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Memo
professor emeritus
Reged: 11/05/04
Posts: 529
Loc: Bogotá, Colombia
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Hi, I just want to know if there's a general rule to calculate the theorical highest magnitude that a given telescope can show.
TIA
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Guillermo Castaño (SIRIO)
Orion XT8i / Intelliscope
Bushnell 10x50
Green eyes -0.25 Astigmatism
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Serg
member
Reged: 10/26/04
Posts: 63
Loc: Ontario, Canada
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As a general guideline, 50x per inch of aperture. However, you can only ever push it this far under the most ideal of conditions (perfect seeing, transparency, etc)
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MMICKELS
Aluminum Knight
Reged: 01/20/04
Posts: 25192
Loc: The Land of Shake and Bake
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Yes there is. I'm sorry, but I don't have the formula to figure it out. I'll try to contact David Knisely. I'm pretty sure he'll know.
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Mark
"The only thing wrong with immortality is that it tends to go on forever."
Herb Caen
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12592
Loc: Cumberland, R I , USA42N71.4W
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Depending on the quality of the scope
my cheap 60mm scope 35x to 45x per inch. I used it up to 138x, or 58x/inch
my mediocre 76mm NewtCass about 40x to 45x. best highest was at 160x for 53x per inch.
my good C5 5" SCT, 45x to 55x per inch, and 65x to 75x on close doubles, seeing permitting. 275x in the C5 gives a pretty good image, I've observed planets at 275x.
my very good TV85 ref., 55x to 60x per inch and 70x to 75x on close doubles
Best high powered view of a double in my CR150 ref was at 450x, that's 75x. I've had it up to 600x to see if I could split 16Vul, a 0.8" double. Best view at 600x, I got to see about 20% overlapped Airy disks. That's 100x per inch.
Most high powered viewing is done at 30x to 40x per inch.
edz
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Anonymous
Unregistered
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I don't know what the formula is, but the program 'Newt' says your 8" theoretical limit is 13.3.
Steve E
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MMICKELS
Aluminum Knight
Reged: 01/20/04
Posts: 25192
Loc: The Land of Shake and Bake
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Hmm, I read the question as magnitude, not magnification. Memo I apologize if I've gotten it wrong.
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Mark
"The only thing wrong with immortality is that it tends to go on forever."
Herb Caen
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12592
Loc: Cumberland, R I , USA42N71.4W
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opps
edz
I have seen to mag 13.1 with the 5" SCT.
I've seen to mag 11.7 with the TV85
It will vary considerably with the naked eye sky magnitude and the magnification you use in the scope. Lower magnifications will not allow reaching the scope limits. These limits were reached in mag 5.8 skies with about a 1.25 to 1mm exit pupil.
edz
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Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
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MMICKELS
Aluminum Knight
Reged: 01/20/04
Posts: 25192
Loc: The Land of Shake and Bake
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Ed, is there a way to calculate the highest theoretical limiting magnitude for a given aperature? (I understand this would be limited by other factors, EP's, LP, ect. )
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Mark
"The only thing wrong with immortality is that it tends to go on forever."
Herb Caen
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David Knisely
Postmaster
Reged: 04/19/04
Posts: 6785
Loc: Beatrice, Nebraska
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Quote:
Hi, I just want to know if there's a general rule to calculate the theorical highest magnitude that a given telescope can show.
TIA
Humm,... let's see,... if I push just enough of these buttons on my calculator... Aha! The answer is: "Umpteen Gazillion" power! :-)
Seriously, there is no 'theoretical' limit on magnification, as with a long enough focal length telescope and a short enough focal length eyepiece (magnification = telescope focal length divided by eyepiece focal length), you can go as high as you can find an eyepiece for. However, if you mean *usable* magnification, there is a very rough limit, but it isn't hard and fast. There are some people who will quote the 50x to 60x per inch of aperture "guideline", and for many purposes, this can be a good rule to follow. However, there are times when people might have to exceed this limit at least to a mild degree in order to pick out one kind of detail. Generally, for a lot of planetary observing, I don't like to go much higher than about 38x per inch of aperture, but there are times when I may push towards the 50x per inch level. For resolving detail in a few select planetary nebulae with larger apertures, I have gone from 45x per inch all the way to 72x per inch (720x on my 10 inch on NGC 6543). For elongating or resolving really tight double stars, I have pushed my Nexstar 9.25 inch SCT to 918x (which is 99x per inch of aperture) to get the Airy disks large enough to detect notching or elongation features. However, viewing other objects at this rather ridiculous power is useless, as most of what you will tend to see is dim fuzzy detail at best. I would consider powers of 100x per inch and above to be "empty magnification", with no useful purpose (except for perhaps some unsavory telescope retailers, who use these power "claims" to sell telescopes). Overall, I would probably say that staying under 60x per inch of telescope aperture is probably a good guideline to follow, and much of the time, you will want to use quite a bit *less* than this level of magnification. Just as an aside, Jeff Medkeff and a friend took the 24 inch Clark refractor at Lowell Observatory in Flagstaff, Arizona to some incredible powers just for fun by stacking a series of Barlows and using the shortest eyepiece they could find. The images were, of course, totally useless, but it was fun to note just how high they had gone (it was, I think, well in excess of 10,000x!). Clear skies to you.
