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Limiting Magnitude in Binoculars



 
 
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  #31  
Old October 5th 03, 04:34 AM
PrisNo6
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Default Limiting Magnitude in Binoculars

I still haven't gotten over to Cloudy Nights to read your materials, but thanks again for your continuing efforts in this area.

"edz" wrote in message om...
"PrisNo6" wrote in message om...

snip
This may be the beginning of true
field tests that will either corroborate or dispute existing
formula. You all need to keep in mind this entire study is absent of any tests relative to diffuse extended objects.




  #32  
Old October 5th 03, 04:48 PM
Tony Flanders
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Default Limiting Magnitude in Binoculars

(edz) wrote in message om...

Tony, before you go any further with this, you need to take time and
ang go read my work. It should answer all your questions.


I apologize profusely; I hadn't realized that the article had
already been published. I hate it when people ask me to write
something that I have already written!

I think that I can explain the discrepancy in our results w.r.t.
NELM vs. BLM, but before I get into that, let me make a few
comments about other aspects of the article.

As I am sure you are well aware, the entire topic, although
interesting, is only one aspect of what people want from
binoculars, and probably not the most important. When I use
binoculars, I am interested primarily in seeing nebulosity
and secondarily in seeing moderately bright stars better.
Seeing faint stars near the limit of vision is rarely very
important to me. But of course, that should not be taken
as a criticism of your article. The subject that you explored
is very interesting in its own right, is certainly relevant
even if it not the whole story, and it has the virtue of
being much easier to quantify than seeing faint nebulosity.

I have some doubts about the methodology of the study of
aperture and magnification; in particular, I disagree with
the statement that masking binoculars down to 50mm is unlikely
to improve aberrations in a way that bears on LM. In fact,
the statement that your 20x80 binoculars generally do little
better than your 16x70 suggests to me that the 20x80 *do*
have serious aberrations. What else could account for
such a huge discrepancy in performance? Certainly not light
loss alone, unless there is some kind of internal mask that
makes the effective aperture much less than 80mm. And why
shouldn't masking them down to 50mm reduce those aberrations
dramatically? Unfortunately, the only truly reliable way
to study this subject would be with a binocular telescope
with interchangeable eyepieces and with known high quality.

Having said that, I certainly agree with your general
conclusion that the benefits of higher magnification in
binoculars have been understated dramatically in the past.
Without a doubt, binoculars with abnormally small exit
pupils, such as my own Canon 15x45 IS binoculars, perform
much better than formulas weighted heavily towards
aperture would predict.

---------------------------------------------------

In the interest of full disclosure, I must admit that I have
spent very little time rigorously measuring the LM of
binoculars. That is because binoculars lose most of their
charm for me once they are placed atop a tripod, and of course
the subject cannot be studied truly rigorously if the binoculars
are hand-held. However, I *have* spent many, many hours
measuring telescopic LM, a subject which is discussed in
my website at
http://mysite.verizon.net/vze55p46.

I should mention three points where my experience differs
wildly from yours. First, you say that you find it much
easier to determine instrumental LM than NELM. I agree
with you in finding NELM very hard to estimate; like you,
I have spent 2-3 minutes trying to determine the visibility
of a single star. But I find it every bit as difficult when
looking through a telescope. Second, you say that once you
have found a star in an instrument, you can then see it with
direct vision. Again, that is wildly discordant with my own
experience. Indeed, I have always found globular clusters
extremely frustrating to sketch precisely because most of the
stars that I can see with averted vision disappear when I look
at them directly, making it extremely hard to pinpoint their
location.

Third, and most relevant to the question of NELM vs. BLM, you
say that you find NELM much harder to estimate under brighter
skies than under darker skies. Again, that is just the opposite
of my own experience. It is true that it is frequently hard to
find a sequence of stars with adequate granularity under
heavy light pollution; this can be an insuperable obstacle
for NELMs lower than 4.0. However, for any given marginal
star, I find the question whether it is or is not visible
much easier to answer under bright skies than under dark
skies. Another way of saying that, perhaps, is that the
benefits of averted vision over direct vision decrease as the
skies get brighter.

--------------------------------------------

But on to the subject of NELM vs. BLM. When you chart BLM on
the Y axis and NELM on the X axis, you get a dramatically
lower slope than I do for ultra-low-power telescopic LM
versus NELM. I believe that the discrepancy lies almost
entirely in your estimates of NELM, and very little in your
estimates of BLM. In other words, under the same skies as
you, I think I would have found only an 0.5 mag variation
in NELM, just as you found only an 0.5 mag variation in BLM.

