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# Putting the "Rule of Thumb" to test

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### #1 WRAK

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Posted 03 September 2012 - 02:49 PM

While the Dawes and Rayleigh limits are quite useful but limited to doubles in the range of +6mag and about 1 delta-m the Lord Rating is more versatile considering parameters like delta-m and seeing but the same time more wishy-washy with indications like "extremely difficult" etc. (reminds me to Clive Coates with his Burgundy reviews - very well indeed). The fuzzy Difficulty Index is a seemingly exact number but without any referencing parameters ignoring even aperture - and is to my feeling of no real value.
What I like is the from Bruce and Fred in another thread on this forum suggested rule of thumb for the required aperture for splitting a double: Required aperture in mm = 116/(sep/delta-m) with delta-m set to 1 if less than 1 - seems quite useful to me and some testing should prove the validity of this formula.
I started with Eps Lyr as entry point near the Dawes limit:
116/(2.2/1)=~50mm. Starting with 140mm this was an easy one with x140. Reducing the aperture with a mask down to 100/90/80/70/60mm did not change very much besides a better saturation of colours. At 50mm there was no longer a clear split but still a clear elongation indicating the position of the companion. Test result positive I would say.
Now comes the interesting part - how will the RoT (rule of thumb) perform with magnitude values and deltas beyond the Dawes limit range? The next clear sky should allow the next step with a larger delta-m. Participation in this test topic is welcome.
Wilfried

### #2 WRAK

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Posted 08 September 2012 - 12:04 PM

Next object: 23 Aql 3.2"DS +5.3/8.3mag giving a delta-m of 3.
116/3.2*3=108,75~110mm aperture according to rule of thumb.
Splitting with a 140mm refractor at x140 was easy, the image was stable and the faint companion was in the correct position. Using aperture masks I reduced to 130/120/110/100/90mm without any significant changes but the companion got fainter each step and was therefore increasingly harder to see. With 80mm things got worse and the companion needed moments of stable seeing for resolution but I still was positive so see it. With 70mm I had only short moments of recognizing the companion as faint fuzzy little spot but that could be interpreted as bad seeing without the knowledge of having it seen before. With 60mm I could not see the companion any more even with long waiting for moments of good seeing. Conclusion: Resolution of 23 Aql with 80mm refractor is possible and this is much better than the 110mm according to the mentioned rule of thumb. But Fred had already explained that this rule is for reflectors with obstruction and his calculation for refractors is 2/3 of this value - this gives a required aperture between 70 and 80mm.
Tests of the rule of thumb will be continued when further candidates of dobules with larger delta-m values pop up in the next observing sessions.
Wilfried

### #3 drollere

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Posted 08 September 2012 - 12:36 PM

point of experimental procedure, wilfried ... start with the smallest aperture and work up. detecting an object when you already know its location is a different task from detecting an object when you don't know where to look.

the interesting issue is that "rules" similar to the ones that fred or i use (or as calculated with chris lord's nomograph) are really a type of personal guidance, not a fixed statement about optics. (at least, that's how i think of them, along with rules about limiting magnitude, system resolution, etc., etc.) the point isn't that the rule i use is correct or incorrect in your experience, but that you discover a rule that is optimal for you.

rules are easily misapplied or misinterpreted. robert aitken compiled a double star catalog, and as part of that process wanted to incorporate the double stars listed in the catalog compiled by sherburne burnham. "too many stars!" aitken declared. so he developed an editorial rule -- a rule to edit a manuscript -- that stars with a separation and primary magnitude (m) of rho > 10^(2.8-0.2m) "could to advantage be omitted". yet many people assume (incorrectly) that aitken was claiming that stars above that limit could not be (or are not) actual double stars. in other words, they mistook an editorial procedure for an astrophysical hypothesis.

we live in human cultures in which rules are assumed to apply to everyone and prescriptions from authority should be followed. and i grudgingly concede that helps to reduce traffic accidents and contractual disputes. but astronomy is really a personal enterprise, a solitary endeavor when most of our peers are asleep, and the key is to find the rule (assuming that a rule would be useful) that works for you.

i've enjoyed your reports. keep at it!

