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# Putting the "Rule of Thumb" to test

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### #101 Asbytec

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Posted 18 January 2013 - 10:05 AM

Wilfred, I completely understand the need to eliminate bias. The subject interests me on many levels. First, it's new aspect I am not familiar with and challenging. Second, it's just a fascinating look into optics and observation.

I'd love to offer some better defined splits, unfortunately I have had few clear nights and none recently. Now with the moon rising into the sky, it appears there will be few dark nights remaining before I travel to the US.

### #102 WRAK

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Posted 18 January 2013 - 11:23 AM

I have meanwhile developped a formula for modifying the Dawes criterion for scopes with central obstruction as follows:
Dawes (CO) = 116/1,2213*(0,0950502775050452+(1,12627632206642)/((1+(A2/0,302756091410027)^2,26536793426585)^0,152776210790626)).
Results are as follows:
CO Dawes_mm(CO)
0 -> 116
0.1 -> 115
0.2 -> 111
0.28 -> 107
0.3 -> 105
0.33 -> 104
0.35 -> 103
0.4 -> 100
0.5 -> 95

So the Dawes criterion for a 150mm scope with 0.28 CO would be 107/150 = 0.71" instead of usually 116/150 = 0.77" and for a C925 with 0.35 CO 103/235 = 0.44" instead of 116/235 = 0.49".
I own a C925 but do not like it for double star observing but occasionally I could try to check this even if verifying such a small difference might get a bit difficult. But I have one very good reason to trust in this calculation: The observations for equal binaries listet from Lord in his paper on "Resolving unequal binaries ..." for scopes with CO are in their relation to the Dawes criterion significantly better than the scopes without CO.
Wilfried

### #103 Asbytec

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Posted 18 January 2013 - 12:08 PM

Wilfried, sure, your calculation for the 150 28% CO is the same as mine derived from:

http://www.telescope...obstruction.htm

### #104 Asbytec

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Posted 19 January 2013 - 10:49 AM

Revisit of HO 20 in 9/10 seeing and mag 4.5 skies resulted in a good split. The faint companion was held steady for seconds at a time at 163x (18mm UP HD ORtho 1.6x Celestron Shorty.)

HEI 670 was a failed split. No indication of the companion. It appeared to be much like C Ori, but the latter did offer some clue to the companion's position. HEI 670 did not.

BU894 and STT133 also failed to get a good clean split. However, with some significant effort, I did manage a few possible glimpses of the companion. But, not enough to be a good, legitimate split and certainly very difficult and time consuming observation.

Wilfried, I am beginning to notice a bit of a trend on the few doubles I have attempted. It does seem somewhere around required aperture 144 or less, I can achieve a good legitimate split and hold the companion's disc steady for a period of time. Around 147 or so they become very difficult resulting in those brief, fleeting, and merely possible glimpses.

I wanted to attempt STT 517, but I lost the sky to high overcast. As a close double very near the 0.71" arc Dawes limit, I think it would have been a good test.

I also revisited BU 1040, but failed to split it, again.

### #105 WRAK

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Posted 21 January 2013 - 05:48 PM

Norme, thanks for putting time into checking doubles from the Ori list. Your troubles with BU894 and STT133 probably give a hint that there may be a current ROT model problem with companions fainter than +11mag. You could countercheck this suspicion with BU13 and STF849, both are in the ~150mm req. apterture range with companions brighter than +10mag and should be no problem for you.
The topic of companions coming near the TML of the scope will be the next extension of the current RoT model after including the factor CO with reasonable results.
Wilfried

### #106 azure1961p

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Posted 21 January 2013 - 06:00 PM

For me with 11 and 12 magnitude doubles in pairs under 2" the vague graininess becomes apparent as the eye seems straddled between photopic and skotopic vision. The way the stars would morph into seperate bodies than rejoin in poor seeing was even spooky. Compelling and beautiful but a little eerie to . Doubles are usually such bright cheery things.