It is hard to tell that for sure, because you omitted one
absolutely critical fact from your report, namely the nature
of your observing site. I have attempted to deduce that
from your reported NELM and other observations, but I put
*very* little credence in NELM, since I have found estimates
of NELM for the same site at the same time to vary more
than one full magnitude from one experienced observer to
another. It sounds as though all of your observations
were done under what most people might call good suburban
conditions, right?

Incidentally, the points graphed on Chart 2 do not seem to
agree with the numbers quoted in the individual observations.
For instance, I see a number of points charted at NELM = 6.0,
but no recordings of mag 6.0 stars being seen naked-eye.
Or did I miss something?

With respect to the individual observations of NELM, you say
that on Aug 20 you saw a mag 5.6 star in Cr 399, but that the
Cygnus Milky Way was only faintly visible. For what it is
worth, any time that Cygnus has been overhead and I have been
able to see a mag 5.6 star, I would call the Cygnus Milky Way
"very bright". I suspect that the difference is in our NELM
estimates; my NELM estimates for dark and semi-dark skies seem
to be consistently on the low side for experienced observers.
But it is possible that the difference is in our notions of
"faintly visible" versus "very bright". It is impossible to
tell in lieu of objective measurements of sky brightness and
extinction.

Much more important, almost all of the data for your NELM vs.
BLM correlation comes from the three points on Sep 10, 11, and 12.
In lieu of the usual careful report of NELM, you note "improving
from about 4.0 ... to 5.0". You seem to have arbitrarily fudged
the lowest figure from 4.0 to 4.4 in your chart, but I suggest
that you still underestimated the NELM dramatically -- unless,
perchance, this was a very hazy night (you don't say).

I have a huge amount of data of all kinds proving that at my
latitude of 42N, the zenith is always considerably darker on a
reasonably clear night at Full Moon in the absence of light
pollution than it is at my own city home on a moonless night.
Yet I consistently measure the NELM here at anywhere from 4.4
to 4.8, depending on the transparency and the time of night.
That suggests that if I had been with you on Sep 10, I would
have estimated the NELM at 5.0 or better.

Why the discrepancy? I can suggest various explanations. First,
perhaps, experience. I do a lot of observing under heavy light
pollution, so I am accustomed to estimating NELM in those
conditions. You, clearly, have much more experience estimating
NELM under semi-dark skies, which is a rather different problem.
Second, sky brightness at Full Moon varies tremendously from one
place in the sky to another; it is even more critical than usual
to measure the BLM and the NELM in the same part of the sky.
Third, even a quick glimpse of the Full Moon wreaks havoc with
one's dark adaptation. Obviously, this won't be an issue as
long as one's eyes are glued to binoculars, but it is hard
to avoid when observing naked-eye. I am particularly good at
avoiding looking directly at bright lights because of my
extensive practice at urban observing.

Another factor worth considering is the pupils of our eyes.
You mention that an optometrist measured your pupils at 6.5mm
to 7mm in subdued room light. That is probably abnormally
large; most people report 7mm or less under fully dark skies,
with considerable decrease under suburban night skies, which
in turn are surely much darker than subdued room light.
My own pupils always seem to measure from 5.0mm - 5.5mm
anywhere from very dim room light to total blackness,
depending how I measure them.

Now let's imagine that under suburban skies, your pupils
typically open to 8mm, but that under the Full Moon, they
close down to 5mm. That could conceivably account for
a full magnitude loss in NELM due entirely to your pupils,
quite ignoring issues of contrast of stars against the sky.
But you would not experience that with any of the binoculars
that you tested, all of which had exit pupils of 5mm or less.
Likewise, I would not experience it for NELM due to my
relatively constant pupil size.

Frankly, I am rather sceptical of that explanation, because
there are numerous reports that people with 8mm pupils do *not*
see a full magnitude improvement in naked-eye observing over
people with 5mm pupils. Some people say that there is no
improvement at all, atttributing this to the massive
aberrations of the human eye at unstopped 8mm aperture.