### #4 WRAK

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Posted 09 September 2012 - 03:03 PM

Good idea to start with the smaller apertures - this way I have better threshold control.
My interst in this rule of thumb is strong because it could be a very good tool for selecting doubles from the WDS catalogue appropriate for a specific scope. The results from the Sissy Haas project will be of high interest for me in this regard.
But as JNW mentioned in another thread magnitude of the primary also plays a role as the Dawes limit may work perfect around +6mag but less so for brighter or fainter stars. So I am looking not for some optical theory but only for a formular useful for session planning.
Wilfried

### #5 Bonco

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Posted 09 September 2012 - 03:58 PM

I'm considering cutting out cardboard optical masks of different apertures to be placed at the front of the dew shield on my 80mm f/15 refractor. Is there any optical problem having the mask several inches in front of the objective? Or, should it be adjacent to the objective? My guess is that it doesn't matter. I ask because its much easier to install/remove the mask at the end of the dew shield.
Thanks Bill

### #6 azure1961p

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Posted 09 September 2012 - 04:36 PM

Doesnt matter.

Pete

### #7 Sasa

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Posted 10 September 2012 - 03:17 AM

Hello Wilfried,

I can confirm your observation of 23 Aql. I was looking at it at the end of August with 80mm refractor (AS80/1200). With strong concentration, I could glimpse at 200x the secondary at PA~20deg and hold it steady for a few seconds. It was a little bit further from the primary than the 1st diffraction ring.
Last year, I accidentally run on this double with my 100mm refractor (ED100). Without knowing what to expect, I noticed with some effort the faint secondary.

Alexander

### #8 WRAK

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Posted 10 September 2012 - 04:17 AM

Wow - two owner of a 80mm f15 refractor, I would like to have such a scope.
To Bill: I had the same question and to minimize any side effects I retract the dew shield when using the aperture masks but as Pete mentioned I think also that the visual effect is neglectable.
Wilfried

### #9 Ed Whitney

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Posted 11 September 2012 - 01:28 PM

I concur with Alexander.

I split 23 Aql first with the C8-EdgeHD to "see" the secondary. Primary is golden color, sec is very pale blue. I also split it with the SW102AR at 200x with a 5mm TMB Planetary II ep. Then, I used an 80mm mask (made of birch plywood) and clearly saw the split with dark sky between. The skies here were Mag ~5.0 with slight haze, but generally a very clear night.

At first I tried using the SW102 to make the split, but think my eyes were still dark adapting, so got out the C8. I was amazed at how dim the secondary was and knew this was the problem with not seeing the split with the 4in. I then went back to the SW102 and saw the secondary, but not easily. I then got daring and again saw the split with the 80mm mask in place. Without the mask, it was 50x per inch of aperture, with mask 63.5x per inch.

Thing is, I probably never would have seen the secondary if I didn't see it first with the C8, which showed me exactly what to look for.

It was a fun night!

### #10 WRAK

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Posted 12 October 2012 - 03:22 AM

Next Delta Cyg (2.7" STF2579 +2.9/6.3mag) with delta-m of 3.4 giving 116/2.7*3.4 =146mm for reflector and 146*2/3 = 97mm for refractor.
Starting with 140mm I could easily split Delta Cyg with a magnification of x140 and a bit better with x208.
I reduced then my aperture using my new 145 to 8mm iris until I could no longer resolve the secondary - this happened a little bit below 100mm but with 97mm I could still call it a split.
Looks quite good for the rule of thumb.
Wilfried

### #11 WRAK

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Posted 14 October 2012 - 08:08 AM

With so far only 3 samples the RoT 116/sep*delta-m (with delta-m set to 1 of less than 1) for reflectors and 2/3 of this value for refractors can not be considered as confirmed but until now it can at least not be considered as falsified. So a lot more samples are required.
Interesting point: Paul Rodman will have this rule implemented in the next release of his AustroPlanner program as criteria for selecting doubles for observation sessions.

From a personal point of view I think this rule is quite useful and easy to apply but needs an enhancement concerning the brightness of the components of the double star, especially of the companion. While I can put a stop at the minimum brightness of the sedondary when selecting doubles (considering light pollution I usually set this parameter to +10.5mag near my resolution limit) this is not flexible enough because this way
- I miss doubles with a slightly fainter secondary but still splittable due to a larger separation which allows me to see companions at the limit of my scope
- I get doubles I cannot split because faint companions with small separations are beyond the resolution power of my scope depending on values I can now only assume.