When time permits I'd like to weigh in on some of the RoT objects . Weather has been so lousy and when it was good I either had the flu or I was eorking or like last nite it was gusting to 25 knots.

This has been a progressively interesting pursuit you guys have taken on. Perhaps I can add something at some point.

Cheers,

Pete

### #107 fred1871

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Posted 21 January 2013 - 07:11 PM

First, some doubles observed - with a fair bit of moonlight, my most recent nights were given to doubles where the companion is not at the fainter levels of magnitude. I figure that with Orion around for a while, I can pursue those after the next Full Moon has departed a while.

Norme didn't get a split on HEI 670 - I was luckier. The 140mm refractor, and at 285x I got glimpses of a small companion; 400x confirmed it, the companion clear in the steadiest moments. Air steadiness good, with very good moments; 8 day moon. This was the night before last.

STT 133 was easier than I expected - moonless night, earlier this month, seeing becoming good by the time I got to STT 133. Moonless night, good dark sky, so the 11.2 mag companion I didn't expect to be a problem. And it wasn't. I found STT 133 with my 80x eyepiece, a Pentax 10mm XW, which gives a field of ~50' or so - first surprise was seeing a hint of the companion at 80x. So instead of going to 160x, I put in the 7mm XW (114x), and that was enough - the companion was a tiny speck close to the primary, roughly NNE. Much easier than expected. Air steadiness must have been better than I thought! The data list gives mags 7.3 and 11.2 at only 3.3" for STT 133 - hence my surprise. I expected it to need higher magnification if it showed.

STT 517 - Norme has reported further on this one in another thread. I have notes on it from this time last year - I've not got back to it again - yet. This one is a long-period binary, orbit currently listed at 530 years but only grade 4, so it'll be refined over time. The pair is slooowly widening these days, but should be near enough 0.7" as per the 2010 measure. The night I observed it was not great for steadiness - only fair-plus, with fuzz and flicker. 140mm refractor, best I could do was an elongated image in a fuzzy surround at 400x. I'll try it again on a steadier night.

Another pair on Wilfried's list is HO 22 - mags 8.5 and 8.6 at 1.0". Being less bright makes such pairs tougher with moderate apertures. I've seen pairs at 0.5" at mag 8.5 with a C14, but a C14 has 2 magnitudes gain over my 140mm refractor. HO 22 - 140mm refractor, visible split (two star points separated) at 285x, using the 7mm XW with 2.5x Powermate. Easier than I expected; seeing good/good-plus.

I'll have a few more to add when I get time to go through my notes.

One thing I'm noticing is a similar effect to that shown in the Petersen diagram - where Harold P found no change in resolution until he got closer to the magnitude limit of his telescope/magnification combination. Then things changed noticeably.

To be expected, I'd think - it's the "fainter doubles" effect, where the interaction of eyesight limits comes more into play as the stars get dimmer. And that becomes evident somewhere around the Couteau Limit of 10th magnitude - maybe around 10.5 or so - for reasons separate from mere dimness as Couteau remarks with regard to bigger (big) telescopes. Magnification goes only so far. Eventually there are trade-off factors between the eye's ability, the atmospheric seeing, and what the telescope is doing.

There's been some good discussion of that in a thread on the effect of CO versus other factors in the Cats forum recently, and elsdewhere - with comments on bringing the eye (and its MTF?) into conjunction with the telescope's abilities/limitations. Rather like the photographic discussions of what you get in an image after considering what the lens can do PLUS what the film or sensor can do - final results depend on both.

### #108 Asbytec

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Posted 21 January 2013 - 10:29 PM

Wilfried, I'd be happy to observe BU13 and STF849, maybe tonight. I was curious about the seeming disparity between RoT and actual aperture. I have not read Fred's comment, yet, but does the RoT use the clear aperture rule? It seems, if close unequal pairs act like planetary contrast (same scale, same problems with diffraction), then those two rated above (D - co) would be difficult. In my case, that would be 150 - 41 = 109mm, same as a refractor according to MTF approximation.