Yet another thing to remember is the effect of focus, something
I am keenly aware of due to my myopia. The optimal prescription
for my eyes varies considerably from one time of day to another,
and also depending on the altitude of my target. The eyeball
compresses as one tilts one's head up, with a fairly large
effect on focus. The eye has some degree of accomodation to
this, varying greatly from one individual to another, but
nowhere near as great as binoculars, where you can tune focus
to your heart's content. Indeed, I find that I am constantly
fiddling with the focus on my binoculars, and frequently change
it from one target to another, probably due to differences
in their altitude.

Finally, let me stress once more that you should get out of the
habit of saying "NELM has an effect ...". NELM is itself an
effect; it is sky brightness and extinction that are causes.
NELM has been used traditionally as a surrogate for sky
conditions for lack of any better substitute, but it is a
truly terrible surrogate in many, many ways. Without a
doubt, NELM is heavily non-linear w.r.t. sky brightness.
Indeed, I am pretty sure that insofar as NELM and telescopic
LM are non-linear w.r.t. each other, it is because telescopic
LM is much *more* linear than NELM w.r.t. the underlying causes.

In summary, let me say that I have spent a lot of time talking
about areas where we disagree and very little about areas where
we agree, which is an awful lot. It's more efficient that way,
but it can be a little disconcerting to read. Despite all of
my criticisms, this was a very impressive study. Now I feel
obliged to try to replicate findings myself!

- Tony Flanders
  #33  
Old October 5th 03, 05:14 PM
Phillip Coker
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Default Limiting Magnitude in Binoculars

This thread is the reason why I wade through all the nonsense that shows up
in this group. Great posts!!

Phillip


  #34  
Old October 5th 03, 10:29 PM
Anton Jopko
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Default Limiting Magnitude in Binoculars

Tony,
another factor to consider is vignetting of the edge of the field of view. I
notice in even premium binoculars that the edge of the field of view is not
fully illuminated. some calculations i've done suggest you could lose about 0.3
magnitudes at the edge of the field compared to the centre. I often wonder why
this is so when you pay big bucks for well corrected binos. must be easier to
stop the view down i guess. where did you publish your research on bino's?
Thanks,
my 2 cents,
anton




  #36  
Old October 6th 03, 07:04 AM
edz
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Default Limiting Magnitude in Binoculars

(Tony Flanders) wrote in message m...
(edz) wrote in message om...

I have some doubts about the methodology of the study of
aperture and magnification; in particular, I disagree with
the statement that masking binoculars down to 50mm is unlikely
to improve aberrations in a way that bears on LM.


I provided a link to a discussion of the affects of masking
binoculars. See binocular performance. Having discussed this method
with others, I think it is valid.

the statement that your 20x80 binoculars generally do little
better than your 16x70 suggests to me that the 20x80 *do*
have serious aberrations.


I clearly stated that the 20x80shave some problems. The exit pupils
cannot be made round. When compared to Fujinon 16x70s, they often are
not significantly better. I stated that in my results.

Unfortunately, the only truly reliable way
to study this subject would be with a binocular telescope
with interchangeable eyepieces and with known high quality.


But this would be avery different test. It would pass right over the
performance deficiencies of low mag binoculars. So It probably
wouldn't be relevant.

However, I *have* spent many, many hours
measuring telescopic LM, a subject which is discussed in
my website


I’ve been to your site.

I should mention three points where my experience differs
wildly from yours. First, you say that you find it much
easier to determine instrumental LM than NELM. I agree
with you in finding NELM very hard to estimate; like you,
I have spent 2-3 minutes trying to determine the visibility
of a single star.
But I find it every bit as difficult when
looking through a telescope.


That is probably true for me also. As I think about it, sometimes I
need a great length of time at the eyepieces to acquire a star and
many times it means coming back several times before finding it.

you say that once you
have found a star in an instrument, you can then see it with
direct vision. Again, that is wildly discordant with my own
experience.


Often! Once I have found a star by averted vision, I can come back to
or pass over the area and catch many more glimpses of that star, even
looking directly at it.

I have always found globular clusters
extremely frustrating to sketch precisely because most of the
stars that I can see with averted vision disappear when I look
at them directly, making it extremely hard to pinpoint their
location.


I find globulars and clusters like M37 difficult because of the
density, the close proximity of stars, not necessarily because of the
magnitudes of the stars.

Third, and most relevant to the question of NELM vs. BLM, you
say that you find NELM much harder to estimate under brighter
skies than under darker skies.


Seems that way to me. But not sure this has any relevance, it just a
perception, not a measurement. it's not used anywhere.