So the next step in testing the RoT will be a set of doubles with given separation and delta-m with incereasing magnitudes to find a hopefully simple relation between magnitude (of the secondary?) and the required aperture for example like magnitude of the secondary divided by 6 (base value for the Dawes limit) as multiplying factor.
But I fear it will not be such simple. To be investigated further.
Wilfried

### #12 drollere

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Posted 14 October 2012 - 02:19 PM

Thing is, I probably never would have seen the secondary if I didn't see it first with the C8, which showed me exactly what to look for.

i'll reiterate that ed points to a significant issue. unless you start with a very small stop aperture and work to larger apertures, you will underestimate the necessary separation required.

### #13 WRAK

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Posted 14 October 2012 - 03:53 PM

Bruce, thank you for the reminder - I think you are completely right. But I am looking for border values representing a small challenge even under favorable conditions and therefore I do not follow the procedure you propose because my observing skills are certainly limited and the conditions of my location are certainly not very favorable. So with going down in aperture I simulate better conditions and skills.
Wilfried

### #14 fred1871

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Posted 14 October 2012 - 08:49 PM

I can only agree with you Wilfried, that we need more data points - though I came to my version of the rule of thumb based on quite a lot of data points, using mostly refractors and SCTs and an occasional Newtonian, some years ago.

Sissy Haas's project is an attempt to devise something more rigorous (if pragmatic rather than based on optical theory) of the same kind.

I'm pleased to see that the AstroPLanner program will use our current rule of thumb - it still seems to me useful in practice, though needing qualification - I don't think it will apply to very big telescopes, and it might be surpassed by small ones. Obviously, too, observer experience/skills make a difference.

When I get time I'm going to dig out, from my long-term observing notes, all of the unequal pairs that can be used for evaluating the RoT from observations I've already done with particular telescopes. Then a follow-up on pairs that fit for my current equipment.

And there's an obvious further limit in terms of sky brightness where one observes - light pollution, sometimes moonlight as well. A delta-m of 4.0 might be possible with stars of mag 6 and 10 at a particular separation, but not at mags 8 and 12 at the same separation. What's the sky limit tonight with telescope X? - and it'll be less good if the star is close to a brighter one.

I haven't begun stopping down my refractor yet to see at what point secondary stars become invisible; but I do know it's easier as Bruce said earlier to detect an object "when you already know its location" - however, like Wilfried, I think I'll mostly stop down, rather than start with less aperture. It does introduce a modest degree of bias, but I tend to be pessimistic about what I think I've seen (was it a seeing artefact? versus an "it should be visible so that possible speck with averted vision should be it"?).

Working at the threshhold is always a bit uncertain. And air steadiness makes such a difference, night by night - I have notes on pairs re-observed, with the same telescope, only days or weeks apart - a secondary star invisible one night was easy on another. The difference is astonishing.

This explains Chris Lord's attempt to factor in 'seeing' in his algorithm; though I don't personally find 'seeing' easily quantifiable, even using the Pickering scale or similar.

I'm currently inclined to think the RoT is close to being as good as we'll get, and useful if applied for typical mid-size amateur telescopes, for experienced observers, and on nights of steady air (I don't find one can always "punch through" the seeing with very high magnification, as Bruce suggests - sometimes yes, sometimes no).

More observing to do.
I had a clear sky last night, so the go-to system went into a sulk, preventing a productive night. Tonight (if fine) I'll be back observing.

### #15 azure1961p

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Posted 14 October 2012 - 09:55 PM

point of experimental procedure, wilfried ... start with the smallest aperture and work up. detecting an object when you already know its location is a different task from detecting an object when you don't know where to look.

Nice call Bruce. Wilfreid I liek your work here.

Pete

### #16 WRAK

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Posted 15 October 2012 - 02:42 AM

... And there's an obvious further limit in terms of sky brightness where one observes - light pollution, sometimes moonlight as well ...

