proposed aperture against the magnitude of the secondary especially for wide doubles is not this bad as I thought lately.
My error was to consider the concept of TML as an analytical one giving a "true" value for resolving faintest stars possible with a given aperture - and this is certainly not the case even if you try hard as for example Schaefer did as in the end besides the influence of all other factors the collecting of photons in a given situation remains a random process.
If we therefore consider TML as statistical concept we can relax a bit and stick with the concept of probability used already in the base RoT model. So I need a TML formula as simple and reliable as possible comparable for example with the Dawes criterion for resolving close equal binaries (is the currently used TML=2.7+5*LOG10[D_mm] good enough?) and a similar reliable algorithm for considering the effects of light pollution and central obstruction.

This means I will stick with the existing structure of the RoT model but consider the TML concept no longer as analytical but statistical one.
Wilfried

#191 WRAK

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Posted 22 July 2013 - 09:49 AM

This topic begins to develop momentum as working with rather faint doubles made me aware that the current version of the RoT model is based on limit observations mostly up to +12mag for the companion and therefore not a really challenge in terms of RoT.
Thus the current algorithm results in an error for doubles with primaries fainter than +14mag as in my struggle to adapt best to the existing observations with not so obvious influences of the value for M1 I came to a rather not so clever formula including a limit for M1<14mag. This limit was not mentioned so far as I simply forgot about it.
Now that I was reminded of it I made a small change that at least no error results but the limit as such remains - I would now even go so far that values of M1>12.5 are not handled this well but I simply do not have enough observations in this range to check this possibility against reality. I could try to change this limitation of the current model but I am not sure if there is any interest for a RoT for doubles fainter than this.
Then there is generelly the topic of wide doubles - if wide enough all other parameters should be of no influence but the magnitude of the companion in relation to TML. The question remains how gracious this change of the rules can be implemented with increasing separation. This topic requires certainly more investigation.

I have now implemented the above mentioned new algorithm for calculating the influence of light pollution in terms of NEML (including in this implementation the extinction due to the altitude of the object) and have uploaded the updated version of the RoT model filled with wide and faint doubles in Oph between 15 and 50 arcsecs separation and up to +15mag for the companion and would be happy to get any responses how this works compared with reality as I have the feeling that I have maybe now under the influence of Schaefers work a tad unterestimated the effects of light pollution.
The model works still in the mode that the larger proposed aperture "wins" - either depending on separation, delta-m, M1, M2, CO and NEML or TML driven.
Wilfried

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#192 WRAK

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Posted 22 August 2013 - 03:03 AM

The current algorithm works with the parameters separation in arcseconds, difference of magnitudes delta_m, magnitude of primary m1 and secondary m2, size of central obstruction CO in terms of % of aperture diameter, light pollution in terms of Naked Eye Magnitude Limit NEML (in the field of view as opposed to the usual definition in zenith) and Telescope Magnitude Limit TML (again in the field of view and not zenith).
Result of the algorithm is the proposed aperture in mm for resolving a double with the given parameters with a standard deviation of 14%. This standard deviation covers all kind of errors in the advertised data as well as in the observation notes and all other influencing parameters not included in the algorithm with the exception of seeing: reasonable fair seeing is assumed as essential for resolving of even not this difficult binaries with resolving meaning getting an image with clear indication of position and separation of the secondary without any doubt.
While it is not feasable to show the interaction between all of these parameters in simple graphs it is possible to show the influence of a single parameter with fixed values for the other parameters to gain some impression how the algorithm works.
I will try this in my next posts.
Wilfried

#193 WRAK

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Posted 22 August 2013 - 03:45 PM

The first component of the RoT model deals with separation - this is the trodden path of Dawes criterion modified with CO size according to diffraction theory, but the effects of the factor CO will be discussed separately.
The basic relation between separation and aperture is an exponential increase of aperture with decreasing separation.
The graph shows this relation with m1=4, m2=6, CO=0 and NEML=5.5. The "x" in the graph means actual observations with comparable parameter values.
It is certainly possible to "beat" Dawes but the standard deviation of 14% (result of statistical analysis of my data set of limit observations) means that a resolution with an aperture more than 28% smaller than the calculated proposed aperture has a probability of less than 5% and requires therefore rather very favorable conditions and especially excellent seeing.

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#194 WRAK

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Posted 23 August 2013 - 03:08 PM

The second component of the RoT model deals with the magnitude difference between primary and secondary - this is the starting point for our discussion regarding resolving unequal doubles.
The basic relation between delta_m and aperture is a moderate exponential increase of aperture with increasing delta_m. For higher values of delta_m an influence of CO is assumed, but the factor CO will be discussed separately later.
The graph shows this relation with sep=3.3, m1=5, m2=6-13.5, CO=0 and NEML=5.5. The "x" in the graph means actual observations with comparable parameter values.
This also shows one of the current weaknesses of my data set: too few limit observations with apertures larger than 140mm. My C925 is more or less of no use for this task as the reduction of the aperture leads to unreasonable high CO values so I depend on reports of other observers.