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David W. Knisely
Hyde Memorial Observatory
http://www.hydeobservatory.info
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Cerberus
Carpal Tunnel
Reged: 10/16/04
Posts: 2689
Loc: Newton, KS 67114
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I can see that on a department store scope: 10,000X power! 
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12592
Loc: Cumberland, R I , USA42N71.4W
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Yes,
In fact threre are several formulas. Sidwick in "Amatuer Astronomer's Handbook provides a table of comparison to show the differences with values derived by observation.
m=6.5-5logd+5logD,
where d is the diameter of the eye pupil and D is the diameter of the aperture, both in inches. This formula assumes the faintest star that can be seen naked eye is mag 6.5. Insert the appropriate value for your sky conditions.
If you would like to go over to the Binocular Forum and access the post "Links to Web", in that post are four or five links to some of the most influential papers ever written on limiting magnitude (mine NOT inculded).
You must read the paper written by Bradley Schaefer. He clearly shows that limiting magnitude is dependant on the magnification in use. For instance, a 6" scope used at 100 power will see stars a full magnitude deeper than when used at 30 power. He also shows that the steepness of the curve flattens out considerable at higher magnifications.
Then read Nils Olof Carlin's analysis of Schaefer's paper and finally Carlin's paper on estimating LM in binoculars (with which I don't completely agree).
Also read the papers by Roger Clark and Mel Bartels, Optimum Detection Mmagnification, which is related to LM.
Links in Binocular Forum
edz
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Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
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Memo
professor emeritus
Reged: 11/05/04
Posts: 529
Loc: Bogotá, Colombia
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Ups, sorry, I didn't explain myself very well (limitations with my english).
I know how to calculate the highest magnification of a scope (40X, 300X, etc).
I want to know how you calculate the apparent magnitude of the faintest object you can actually see. (5.6, 10,3, etc).
Thanks and sorry
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Guillermo Castaño (SIRIO)
Orion XT8i / Intelliscope
Bushnell 10x50
Green eyes -0.25 Astigmatism
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Memo
professor emeritus
Reged: 11/05/04
Posts: 529
Loc: Bogotá, Colombia
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Quote:
Hmm, I read the question as magnitude, not magnification. Memo I apologize if I've gotten it wrong.
You were right
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Guillermo Castaño (SIRIO)
Orion XT8i / Intelliscope
Bushnell 10x50
Green eyes -0.25 Astigmatism
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lighttrap
Reged: 02/06/04
Posts: 3833
Loc: cloudy, foggy, humid NC, US
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Memo,
Here's a link from the Useful External Links pinned to the top of the Beginner's forum. Limiting Magnitude Table
Note that it gives 2 different formulae at the bottom, for those that like to do their own number crunching. Also note that I think even the lower set of values given is somewhat optimistic and would require good conditions and seeing. Personally, I don't think you can pin down exact numbers with a calculator. Rather, it depends on conditions, magnifications, and the skill of the observer. You can get a rough approximation with these charts, but just be aware that even experts differ on how to best calculate these figures. And experts certainly differ on their experiences trying to push these numbers in actuality.
Mike
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18" Starsplitter II f/4.5
8" Hardin Dob f/6
C5 workhorse mini SCT f/10 or f/6.3
70mm TV Ranger dual purpose birding/astro
77mm Leica Televid APO
16x70 Fujinons on UA Deluxe Mt.
12x50 Nikon SE
8x30 Nikon E2s
and many others
Edited by lighttrap (01/11/05 07:52 AM)
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12592
Loc: Cumberland, R I , USA42N71.4W
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The formula in Method 2, listed in the table provided in Mike's link, is the same formula I provided above.
m = 6.5 - 5logd + 5logD ,
where d = eye pupil and D = aperture, in inches
6.5 represents an assumption of NELM, sky magnitude.
The portion of the formula [ 6.5 - 5logd ] becomes 9.5 if you insert
7mm (7/25.4) for the eye pupil and 6.7 for sky magnitude (NELM).
or
6mm (6/25.4) for the eye pupil and 6.4 for sky magnitude (NELM).
or
5mm (5/25.4) for the eye pupil and 6.0 for sky magnitude (NELM).