I am doing most of my observing from a light polluted location and I have the impression that while I "loose" about 2 magnitudes from my telescope limit this does not have serious impacts for splitting doubles up to this reduced limit - may be for very faint and very close companions. In my observations concerning the RoT I do not consider light pollution as serious influence - as stated elsewhere I even have the experience that the seeing her is most of the times better than in darker places with a stronger drop in temperature in the evening.

... A delta-m of 4.0 might be possible with stars of mag 6 and 10 at a particular separation, but not at mags 8 and 12 at the same separation ...

I am working now on a list of doubles with same separation and delta-m with increasing magnitudes to check the influence of different magnitudes to the RoT.
Wilfried

### #17 drollere

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Posted 16 October 2012 - 01:33 AM

wilfried, maybe you mentioned this already, but how are you choosing your magnification? you mention 140x frequently and 208x once.

one concern is the use of magnification to get the optimal contrast or glare suppression for faint close companions. it's typical to try different magnifications on a tough split.

i agree that light pollution isn't disqualifying. a good RoT would take sky brightness into account in terms of the contrast it produces with the fainter companion. it will raise the "floor" on pairs you can resolve. but i think it is probably ok to omit it. i think there is going to be so much uncertainty and inaccuracy in any RoT that making it complex is not productive. simpler the better.

### #18 WRAK

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Posted 16 October 2012 - 02:24 AM

... how are you choosing your magnification? you mention 140x frequently and 208x once ...

Bruce, I navigate the old fashioned way with star maps (I have DSC and Sky Commander available but use it only occasionally for specific targets). After locating the target with a 55mm eyepiece (FoV about 3°) I go down my preferred eyepieces with 24/13/7/3.5mm until I split the double and sometimes I use in between eyepieces with 10mm and 4.7mm if I think this may give a better view.
7mm gives with my 980mm focal length scope x140 and 4.7mm gives about x208.
Wilfried

### #19 WRAK

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Posted 18 October 2012 - 11:46 AM

As substitute for new sessions I looked for splits at the limit of my scope and found for example 1.6" +9.1/10mag STF2488: RoT gives 48.3mm refractor for this and I needed 140mm. This is a factor of 2,90.
Next I found 1.6" +9/10.2mag STF2482: RoT gives here 58mm. This is a factor of 2.41. Must think about this.
Wilfried

### #20 fred1871

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Posted 18 October 2012 - 07:33 PM

One of the limitations of the RoT is that it needs a different version when applied to the fainter pairs. This is why I think the Sissy Haas project is not going to come up with a simple rule that applies universally.

Thomas Lewis of Greenwich Observatory made an attempt on this issue in a publication back in 1914 - and while his numbers are not regarded as definitive, there was a clear difference between fairly bright and rather dim pairs in resolvability, in relation to telescope aperture.

Lewis looked at the most difficult pairs observed by quite a few double star astronomers with a variety of telescopes. And based his conclusions on his analysis of their published measures.

The limit of resolution for a telescope was less good for faint pairs than for relatively bright ones. You couldn't expect to reach the Dawes Limit on dim pairs; also the uneven dim pairs required larger telescopes than fairly bright uneven pairs of the same delta-m and separation.

How much different? Lewis's numbers are reasonably easy to surpass on the dim pairs, even or uneven, with moderate size telescopes. And his numbers for brighter uneven pairs can be surpassed as well - again, I'm referring to moderate size telescopes - roughly, in the 13-25cm range. Not unlike the telescopes used by Dawes in his study of equal 6th magnitude stars.

Small telescopes (6-10cm) seem to do better than expected at times; the bigger mid-sized, say from 30cm upwards, are less able to push the boundaries because of atmospheric turbulence. Even so, the big-un's will beat the mid-size as a general rule - just by not as much as the size increase suggests. Personally, I'd be happy with an 18-inch (46cm) refractor in a dome in my yard, so I could tackle a lot of the closer and fainter pairs. But I know, from years of using (a borrowed) C14, so I can compare with my current C9.25 and past C8, that the improvement while large isn't as big as one would hope. All three telescopes were optically good for their type; the best was a hand-picked C8, and that had the benefit of less effect from atmospheric seeing. Even so, the C14 surpassed it easily on difficult pairs. So if the next lottery ticket comes good I'll have a C14 again
And it'd fit in my small observatory, unlike an 18-inch refractor. The 140mm refractor will stay, regardless - the images are so neat. And it's also a portable scope.