But on to the subject of NELM vs. BLM. When you chart BLM on
the Y axis and NELM on the X axis, you get a dramatically
lower slope than I do for ultra-low-power telescopic LM
versus NELM. I believe that the discrepancy lies almost
entirely in your estimates of NELM


Actually, I think I took great care in estimating NELM and I think I
thoroughly explained my procedures. But if you think that I
underestimate NELM, you would not have any reason to say I
underestimated selectively at either the high end or the low end.
Typically, when someone develops a process and follows it regularly,
if the procedure produces results that are off, they are all off,
usually by the same amount.

If I underestimated all my NELM readings by 0.2 or 0.3 or even 0.5mag,
the slope of my observations would not change. All my observations
would just move further to the right with the same slope. The slope
of the plot of my observations is one of the most relevant findings of
this entire study. It’s what shows that BLM does not act
linearly with NELM.

It sounds as though all of your observations
were done under what most people might call good suburban
conditions, right?


I'd say rural suburban. I've got no street lights within a quarter
mile. 15 miles north of Prov. probably only 40-50 miles south of
you.

Incidentally, the points graphed on Chart 2 do not seem to
agree with the numbers quoted in the individual observations.
For instance, I see a number of points charted at NELM = 6.0,
but no recordings of mag 6.0 stars being seen naked-eye.
Or did I miss something?

With respect to the individual observations of NELM, you say
that on Aug 20 you saw a mag 5.6 star in Cr 399, but that the
Cygnus Milky Way was only faintly visible. For what it is
worth, any time that Cygnus has been overhead and I have been
able to see a mag 5.6 star, I would call the Cygnus Milky Way
"very bright". I suspect that the difference is in our NELM
estimates.


I've seen the Milky Way, very recently, under mag 6.5 skies. The
Milky Way was so bright, I mistakenly though I was looking at clouds.
That's bright. In my backyard, it sometimes gets a lillte bright
after midnight. I expect how I percieve the Milky Way has no bearing
on what stars I can site for NELM.

Much more important, almost all of the data for your NELM vs.
BLM correlation comes from the three points on Sep 10, 11, and 12.
In lieu of the usual careful report of NELM, you note "improving
from about 4.0 ... to 5.0".


First you need to realize that all of this data is not a word for word
transcribe of my field logs. On different nights when I sat down to
type, it appears I had a different style. I have probably 3 or 4 more
nights of data that is not even shown in the daily reports in the
paper.

Tony, I must say you seem to be taking on the qualities of Quincy.
Any particular reason why. Or do you just like being forensic?

You seem to have arbitrarily fudged
the lowest figure from 4.0 to 4.4 in your chart, but I suggest
that you still underestimated the NELM dramatically -- unless,
perchance, this was a very hazy night (you don't say).


I wrote several paragraphs explaining why I did this. Go back and
read again the sections on why I felt I under-estimated some nights.

I have a huge amount of data of all kinds proving that at my
latitude of 42N, the zenith is always considerably darker on a
reasonably clear night at Full Moon in the absence of light
pollution than it is at my own city home on a moonless night.
Yet I consistently measure the NELM here at anywhere from 4.4
to 4.8, depending on the transparency and the time of night.
That suggests that if I had been with you on Sep 10, I would
have estimated the NELM at 5.0 or better.


I observed just tonight under very clear skies with a moon similar to,
not quite as full as last month. I recorded NELM 3 or 4 times
throughout the night tonight at 4.4 to 4.7, it varied throughout the
night. Two sample 5.0 stars could not be seen, even after many
attempts. Looking completely away from the moon towards the north I
observed NELM of 5.0, but this was not in the vicinity of my study
observations, so I would not use it.

it is even more critical than usual
to measure the BLM and the NELM in the same part of the sky.


As I stated above and in the article, I also recommend this procedure.

Third, even a quick glimpse of the Full Moon wreaks havoc with
one's dark adaptation.


I try to hide from the moon.

Likewise, I would not experience it for NELM due to my
relatively constant pupil size.


I even close my eyes when infrequent cars go by to eliminate reflected
light off the house. Why would you assume other’s pupils change
but yours remain constant. isn't that odd. Anyone, with any exposure
to light will experience a pupil change, no matter how large they
start out.

I find that I am constantly
fiddling with the focus on my binoculars, and frequently change
it from one target to another, probably due to differences
in their altitude.


I seldom find that I need to change focus, but yes I do occasionally,
and it is sometimes due to differnet altitudes. Usually it's because
the dials have been touched. I don't think I've refocused my Fujinons
in the past week or so.