There are so many variables that most every table published is calculated for the variables selected by that author. Unfortunately, it is almost always not stated what values were used for the variables.
What is even more significant is none of these tables of values even begin to address the affect of magnification. The graph shown in Bradley Schaefer's article does address magnification. Of course, the intent with these tables is to give a maximum value, and with the exception of the graphs provided by Bradley, that is always given for optimum magnification. In the case of limiting magnitude that would be magnifications on the order of 20x to 30x per inch, or magnifications that give exit pupils of about 1.2mm to 0.8mm.
edz
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Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
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BillFerris
Carpal Tunnel
Reged: 07/17/04
Posts: 2582
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Hi Guillermo,
Here's a site where you can get a reasonable estimate of what telescopic limiting magnitude should be given a range of variables: Determination of the Limiting Magnitude of a Telescope
The program was originally written by Brad Schaefer, who's done significant research into this question. Simplified formulas give you a ballpark number but don't account for all the relevant variables. These include quantifiable variables such as magnification used, the elevation of the site, color index and zenithal distance of the star and the seeing. Other variables include factors like the experience and age of the observer, and naked eye limiting magnitude.
Schaefer's program takes all of the above into consideration in calculating a theoretical telescopic limiting magnitude. It's not perfect for all observers but is about as good as you'll get.
Regards,
Bill in Flagstaff
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Grand Canyon Adventure
Lowering the Threshold
18" Obsession
4.5" Meade 4500
10x50 Swift Audubon
Cosmic Voyage
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celestial_search
Carpal Tunnel
Reged: 11/18/04
Posts: 2285
Loc: Iowa, USA
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Ed:
Thanks for that info. I liked what you said in your bio about what happened to your running at age 45. Now I don't feel so bad! 
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Frank
C-11 XLT
8" f/6 Newt on GEM
Tak FS-102II
SV 80L Triplet APO
Orion Mak 127mm
EQ-6 Mount on pier in backyard observatory
CG-5 AS (GOTO)
Surveyor's tripod/Hercules single-arm alt-az mount
SBIG ST-5C CCD and Canon Digital Rebel XT
Oberwerk 15X70s and Pentax 10X21s
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RCS
member
Reged: 12/30/04
Posts: 78
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Ok I am confused. I thought the higher the magnification the dimmer the object will be. How do you see brighter objects as you increase your magnification?
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12592
Loc: Cumberland, R I , USA42N71.4W
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At age 30-35, I could just barely get close to a 6:00 mile for a 5k, and for 10 miles the best I could do was 67 minutes. I couldn't even think of running a marathon.
At 45, I was averaging 5:07 for a 5k, ran a 4:41 indoor mile and and ran the 10 mile in 52:17. I'd run 20 mile runs on Saturdays for fun. Did finally get a few marathons under my belt, but never broke 6:00 pace.
It's not how old you are, it's how well you apply what you learn to what you do.
edz
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Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 12592
Loc: Cumberland, R I , USA42N71.4W
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Quote:
Ok I am confused. I thought the higher the magnification the dimmer the object will be. How do you see brighter objects as you increase your magnification?
Increasing to excessive magnification will result in greater difficulty in seeing objects, but not increasing from minimum magnification to optimum magnification. Different sources will quote a somewhat different range, but optimum magnification for LM is gererally thought to range just above or below that which gives an exit pupil of 1mm.
You definitely need to go read the articles on ODM, Optimum Detection Magnification.
As far as stars are concerned, they do not appear dimmer or brighter with changes in magnification. However, minimum magnification does not allow you to fully take advantage of the maximum ability of your aperture. Schaefer describes that in his article and I proved that in my Limiting Magnitude studies with binoculars.
Try this for yourself;
take a 4" or 5" scope out on a good night. Put in an eyepiece that gives you 30x to 40x. Observe this chart and write down the stars you can identify. You don't need to do the whole chart, pick the stars in one section if you'd like. Now put in an eyepiece that gives you 100x and observe the chart again. In which observation did you see more and fainter stars? The table of identifying star labels and magnitudes is linked from the chart description.
Chart of M45 with stars labeled to mag 12.0
With a 5" scope at about 30x to 40x, in mag 5 skies, you won't get much above stars to mag 11.0. With the same scope at about 100x in mag 5 skies, you should reach stars to mag 12.0.
Under mag 5.5-5.8 skies with my 5" SCT at about 100x to 150x, I can see to mag 13.1, the star just east of M57. I have never seen it at low magnification.
edz
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Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
Edited by EdZ (01/11/05 10:52 AM)
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