Telescope Light Grasping Table

[Mr Q]

I thought this table would be useful for beginners to show them the faintest star magnitude any one size scope can detect.

Remember, this is for stars! For any other deep space object, the "surface brightness" of an object considers the object's size and intergrated magnitude to give the visual observer an idea of whether any one object can be detected or not. Most useful object data lists give the object's surface brightness as in the link below.

Also, this grasping table chart is for perfect sky conditions which rarely we ever have so perhapes 1/2 to 1 magnitude brighter (smaller number) than the chart gives would be a more practicable limit.

GRASPING TABLE

7000 BRIGHTEST OBJECTS

Perhaps these two links can be used as a sticky for this forum???

[sologuitarist61]

That is interesting - thanks for posting

[Eastridge]

Thanks for this.

[acey]

The limiting magnitude of a telescope is not solely dependent on aperture but also depends on the following additional factors:

Sky brightness

Eye pupil size

Observer acuity (how good your eyes are)

Adaptation brightness (i.e. the extent of the eye's adjustment to ambient light)

Telescope quality (cleanliness of optics, effectiveness of coatings etc)

Object and atmosphere (how high in the sky, how clear the air etc)

All of this makes tables of limiting magnitude rather meaningless and potentially misleading to beginners. More meaningful is to consider the relative gain of one aperture over another, i.e. if you can see stars down to magnitude X with telescope A then what magnitude do you expect to see with some other aperture. In that case there's a simple formula. Let A = bigger aperture and a = smaller aperture, and let G be the extra magnitude you'll see with the larger aperture A, compared with the smaller one. Then

G = 5log(A/a)

For example, suppose I can see down to magnitude 10 with a 50mm scope. Then with a 100mm scope the gain will be 5log(100/50) = 1.505. Hence I expect to see down to magnitude 11.5 with the 100mm scope, when used under exactly the same conditions.

Another question could be the gain you expect to see for a given aperture compared with what you can see with the naked eye. This would be more accurate than a table giving limit solely as a function of aperture, but is still far less accurate than the formula for the gain of one aperture versus another. The reason is that we look at the sky with two eyes, possibly also while wearing spectacles, and the sky and ground around us are not all at the same brightness: our adaptation brightness is set in relation to the brightest sources (e.g. the horizon or a neighbour's security light). When looking through the telescope we generally use one eye, we may or may not use spectacles, and if we put a hood over our head then the adaptation brightness is fixed by what comes at us through the eyepiece. Plus we've got to take account of telescope transmission coefficient and optical quality. All of these factors make it impossible to predict accurately what the gain will be for the telescope compared with naked eye.

If you're interested in seeing the maths then the paper by Bradley Schaeffer is the standard reference.

http://adsabs.harvard.edu/full/1990PASP..102..212S

In the "light grasp table" they've used the classical formula

M = 5logA + K

where M is limiting magnitude, A is aperture, and K is a constant. From the figures in the table I can see that they've used K = 2.7, i.e. they've just tabulated 5logA + 2.7 for various values of A in mm. Formulas of this type appeared in optics books in the 19th and 20th centuries but it has been known for at least half a century that the formula is inadequate, because of the factors I've already outlined (and which are discussed by Schaeffer). Instead the formula should be

M = 5logA + F

where F is a function of the other factors. But either way, the gain of one aperture over another comes out as G = 5log(A/a). If you look at the "light grasp table" you'll see that in all cases doubling the aperture is predicted to give a gain of 1.5 magnitudes.

The table also offers lowest and highest powers; I assume that these are just exit pupil calculations. From a quick look it appears that they haven't used fixed extreme values (the usual are 7mm and 0.5mm); it looks like they've taken a largest exit pupil of about 6mm and a smallest at about 0.6mm. E.g. from the figures for a 100mm scope:

Lowest power 17, highest 158.

Exit pupils 100/17 = 5.9mm. 100/158 = 0.6mm

A person with a dilated pupil size larger than 6mm will be able to use lower powers than the ones specified in the table. And for a person for whom diffraction in the eye becomes significant with an exit pupil of anything less than 1mm, the highest powers in the table will not be useable.

We all have different eyes and just have to find out from experience what our own are like, and what we can do with them.

[8kids]

I was satisfied until I read that chart I now need a bigger scope.

[acey]

As a follow-up it occurs to me that if people find some utility in a tabulation of the function 5logA + 2.7 then they might also find some use in a tabulation of 5logR, giving magnitude gain as a function of aperture ratio. This is tabulated below. As an illustration of its use, here are some examples.

1. I have a 100mm scope and I'm thinking of upgrading to 150mm. How much fainter will the faintest visible stars be, through the larger scope compared with the smaller? I calculate 150/100 = 1.5 and look in the first column for this figure. I see from the second column that the larger scope will show stars 0.88 magnitude fainter than my present scope.

