Telecope Limiting Magnitude- A Different View

[Robh (Rob)]

The limiting magnitude of your telescope is the magnitude of the faintest star that can be seen through your telescope.

The commonly used formula for the limiting magnitude of a telescope is M = 9.1+5 logD where D is the diameter of the aperture in inches. The number 9.1 can be considered as the limiting magnitude of a 1 inch scope and 5 logD as the gain in magnitudes due to the extra light gathering capacity of a larger scope. Notably, the formula gives the false impression that the telescope limiting magnitude depends solely on the aperture diameter.

However, this formula is the result of some basic assumptions applied to the more general formula M = m + 5 log(D/d) where m is the naked-eye limiting magnitude (or magnitude of the dimmest star seen with the naked eye) and d is the diameter of the pupil of the observer's dark-adapted eye in inches. The naked-eye limiting magnitude will itself depend on factors such as the skyglow, seeing, transparency and the size of the observer's pupil. These factors are often very significant in determining the faintest
magnitude seen in the telescope.
The earlier formula can be obtained by assuming the naked-eye limiting magnitude m = 6 and the pupil size d = 6mm (0.24 inches).
Thus, M = 6 + 5 log(d/0.24) = 6 - 5 log 0.24 + 5 logD = 9.1 + 5 logD as above.

Therefore, a more realistic view, would be to use a set of naked-eye limiting magnitudes:
Very dark sky 7, rural sky 6, suburban sky 5, city sky 4.

We can then generate a table of telescope limiting magnitudes under varying skies (magnitudes rounded off to the nearest 0.5) ...

Size of aperture in inches
2 3 4 6 8 10
Very dark sky 11.5 12.5 13 14 14.5 15
Rural sky 10.5 11.5 12 13 13.5 14
Suburban sky 9.5 10.5 11 12 12.5 13
City sky 8.5 9.5 10 11 11.5 12

Size of aperture in inches
12 16 20 24 30 36
Very dark sky 15.5 16 16.5 17 17.5 18
Rural sky 14.5 15 15.5 16 16.5 17
Suburban sky 13.5 14 14.5 15 15.5 16
City sky 12.5 13 13.5 14 14.5 15

Seeing and transparency (and perhaps, skyglow) are so variable at any site that they cannot be figured accurately into these results. No two days are ever the same!

Part of the reason for this thread is to illustrate the dangers in using a formula blindly as “the be all and end all”. Many a time I’ve heard amateurs say they have seen stars beyond the specs of their telescope or, conversely, have wondered why they are having trouble seeing a “bright” object in the suburbs.

Regards, Rob

Just realised I can't get table values to line up.
If you want this page intact, you can download it as a Word file below.

[Davekyn (David)]

Thanks Rob,
I don't understand it all...but its all sinking in slowly and helps.
Cheers

[Robh (Rob)]

Dave,

Probably didn't help that I couldn't line up the table values in this editor, so I've attached the whole page as a Word document.

Apologies, Rob.

[lacad01 (Adam)]

Good info, thanks for posting.

[mozzie (Peter)]

great read rob very interesting how the people in cities do miss a lot due to light pollution

[pgc hunter]

interesting.

I have seen Mag 15.9 stars from my outer suburban backyard with my 12" dob, on a night with excellent transparency.

[Robh (Rob)]

Originally Posted by pgc hunter

I have seen Mag 15.9 stars from my outer suburban backyard with my 12" dob, on a night with excellent transparency.

Wow! Love to have your night vision. I have trouble getting to 14th magnitude with my 12 inch DOB at Linden (Blue Mountains). Eye sensitivity and pupil diameter can be quite variable. One of my mates easily sees naked-eye stars a good magnitude or so fainter than I can.

Regards, Rob.

[pgc hunter]

Originally Posted by Robh

Wow! Love to have your night vision. I have trouble getting to 14th magnitude with my 12 inch DOB at Linden (Blue Mountains). Eye sensitivity and pupil diameter can be quite variable. One of my mates easily sees naked-eye stars a good magnitude or so fainter than I can.

Regards, Rob.

thanks! But actually my eyesight is crap and my night vision even crapper

[astroron (Ron)]

Originally Posted by pgc hunter

thanks! But actually my eyesight is crap and my night vision even crapper

Well that makes most peoples eyesight worse than yours

[pgc hunter]

Originally Posted by astroron

Well that makes most peoples eyesight worse than yours

are you sure? My eyesight is genuinely crud!