Finally, let me stress once more that you should get out of the
habit of saying "NELM has an effect ...". NELM is itself an
effect; it is sky brightness and extinction that are causes.


As NELM is a value (a result) used in the application of Carlin's
formula, it has an affect on the outcome. Which brings us full circle
to why we are here. I attempted to determine the influence of various
pieces of the puzzle.

NELM is heavily non-linear w.r.t. sky brightness.
Indeed, I am pretty sure that insofar as NELM and telescopic
LM are non-linear w.r.t. each other, it is because telescopic
LM is much *more* linear than NELM w.r.t. the underlying causes.


There are probably a dozen different factors needed to measure NELM by
way of sky conditions, if you use Schaefer's method, but it's so
complex it's not practical. It's precise, but not practical.
Obviously star magnitude determination of NELM is the simplest,
crudest way to get at a factor, but it's something anyone can
understand. It may not be precise, but it's the best method I know.

AND, it's the factor used in the application of Carlin's formula. If
it's applied incorrectly, the predicted results will be wrong.

In summary, let me say that I have spent a lot of time talking
about areas where we disagree and very little about areas where
we agree, which is an awful lot. It's more efficient that way,
but it can be a little disconcerting to read.


Without that, no questions would be raised. And I've left one
unanswered.
Why did I plot some points at 6.0 instead of 5.8. I felt that on a
particular night when I observed TX Pisces (5.8) that its
instantaneous appearance indicated a darker sky than another night
when I needed to spend several minutes to acquire that same star with
much difficulty. It is an interpretation of my field notes to try to
more accurately reflect what I felt to be the conditions.

Despite all of
my criticisms, this was a very impressive study. Now I feel
obliged to try to replicate findings myself!


That could only be beneficial. I'd appreciate that.

edz
  #38  
Old October 6th 03, 09:49 PM
edz
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Default Limiting Magnitude in Binoculars

Tony, and others.

As a result of all the in-depth and detailed questions Tony raised, I
felt it prudent to post this summary of post-publish notes.

These additional notes should help provide understanding for some
apparent questions raised concerning the data in the "Limiting
Magnitude in Binoculars" article.

edz

Notes Oct. 6, 2003 supplement to "Limiting magnitude in Binoculars"
article.

I have since gone back thru my log to make note of those observing
nights not published, observing conditions not detailed and to note
some specific clarifications. This provides answers for some of the
questions raised post-publish on s.a.a. Also, this provides some
additional supporting documentation for the article "Limiting
Magnitude in Binoculars."

I have a page in my log book that I developed shortly after the start
of this exercise. It has sketches of Delphinus, Sagitta, the circlet
of Pisces and Ursa Minor. All the stars, 48 stars in total, than can
be used for NELM determination are plotted in these sketches. Often
throughout the many nights of log notes, a NELM observation, if not
recorded in detail, will simply be listed as a single value. These
values are the magnitudes of the stars shown on my sketch page. There
are several values, such as 4.37, 4.43, 4.68 and 5.05, that are
unmistakable since they only occur in one location within the four
constellations.

Aug 23 was recorded as NELM 5.8. Log notes indicate I was able to
acquire TX Pisces (5.8) instantly. Never before and never since have
I seen Tx Pis that easily. This was undoubtedly the best NELM I have
ever recorded from my home.

Very late observing improved on this night. This was the night of all
objects listed in the section "What Else Can be Seen by the Best
Binoculars?" I observed the North America neb., portions of the Veil
neb. and I suspected seeing nebulosity around IC1805.

Based on these records, after the fact I elected to tabulate
observations at NELM mag 6.0. It is significant that although these
NELM sky conditions have not been repeated, I have since been able to
duplicate on several occasions the BLM observations recorded on this
night.

On Sept. 10, observations were recorded very early in the evening,
completing the viewing session around 8:30 to 9:00 PM. This was full
moon night and I ended my observing session before the moon completely
interfered. Log indicates viewing was difficult, sky was washed out,
Sagitta was barely visible. This would have indicated difficulty
seeing the back end of the arrow, two equal stars both of mag 4.37.
The 5.0 star in Sge was not seen as it is always specifically noted if
seen. This star is usually not seen until some other mag 5 star is
seen first. Observations of Delphinus do not indicate seeing the 5.05
star off the end of the tail or the mag 4.68 star just off the sw edge
of the diamond body. This is a difficult star and is always noted if
seen. Maximum NELM seen Sept. 10-11 was 4.4 Del and 4.37 Sge.