2. I have an 8" scope and I'm thinking of upgrading to 10". What will the gain be? I calculate 10/8 = 1.25 and from the nearest values in the table (1.2 or 1.3) I see that the 10" will show me stars between 0.4 and 0.57 mag fainter than the 8", assuming identical viewing conditions. If I want a more exact figure then I just get a calculator and find 5log(1.25) = 0.48. The 10" will give me about half a magnitude more than the 8".

3. I want a bigger scope that will show stars a whole magnitude fainter than what I currently see. I look in the right column for a magnitude gain of 1 and find the nearest figure is for an aperture ratio of 1.6. So to get an extra magnitude I need to multiply my aperture by 1.6. If my present scope is a 10" I need to go to a 16". If I want a more exact figure then I use a calculator to find 10^(1/5) = 1.58. Note that going from a 100mm scope to a 160mm scope would give the same gain as going from 10" to 16" (though obviously the 16" would reach far fainter than any of the other scopes, assuming identical conditions).

How much of a magnitude increase do you need in order to make an upgrade worthwhile? That's a matter of experience - and also a question of how much the extra weight and cost will justify the gain you get.

R---- 5logR

1.1 0.21

1.2 0.40

1.3 0.57

1.4 0.73

1.5 0.88

1.6 1.02

1.7 1.15

1.8 1.28

1.9 1.39

2.0 1.50

2.1 1.61

2.2 1.71

2.3 1.81

2.4 1.90

2.5 1.99

[knobby]

Its all irellavant really, we all end up getting the biggest scope we can manage/afford anyway...

And even then we're just wondering if we could go... Just a little bit bigger

Seriously though thanks for the informative thread and the time taken for the lengthy replies.

[Mr Q]

Acey - Thanks for the info explanation. I understand it but wonder if it's too much for a very basic beginner to understand.

My intentions was to give a general, simple example of the limits of any one size aperture over another. Other conditions (transparency, light pollution, etc.) would be considered later when the beginner becomes acquainted with these conditions.

If there is another light grasping chart out there that's more practical, I hope someone will post it in this thread.

[acey]

Thanks Mr Q - my point was simply that there isn't really any such thing as a meaningful light grasp chart. There's an empirical formula that was proposed in the days when there was no light pollution and everyone observed with skies of mag 6 or better, but the formula was wrong then and is even more wrong now. Far better to think of the gain of one aperture over another under equivalent viewing conditions - the formula in that case appears to be pretty accurate. For the beginner the essential thing to understand is that sky and eye are as important as aperture. The common error is to assume that the more money you spend the more you'll see, when maybe the cash would be better invested in petrol or a plane ticket to reach a dark site with a pair of binoculars.

I also think that for beginners a list of 7000 DSOs may be a little ambitious. Anyone taking on a list of that size might want to consider the NGC, which has about 7800 listed objects, all discovered visually. The early 20th century professional astronomer Guillaume Bigourdan observed and positionally measured all of them down to his horizon limit (more than 6000), over a period of about 20 years, using the 12" refractor at Paris Observatory. That gives an indication of the sort of aperture sufficient to see nearly every DSO that was ever discovered by eye, assuming the sky is dark enough.

[Mr Q]

Acey - The DSO list was posted due to its arrangement by constellation and magnitude. I can't imagine anyone in modern times observing just most of them never mind all. Because of its listing of the brighter objects first, I find it very useful for varying sky conditions even though some constellations contain only a few objects bright enough for light polluted skies. I used to use the original SAC database and it took lots of time going through each constellation looking for the brighter objects and recently found this list to be very useable for all stages of observing experience. A very important (to me) part of the list is the surface brightness column, which some lists fail to include.

Yes, the list is extensive and perhaps intimidating to the beginner observer but one only has to look up the constellation in question, then look down the list of objects arranged by magnitude to determine if any one object can be observed under the observer's sky conditions.

While in a beginners' forum, how about some simple easy to read posts/links on beginners' essentials such as light pollution, celestial coordinates, surface brightness, seeing conditions, sky transparency, sky steadiness, etc. Perhaps grouped in stickies?

[paul schofield]

Great post, very interesting, thanks for the post I am off to look for a 14.2 magnitude star........maybe not, the sky is doing its usual cloud thing.

[Mr Q]

Paul - Though it's a big event to see what the faintest star your scope can detect, most of the time the sky conditions won't permit it. The chart I posted should be only a rough guide as the above post responders noted. Perhaps, with good sky conditions, you should be trying for a 13.5 mag star or better yet, an elusive galaxy near 12th mag. Practically speaking, that would be a fair challenge for your size scope providing those pesky give you a break.

After years of observing with my 10" newt, the faintest galaxy I observed from a dark sky site with good transparency and with little light pollution, was at 13th mag and was hard to detect with averted vision. From my back yard with slightly less favorable conditions, I detected a 12.5 mag. galaxy in Pegasus when it was near the zenith. Have I tried to get to the limits of my scope's magnitude detection visually? No, not yet. But I do try for challenging objects from time to time just to spice things up visually.

[jon1000]

Going to work but will take a look at this later, thanks.

[paul schofield]

Thanks for that Mr Q To tell the truth I would find it hard to locate a mag 6 star most of the time with my sky conditions.