Forgot to mention: Delta_M of less than 1 is considered equal bright.

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#195 Asbytec

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Posted 23 August 2013 - 07:51 PM

Excellent work, Wilfried. I cannot wait to try your RoT in the coming months.

#196 WRAK

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Posted 24 August 2013 - 12:29 PM

The third component of the RoT model deals with the magnitude of the primary.
The basic relation between m1 and aperture is a moderate more or less linear increase of aperture with increasing magnitude but only if separation requires this.
For wide pairs the increase of m1 is no issue - only the telescope magnitude limit could be a topic in this regard but this is anyway handled with the magnitude of the secondary, so there is no need to deal with TML here.
The graph shows this relation with sep=2, m1=4-12.5, delta_m=2.5, CO=0 and NEML=5.5. The "x" in the graph means actual observations with comparable parameter values.
The impact of the TML check for M2 would be effective for M1=12 and 12.5 as with the delta_m of 2.5 we reach already larger values than the TML for the resulting pA - but the graph does not show this effect as the TML check will be discussed separately.
Note: M1 less than 6 is considered to be no issue and +12.5mag is considered to be the upper limit for useful results

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#197 WRAK

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Posted 25 August 2013 - 02:57 PM

The fourth component of the RoT model deals with the magnitude of the secondary.
The basic relation between m2 and aperture is a moderate more or less linear increase of aperture with increasing magnitude - this time interestingly without relation to separation. Don't remenber the details but it seems that for this component there was no statistical relevance of separation.
The telescope magnitude limit is certainly a topic for increasing values of M2 and this will be handled in the next step.
The graph shows this relation with sep=5, delta_m=2, CO=0 and NEML=5.5. The "x" in the graph means actual observations with comparable parameter values.
Note: M2 larger 9 is considered to be the critical value with which M2 is beginning to influence the proposed aperture

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#198 WRAK

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Posted 26 August 2013 - 07:43 AM

As the TML check is so far the last step next comes the influence of light pollution.
The fifth component of the RoT model deals with this factor in terms of naked eye magnitude limit NEML (in the field of view in contrary to the usual approach relating to zenith means also including extinction).
In the very beginning of this RoT discussion I thought light pollution a serious impact for resolving doubles - meanwhile I see this rather relaxed. The influence of LP on resolving doubles seems rather moderate.
The basic relation between NEML and aperture is therefore a very moderate more or less linear increase of aperture with decreasing values of NEML.
The graph shows this relation with sep=2, m1=7, m2=10, CO=0 and NEML=2-6.5. I don't have many actual observations with comparable parameter values in my data set but it is clear that the difference between a very dark and a heavily light polluted sky is only about a few mm in aperture, may be up to one aperture class.
Note: It is assumed that +6.5mag is the best possible value for NEML (being aware that this is depending on personal acuity) and Light Pollution is considered to be of impact only for doubles with secondaries fainter than +9mag

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#199 WRAK

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Posted 27 August 2013 - 04:51 AM

Next comes the sixth factor: telescope magnitude limit TML - for close pairs this is not really an issue as the other parameters do their job but for wide pairs TML becomes the limit for resolving.
The influence of TML was for some time rather difficult for me as I assumed this to be a given technical parameter mentioned in the specs for scopes - so it took me some time to realise that TML is also a statistical concept with high impact not only of seeing but also of personal acuity and a lot of other factors.
There is a list of TML observations in the paper of Schaefer on the topic of creating a TML model - the variation is enorm and can not be explained fully despite the relatively high number of parameters in the model.
Next issue is the from Schaefer not even considered rather inadequate precision regarding reported magnitudes for fainter stars - so it does not make much sense to try own TML limit observations for this porpose (but I will stay on this topic as I consider it still interesting).
In the end I adopted the often used simple and probably somewhat inprecise formula TML=2.7+5*LOG10(D_mm) as average value with a standard deviation hopefully similar to the 14% of my RoT algorithm.
To consider the most obvious side effects I included of the influence of light pollution (here comes NEML again) with values according to the model of Schaefer and a modification for CO reduced apterture.
The TML check is applied after the use of the RoT algorithm with the so far discussed parameters and if M2 is fainter than the calculated TML for the size of the proposed aperture then the pA is increased to match this value.
The results seem so far realistic if sometimes a bit optimistic.
The graph shows the few examples in my data set of limit observations of TML checks with a positive result - all with separation larger than 10" and rather high values for M2 else rather different parameters.The "x" marks again the aperture according to the observation reports

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#200 Asbytec

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Posted 27 August 2013 - 06:59 AM

Wilfried, I applaud your work and wish you continued success toward a very difficult goal.

Norme






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