Limiting Mag calculation

[johnrt]

Just learning this so hope this is correct.

If I assume the diameter of my pupil is 6.4mm, and my limiting visual mag is 6, then I can calculate the limiting mag of my 72mm refractor thus.

(72/6.4)^2 = 11.25^2

ratio = 126.56

using Pogson's Relation;

m-n = -2.5 log fm/fn

m-n = -2.5 log 126.56

m-n = -2.5 x 2.1

m-n = -5.25

So given my limiting mag by eye is 6, my limiting mag with my scope is 11.25

(6 + 5.25)

[brianb]

Yes but you failed to allow for:

(a) light loss in the scope - probably about 20% i.e. 0.2 mags

( the effect of magnification, which darkens the sky background. Using a magnification of approx. 20 per inch spreads the light of the sky but leaves stars as points. The effect is to reduce the limiting mag. by approx. 1.5 mags.

In my experience a 3" scope will reach mag. 13 quite easily, given good dark skies. I regularly achieve mag. 16 with my 11" SCT.

[acey]

To make the calculation a wee bit quicker I usually do it as 5log(aperture ratio) i.e. 5xlog(72/6.4) = 5.3.

Good points about light loss and sky darkening. Does the 1.5 mag figure come from theory or observation?

[brianb]

Does the 1.5 mag figure come from theory or observation?

Observation: some people claim 2.0 with small apertures but medium/large apertures usually suffer a bit from star image bloating by poor seeing. And values vary depending on what you can just glimpse occasionally with averted vision, what you can hold steadily with averted vision and what you can hold steadily with direct vision.

[acey]

I've had a look at Clark's Visual Astronomy Of the Deep Sky to see how he does the limiting magnitude calculation there. If I understand correctly, he effectively assumes that when the telescope is at highest power then the sky attains maximal darkness, making visibility equivalent to what you would see with the naked eye at a maximally dark site. The calculation then reduces to the assumption you make of the maximum naked-eye limiting magnitude. Clark assumes 8.5 , which I think turns into adding 2.5 to the magnitude calculated from Pogson's formula for a sky of magnitude 6. Adding 1.5 would be equivalent to taking 7.5 as the maximum limiting magnitude. Clark also takes light loss into account. But in practice I think things are made more complicated by the factors you suggest: star bloating, variable accuity etc.

[perrin6]

Try this handy-dandy limiting magnitude calculator:-

http://www.scopecity.com/limiting-magnitude-calculator.cfm

Alan

[acey]

Nice. Would be interesting to know how it does the calculation - it returns diminishing limiting mag for very high powers (the turning point appears to be about x600 for all apertures with the default seeing value) so there's some further assumptions going on in there. Will see if I can find the S&T article online - my issues don't go back far enough.

[johnrt]

Interesting discussion.

I was approaching this from a purely theoretical standpoint as part of a forthcoming project writeup, but your discussion has has given me some ideas of other things to note and discuss in my report.

[acey]

You might find these useful:

Visual astronomy of the deep sky - Google Books

Limit of Telescopic Photopic Vision

1990PASP..102..212S Page 212

The latter is the paper on which the magnitude calculator appears to be based. The seeing assumptions I was wondering about are given by equation (7).