Still, I am getting the feeling something is working in the RoT. There seems to be a cutt off point for my own aperture/CO ration between 144mm and 150mm. They do progress from confirmed, distinct Airy disc for the companion to being extremely difficult or impossible within that range. So, it seems the scaling is working, but maybe the scale might shift entirely up or down to fit. But, again, my own sample size is small to say. It's just an impression that seems to hold over the samples tested.

Pete raises an interesting point on scotopic and mesopic vision. One of the reasons I did not go after some dimmer samples is the increasing use of averted vision needed to observe them. Using rod based vision does seem to reduce visual acuity, but offers increased sensitivity. Not sure which is most important when observing point sources.

Fred, yes, HEI 670 has a sep very near the bright first ring. It really makes some sense it is very difficult in an obstructed aperture. I found it impossible, more difficult than c Ori.

Likewise, STT133 sits on the fourth ring, which is not really bright but more broad (as seen on the brightest stars.) The second and third rings are bright with a 28% CO, but very thin in comparison. So, it's curious, even though the fourth ring is well below the visible threshold, it seems to have some effect on resolution.

I cannot 'explain' why BU 894 companion was not seen at over 5" arc sep. That was one that seemed to be easy, but it was not. Maybe the Couteau effect has something to do with it, both ST133 and BU 894 have companions below 11th magnitude.

Revisiting HO 20, I got a clean, steady split, too.

### #109 WRAK

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Posted 22 January 2013 - 04:01 AM

Pete, would be great if you could join in with some hints and observations.
Fred, great to get some more observations for my data set.
Norme, depending on the degree of light pollution we get with secondaries fainter than 11mag already rather close to the 150mm telescope magnitude limit of ~13.6 (for NEML of 4.5 I calculate currently TML ~12.6) and then it seems to get really hard even with not this small separations. I have still not figured out what separation is then necessary to be able to see a companion effectively at the scopes magnitude limit - it seems to require at least a two digit number.
Wilfried

### #110 azure1961p

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Posted 22 January 2013 - 11:01 PM

I've never ever tried for 11v at any appreciable separation under 10". Pairs of that magnitude but neverv, say, mag 11 at 2" from mag 6. I think my cut off for whatever reason was 9.5v. I think I was so put off with that difficulty I backed off a bit. I want to contribute when the weather obliges.

Pete

### #111 fred1871

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Posted 23 January 2013 - 03:03 AM

I've now found I can see fainter stars than I'd thought likely when there's moonlight. No, maybe not around full moon, but a few nights ago, with an 8 day moon in the sky, I had a look at HJ 697 in Orion (0521.5, -0025). The two wide companions had "old" magnitudes on my observing list, 10th and 11th mag.

I found both stars were fainter than I expected, even allowing for moonlight - the brighter companion was clear enough at 160x (glimpsed with less) and the fainter was averted vision only; both were easier at 230x, though the fainter remained near the limit of visibility.

Later I looked up the data in the Washington Catalog, and found modern photometry for both (double-digit) - the easier companion was mag 11.9 (not 10.6) and the fainter one was 13.05 (!! - I had 11+ listed). So, 13.05 in fairly bright moonlight - with 140mm aperture.

Because both are very wide of the magnitude 5.7 primary there's no significant effect from it - the brighter companion is at 42", the fainter at 33".

So I'll now be willing to try for fainter companions in moonlight.

Obviously, for the tight pairs, unlike this one, bright moonlight will remain a problem for faint companions, adding to the primary star's effect. But I now think it's less destructive than I'd expected (except maybe for a few days around Full Moon).

### #112 WRAK

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Posted 23 January 2013 - 04:04 AM

Fred, interesting report - this would mean that at least for a separation above 30" there is no longer a resolution effect on the companion. I assume this could be valid down to about half of this separation.
Anyway it is quite a feat to resolve a +13.05mag star with a 140mm refractor in "fairly bright moonlight" - this is already very near the advertised telescope magnitude limit of 13,4 for 140mm and to reach such numbers requires already perfect seeing near zenith and exzellent skills on the side of the observer. This would also support the claim in the article "Some notes on Visual Urban Astronomy" from Tom Bryant that you can resolve stars up to the TML even under severe light pollution. From my own experience I do not buy this - my 140mm TML with average NEML 3 is so far about +11.5mag but I have to admit that I never pushed this topic very much.
Wilfried

### #113 Asbytec

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Posted 23 January 2013 - 04:59 AM

I assume this could be valid down to about half of this separation.

