Naked Eye Limiting Magnitude: Assessing Sky Brightness

There are a variety of ways of measuring your night sky quality, and one of the most effective ways is by looking for the faintest star you can find with your naked eye, and noting its brightness, or magnitude. This provides what is known as Naked Eye Limiting Magnitude, NELM.

Of course just randomly casting about the sky for faint stars can lead you on a merry chase, and so a very useful method is to use one specific constellation – one you can always see, no matter what time of year – and look only at stars within that one constellation. This narrows the field somewhat, and makes your task that much easier.

For observers in Europe and North America the constellation of Ursa Minor, the Little Bear, provides an excellent choice for estimating NELM.

The overall shape of Ursa Minor is made up of seven bright-ish stars, but around and amongst these are many more fainter stars.

Ursa Minor

Bright Star Name (Bayer Designation)	Magnitude
Polaris (α)	1.95
Kocab (β)	2.05
Phercab (γ)	3.00
Yildun (δ)	4.35
Urodelus (ε)	4.20
Ahfa al Farkadain (ζ)	4.25
Anwar al Farkadain (η)	4.95

Even some of these “brighter” stars might not be visible from city centres. For example, if you are observing from a site with Bortle Class 8 you would not see η-UMi, while those unhappy stargazers under a Bortle Class 9 sky would only be able to pick out the three brightest stars, α-, β-, and γ-UMi. Only at Bortle Class 7 and darker will you make out all seven of the main stars of Ursa Minor.

But what if you’re at a good dark sky site? Well, you’re going to need a longer list of magnitudes, and a more detailed map of Ursa Minor.

Star Number on Above Map	Star Name	Visual Magnitude	Bortle Class
1	α UMi	1.95	9
2	β UMi	2.05	9
3	γ UMi	3.00	9
4	ε UMi	4.20	8
5	5 UMi	4.25	8
6	ζ UMi	4.25	8
7	δ UMi	4.35	8
8	4 UMi	4.85	7
9	η UMi	4.96	7
10	θ UMi	5.00	7
11	11 UMi	5.02	6
12	19 UMi	5.45	6
13	24 UMi	5.75	5
14	λ UMi	6.30	4
15	20 UMi	6.35	4
16	3 UMi	6.40	4
17	π1 UMi	6.55	3
18	HIP74818	6.65	3
19	14 UMi	7.35	2

The stars in the map and table above have been numbered (by me – these aren’t official designations) from 1 to 19, with 1 (Polaris) being the brightest, and 19 (14 UMi) being the dimmest. You will only be able to see all 19 numbered stars from exceptionally dark places, virtually free of light pollution, what Bortle called “typical truly dark sky sites”. From my garden in the outskirts of a major city I can see numbers 11 and 12, but not number 13, giving me an NELM of 5.45.

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Limiting Magnitude

Astronomers describe the darkness of the sky under which they are observing by referring to the limiting magnitude, that is the magnitude of the faintest star we can see.

We might use a very broad brush approach, and describe a sky as “fourth mag” (roughly what you’d see from the suburbs of a big city) or “sixth mag” (very dark indeed, with almost all but the very faintest stars visible).

Orion Star Map showing stars down to approx. magnitude 4.5, or what you would see from a darker suburban site. In very light polluted big cities you would struggle even to see the three belt stars!

The absolutely faintest stars anyone can see with the naked eye in perfect conditions (i.e. looking towards the zenith on a moonless night) are around 8th mag (this is for someone with exceptional vision), and so we refer to a perfect sky, utterly free of light pollution, as being magnitude 8.

However, most star maps and charts will only list stars down to a more modest limiting magnitude of 6.5, which number is often used as the standard limiting magnitude of a very dark sky.

The limiting magnitude of a sky has implications for how many stars you can see with the naked eye, and as a very rough rule of thumb for every one point of magnitude darker your sky is, you will see three or four times as many stars.

There are around 50 stars of magnitude 2 or brighter, which will therefore be visible in even the most light polluted skies with limiting mags of 2. Of course these 50 stars are spread over the whole sky so you’ll only ever see around half of them at once, and so in a very light polluted place like Manhattan, Las Vegas or Tokyo you can see around 25 stars only.

In the centre of other big cities, where the limiting magnitude is 3 you will see roughly 100 stars, and from the suburbs under magnitude 4 skies you will see around 300 stars (these star counts, and the ones that follow, are for half the sky only, i.e. in your visible hemisphere)

Once you get to a limiting magnitude of 5 in rural areas with a bit of light pollution you can expect to see 1000 stars or more. Further from big towns and cities, where your sky has a limiting magnitude of 6 you’ll see 3000 stars. At the limit of most star maps and charts, limiting mag 6.5, there are around 4500 stars to be seen in the sky at any one time, and so there are around 9000 stars altogether – over the whole sky – that are magnitude 6.5 or brighter. (As a little aside, the planetarium that I used to run in Glasgow Science Centre, had a Carl Zeiss starball projector that claimed to show 9000 stars, and so was obviously built to show every star that would feature on any standard star map or chart).

And beyond that you’ll need a telescope or binoculars to see more. Remember, those 9000 stars are only a tiny fraction of the 100,000,000,000 stars in our galaxy!