On Sept 12, I wrote a note "better than last night, 5.0?". In my
notes, I questioned marked the 5.0. This would have been an
indication that I was questioning whether or not I saw the 5.0 mag
star in Sagitta, probably because I did not note seeing the 5.05 star
off the tail of Delphinus. Also I did not specifically note seeing
the mag 4.68 star just off the body of Del.

Sept. 14th includes a note to the effect "clearly better than any of
the three previous nights." Although that note in itself is not
definitive, it is a common practice of mine to sometimes write short
notes referring to improving conditions as it reflects a notation of
relief from previous difficult conditions, kind of like a written sigh
of relief. Sketches made on the 14th show NELM reached 5.0 direct and
5.2 averted, but these were well away from my target area and even
further away from the moon.

Sept. 25 notes were not included in the BLM Observations section.
They are the body of the work that was the basis for determining the
affect of changes in aperture. The observations are included in my
BLM analysis.

Skies started out around 8PM at NELM 5.0 Sge. Seeing was poor to fair
with a thin haze. NELM deteriorated by 9 PM to 4.68 Del and later
even lower to 4.4 Sge and 4.43 Del.

At NELM 5.0, 20x80s saw BLM of 10.76 and two stars of 10.83.
The16x60s saw BLM of 10.6. At NELM 4.7 to 4.4, 15x70s saw BLM of 10.6
and 16x70s saw BLM of 10.6 in worsening conditions.

These Sept. 25 observations support the observations of Sept. 10, 11
and 12 plotted for the lowest NELM of 4.8 and 4.4. Had these Sept 25
observations been used instead, the resultant slope of the actual
observations would be even flatter than that shown plotted.

Minor observation notes were entered on Aug. 31, Sept. 5 and Sept 6.
NELM varied from 5.8 to 4.8. Additional observations are recorded for
8x42, 10x50, 12x50 and 16x70 over various nights of conditions ranging
from NELM 5.0 to 5.8.

I stated that I find it easier to observe BLM thru the lens than I
find it to observe stars at the limits of NELM. Having reviewed these
notes, I believe there is reasoning behind this. There is so much
(50°) brightly lit sky pouring light into the eyes during the NELM
assessment that it makes observations difficult. During binocular
observation for BLM, even though stars are difficult to acquire at mag
10.0 to 10.8, the area of the sky lighting the eye is only 3° to 6°.
So much less light thru the lens provides for a much easier filed of
view for the eye to look at. This shows the affect of contrast
improvement by apparent darkening of extended background sky. I
believe this is what seems to make it easier to observe at the limits
of BLM vs the limits of NELM even though still it may take time to
acquire targets in both assessments.

edz
  #40  
Old October 7th 03, 11:46 AM
edz
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Default Limiting Magnitude in Binoculars

(David Knisely) wrote in message . com...
(edz) wrote in message . com...

Aug 23 was recorded as NELM 5.8. Log notes indicate I was able
to acquire TX Pisces (5.8) instantly.


Be careful here, as TX Piscium is a variable star (runs from as bright
as 4.79 to as faint as 5.2 or so). It is also a *very* red star (a
"Carbon Star", among the reddest known). It may not be a good star to
be doing a NELM estimate on. 22 Piscium is not far away and it is
about 5.58, so that might fit the bill better. Clear skies to you.

David Knisely
Prairie Astronomy Club:
http://www.prairieastronomyclub.org


Hi David,
You say
TX Piscium is a variable star (runs from as bright
as 4.79 to as faint as 5.2 or so).


I checked TX Pis with AAVSO and got 5.8 as the current (August) value.

There's no question it is by far the faintest in the circlet, #7 Pis
next faintest is 5.2 and is easily seen in comparison. I can always
see the small group north west of the circlet, 55Peg, 57peg, 58Peg,
59Peg containing 5.3 and 5.4 stars before I can see the circlet. TX
is still fainter than these.

In the two years I've been using the circlet as a reference, up until
recently, I've never been able to see TX. I'm assuming it is now not
near minimum. However I still have never been able to see 16Pis,
21Pis or 22Pis, all nearby to TX, all very close in mag, all brighter
than 6.0.

Usually when I can see TX, I can also see the 5.7 mag star off the
east end of the tail of Delphinus.

edz
 




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