Anyway it is quite a feat to resolve a +13.05mag star with a 140mm refractor in "fairly bright moonlight"...This would also support the claim in the article "Some notes on Visual Urban Astronomy" from Tom Bryant that you can resolve stars up to the TML even under severe light pollution.

I would assume the same, Wilfried. Of course diffraction is infinite, but at some angular distance it becomes meaningless.

On TLM, I have to say on some nights (near the crab nebula) I picked up stars about 14th magnitude, but other nights failed to see stars down around 12th in weak sky glow to the north (Iota Cass, for example.) On BU 1040, I spotted some field stars other than the two nearby bright ones. I cannot find magnitudes on them, but if the dimmer "bright" one was 13th mag, the fainter field stars had to be pushing 14th mag (at around 250 to 300x.) And I saw them both on dark nights and with a crescent moon in the sky. NELM was 4.5 and 4, respectively.

### #114 WRAK

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Posted 23 January 2013 - 10:04 AM

Concerning the validity of "modern photometry double-digit" magnitudes in the WDS catalogue I tend to "believe" them but not without some reservation. One example for "being not so sure" is STF450 in the Pleiades (one of the stars in Ally's braid) with advertised data 6.2" +7.29/9.10mag suggesting an easy resolution with a small scope down to 50mm aperture. But I failed several times with an 120mm refractor despite two fainter than +10mag stars were easyly seen in the same field of view. I have no explanation for this besides assuming a clearly wrong magnitude in the WDS catalogue as I would estimate the STF450 companion around 11mag.
Wilfried

### #115 Asbytec

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Posted 23 January 2013 - 10:18 AM

I am very new to double star observing, but even I am getting the feeling there is just so little data on doubles. Few reports, discrepancy in reporting, and maybe few are recent. There must be errors in the catalogs.

### #116 fred1871

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Posted 23 January 2013 - 06:31 PM

Wilfried, I'm a little puzzled about STF 450 in the Pleiades - I'll have to re-observe it with my 140mm refractor. My only notes on it, from 4 years ago, were with my C9.25, and I described it as "an elegant, uneven moderately close pair" with 98x (24mm Panoptic eyepiece). In other words, it looked easy at that power and I didn't think at the time the listed magnitudes were wrong - that's something I do make a note of when I have that impression - as happens with, for example, some of the Jonckheere pairs.

Errors in photometry? - of course, and you picked up an example with a J pair, when the AAVSO photometry survey appeared to give more accurate magnitudes than those in the WDS. The WDS typically uses Tycho for its modern magnitudes. Generally, these are of good accuracy. Obviously there are other sources as well, as we've both noticed with some of the IR magnitudes for some doubles. The WDS collects data from many sources.

Norme, it's not generally true that "there is just so little data on doubles". For some, yes; for others, a great deal of data, and the typical double has quite a lot. The WDS gives summary lines on each pair. There's a lot more known for most of them, and a data request for a double of special interest will show that. Of course, requesting floods of data files won't be appreciated by the good folk who are responsible for the WDS; but I like others do put in occasional data requests, when there's good reason for it, and usually there's a lot of data that comes back.

Errors in the catalogs? Of course. But many doubles have multiple examples of photometry, many measures over the years, and sometimes detailed studies or calculated orbits. The quality of the material varies, that's to be expected. But getting all the data together can often give patterns, or allow analysis that gives more accurate information than the summary line might suggest.

One recent example of this - I requested data on a double where the earliest and most recent measures suggested the separation had been 1.5" in the 1870s, and 2.3" now - the full data suggested the first measure was in error, and 2.0" was the likely correct figure. So the pair has changed much more slowly than the summary line suggested.