To return to the main point. Yes - I agree, Wilfried - dim pairs don't behave like bright ones. And if you try your 140mm refractor, stopped down to the small apertures you've calculated from the RoT, you'll not be likely to see the doubles as double. In a very dark sky, away from artificial light and without moonlight, you'd do better - what needs 140mm in a poor sky might be possible with 100mm in very good conditions. I've had that experience, both for double stars and other DSOs. So I think that, given your heavy light pollution, you'll have more difficulty establishing an RoT for dim pairs than people who can observe in a darker sky. But you should be less affected with brighter pairs.

### #21 fred1871

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Posted 18 October 2012 - 07:46 PM

For those who want to look at Lewis's original paper, it's in a journal called The Observatory - Lewis is in volume 37, p372 onwards. It's online through the ADSABS database of old journals.

His conclusions, often reprinted, where 'a' is the telescope aperture in inches:

Equal bright pairs 4.8/a , mean mags 5.7 and 6.4

Equal faint pairs 8.5/a , mean mags 8.5 and 9.1

Unequal 16.5/a , mean mags 6.2 and 9.5

Very unequal 36.0/a , mean mags 4.7 and 10.4

He doesn't give a figure for unequal and faint - such as 8.5 and 11.5. I suspect that that one would vary with telescope size, although thinking about Paul Couteau's remark in his book, that 10th magnitude is a sort of limit for visual sharpness of star images even with big telescopes, it might prove not usefully quantifiable regardless of aperture.

### #22 WRAK

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Posted 19 October 2012 - 03:25 AM

A lot of useful information, thanks Fred. The Haas list does not include a serie of increasing mags for given sep and delta-m as far as I remember so this project will probably not consider this aspect.
I still think that it should be possible to find a factor to adapt the RoT for fainter doubles. But the concept of considering difficult pairs for a given scope is probably misleading as the limit is a bit unprecise - so I made the error of including STF2488 beside STF2482 as the latter is certainly more difficult. So I will return to my concept of reducing the aperture with masks to be on the safe side considering limits. I am working now on my list of doubles with similar sep and delta-m but changing mag. And I do not look for perfection here but only for an useful approach for selecting doubles for observation sessions.
Wilfried

### #23 WRAK

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Posted 21 October 2012 - 02:00 PM

Found a glitch in adapting the RoT formula 116/sep*delta-m (delta-m set to 1 if smaller) for refractors by reducing the required aperture by one third. This results for doubles with delta-m smaller than 1.5 in suggested apertures smaller than the Dawes-Limit requires. First idea would be to set the suggested aperture in this case to the Dawes-Limit. I am not sure if this makes sense because this means ident suggested aperture for refractors and reflectors for doubles with delta-m below 1.5.
Wilfried

### #24 fred1871

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Posted 21 October 2012 - 11:27 PM

I was expecting others to notice this glitch. In another thread - somewhere - I'd noted a problem with the RoT when Delta-m is small, particularly when it's less than 2 magnitudes. I've been thinking that there needs to be an adjustment for pairs where Delta-m is around 1.5 to 2.0, and likely a slightly different version again with pairs ~1-1.5 delta-m. For pairs with delta-m below ~1 mag, Dawes or Rayleigh will do, though with a large CO (as in SCTs) a delta-m near 1 is becoming noticeable as making a pair harder than the same delta-m with a refractor. There might be less of this effect with fainter pairs, because the diffraction rings are less bright and don't interfere as much. Hmmm. More things to check.

I'm still fiddling with the numbers at the moment, so I can't immediately offer a series of adjusted RoTs.

Separately, I've been looking through my files of notes and looking at pairs, bright and faint, and of various delta-m levels, to see which pairs I could use based on my own observing to refine the RoT further. That's a work in progress - I'll report later.

### #25 WRAK

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Posted 27 October 2012 - 03:07 PM

It seems then probably better to develop a RoT formula for refractors and calculate the required aperture for reflectors by using the percentage of obstruction on top.
Wilfried

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