Another - first and last measures suggest no change in separation - getting intermediate era measures shows a changing binary that has closed, then widened again. This kind of thing might be picked up from getting data listed in Sky Catalog 2000, or other readily available sources, so as to have measures from an "in-between" time. Two data points can be not enough to have an accurate picture.

Agreed - sometimes there's not enough data. The recent experience with Gamma Equulei, discussed here in some detail, tells us this - we need a new measure to see what's happening there, as it appears likely the pair has been closing quickly in recent years, perhaps with a significant change of angle as well. We won't know until someone with a large telescope re-measures it, probably using adaptive optics (as with the most recent measure) because the large delta-m makes it a problem for speckle interferometry. Then we'll have a better picture of the orbital change. And further measures, in years to come, should eventually allow an orbit calculation. For now, we're guessing about the orbital period and shape. One of many like this.

### #117 Asbytec

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Posted 23 January 2013 - 09:26 PM

Fred, okay, thanks for the enlightenment.

### #118 WRAK

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Posted 24 January 2013 - 06:58 AM

Wilfried, I'm a little puzzled about STF 450 in the Pleiades - I'll have to re-observe it with my 140mm refractor...

Fred - it is a curious positive side effect of light pollution and smaller apertures that you can see resp. not see stars at the fringe of a rather low level of TML. This way you can detect questionable data on magnitudes you will not notice with greater apertures and excellent seeing. With 140mm and NEML > 4 you will most probably resolve the STF450 companion without trouble and therefore not bother to compare its brightness with advertised fainter but visually brighter stars in the same field of view - but as you have now a hint you will may be also find that there is something wrong here.
Wilfried

### #119 Asbytec

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Posted 24 January 2013 - 09:58 AM

Wilfred,

I was able to split both BU13 and STF849. They are what I would consider easy splits with both primary and companion resolved into distinct discs. BU 13 companion appeared to rest just inside the first ring, while STF849 appeared more like other very tight, nearly equal magnitude doubles. At 320x, I could tell STF849 companion (preceding the primary) was a tad dimmer. BU 13 companion was held steady at moments, but drifted in and out. Still, it was distinctly residing at PA 140, and at 263x it was split while 320x was easier.

Now, the exciting thing is, this is with a gibbous moon about 4 degrees away. In fact, the FOV was so bright I could see floaters. (LOL) Star hopping to STF849 was pretty difficult, it took several tries to nail it's tiny speck and position from 69 Ori (using HIP 28978 and 29001 as pointer stars) against a well lit finder background. It was just faintly visible only during moments in the finder. But, I managed to find it with perseverance.

NELM was about 3.5 in the vicinity of Meissa and seeing averaged 7/10 or better.

I have about a week of observing time, if there are others you are curious about, please post. Weather permitting, I will observe them. The moon will be moving away from Orion in the coming nights, so star hopping should get easier.

Anyway, I am going to post this as a separate observation, too.

Thanks, Norme

### #120 WRAK

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Posted 25 January 2013 - 03:32 AM

Norme, thanks - glad to hear that there exists such a thing like a clear sky. So BU13 and STF849 behaved like expected. Next step could be to go to a bit fainter companions like A320 1.1" +10/10.5mag (may be a bogus double as it was observed last time 1963) or A2804 1.1" +9.79/10.46mag.
Then very interesting could be BU1190 1.4" +6.95/9.81mag with a req. ap of 156mm - this one could be already a bit difficult despite a companion brighter than +10mag.
Then with A2634 1.6" +8.7/11.34 you could try another double with a companion fainter than +11mag - this one should be already very difficult - no split would be of no surprise.
Wilfried

### #121 Asbytec

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Posted 25 January 2013 - 03:54 AM

Wilfried, will observe those and some Fred mentioned in my other thread. Will report back when I get a chance to observe them. Weather looks to hold tonight, fortunately. Wish I had some spare good weather to share with you, but it's been in short supply here, too.

### #122 fred1871

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Posted 25 January 2013 - 08:51 AM

Wilfried, some thoughts.

First, regarding some of the suggested pairs - A 320, A 2804 - I'm inclined to think they're becoming as much a test of the observer's eyesight as of what the telescope can do, if we're talking about 150mm telescopes. These pairs seem to be a test of Lewis's "faint pairs" visibility. I observed some pairs like this in the 1990s with a 7-inch (18cm) refractor, and thought such doubles were as much a test of sky brightness and observer vision, along with air steadiness, as a test of what the telescope could do.

They're of interest of course, but I suspect results will prove even more varied than with less faint pairs, making an RoT for such pairs uncertain, and if factored in perhaps reducing the accuracy of an RoT for less faint pairs as seen with modest telescopes. I'm thinking aloud here, not attempting anything definitive.

BU 1190 is a different category - obviously difficult, but depending more on nearly 3 mags delta-m at quite close separation (1.6") - because the secondary star is mag 9.8 this is less of a test of eyesight.

I'd be surprised if A 320 is a "bogus double" - as 7 measures are listed in the WDS. Of course, if the detailed list tells us that most of these were attempts without success it could be "bogus", but that seems an unlikely scenario. More likely is that it's a neglected double because it had not changed very much between 1902 and 1963.

### #123 Asbytec

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Posted 25 January 2013 - 09:48 AM

Wilfried, I have A320, A2804, BU1190, and A2634 on my short list. Weather was clear tonight with a nearly full moon. A quick observation of Psi 2 Ori, a nice, clean split, however showed seeing was going to be a problem.

So, working up the list in order of Ra, I struggled with A2705, an equal magnitude, close pair. It should have been pretty easy, but truth is I could only get a hint of it's companion. And it was not easy, not at all. So, I tried STF 849 again with the same result. I just could not get a good split in those conditions.

Seeing is weird here, I could hold the Airy discs pretty steady for periods of time, but the star images were jumping around quite a lot. I suspect some larger scale seeing issues. And, the moon was not far removed from last night, yet there was no improvement in NELM (still about 3.5.) The sky was still fairly well lit, about the same or worse. Visually, I just could not make out stars near 11th magnitude.

I am sure I can get a better split on A2705, but it will have to wait for steadier seeing. I did not pursue any others, observing Jupiter and the moon just showed me how futile it would be to attempt some difficult observations.

### #124 WRAK

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Posted 25 January 2013 - 05:06 PM

Norme, sorry to hear that conditions were not good enough to give this a serious try.
Fred, concerning A320 and A2804 you are probyably right - this is why I have a +9mag switch in my model for the influence of the magnitude of the secondary for the required aperture. Even the statistical analysis tends in the same direction as as the least square method for the parameter pr2 in pr1*(m2-pr2) results in a value near 9.
Now I am considering a further component for the influence of m2 fainter +11mag as there seems to begin another level of difficulty here.
Wilfried

### #125 Asbytec

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Posted 27 January 2013 - 09:31 AM

Wilfried,

I was able to observe A2705 and confirmed a clean split at 263x and 320x: a tiny disc and a faint speck of a companion at PA ~250. I could hold the faint companion steady for brief periods. In fact, it looks pretty close to any limit with NELM 3.5 to 4 in good seeing on this night. Since I had trouble with STF 489 on the previous night in rough seeing, I reconfirmed the split made a few nights earlier. STF 489 was indeed split.

I attempted A2804, but failed to split it. The primary was bright enough, barely, but I did not see the companion. On this pair, I found myself using more averted vision. I had some difficulty finding it, it did not show in my finder, but nearby HIP 25066 was, so I hopped over HIP 24997 to get on A 2804. I am sure I was on the right star. Want to try again later this week when the moon moves away.

I could not find BU1190 at the stated coordinates. It is near 59 Ori. I got clouded out and was unable to try A320.

Anyway, seeing was pretty good at 8 or 9/10 and 3.5 < NELM < 4.0. The moon is one day past full, I believe.

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