The Bortle scale is a nine-level numeric classification which indicates the quality of the night sky based on the visible objects. As the Bortle number increases, the sky quality deteriorates, with Class 9 being an 'Inner-City' sky and Class 1 a perfect dark sky site.

The scale was developed by John E. Bortle and first published in Sky & Telescope magazine in 2001.

In the UK the best skies come into the Bortle Class 3.

The Sky Quality Magnitude (SQM) is a measurement of the brightness of the sky at or near the zenith, measured in terms of magnitude per square arcsecond.

Eg. if the sky has an SQM of 20.0 that is equivalent to saying that a light from a 20^th (apparent) magnitude star was spread over one square arcsecond of the sky.

The term arcsecond comes from an arc being divided up into seconds. There are 360 degrees in an circle, and each degree is divided into 60 minutes, and each minute is divided into 60 seconds. A square arc second has an angular area = one second × one second.

Magnitudes follow the Apparent magnitude, convention with each magnitude lower (numerically) meaning 2.512 × as much more light is coming from a given patch of sky. A change of 5 mags/sq arcsec means the sky is 100× brighter.

In the Leeds City Council area the SQM varies from 17.9 to 20.4 mags/sq arcsec, a difference of 2.5, meaning that the sky in the inner city is 10× brighter than in surrounding countryside.

SQM can be measured with Unihedron meters. (NB: LAS has two meters which members may borrow.)

Naked Eye Limiting Magnitude (NELM) refers to the faintest apparent magnitude of stars that may be detected, using averted vision, at or near the zenith with the naked eye & perfect vision.

The actual limiting magnitude will depend on your visual acuity. As we get older our eyes have less ability dilate. The pupils in a 25 year old can dilate up to ≈7mm in diamter, whereas the pupils of a 70 year old only dilate to ≈5mm. This represents a factor of 2× the area or a drop of ≈0.75 (apparent) magnitude.

At the limiting magnitude occurs when stars appear to be on the edge of our perception with averted vision, i.e. when not looking at them directly. Photons from the star will hit different parts of the retina randomly, so that at the limit, the star will appear to blink in & out of vision over a short period of time, as the eye 'integrates' images over a period of 1/30^th of a second.

Altitude and location also affects the NELM as in high altitudes reduce the air mass you're looking through, whilst greater humidity impairs the visibility.

The NELM is related to the SQM measurements by the formula:-

NELM=7.93-5*log(10^(4.316-(SQM/5))+1)

i.e. where the best achievable NELM is a magnitude of 7.93.

Sky brightness is shown in millicandela per square meter, where a millicandela is 1/1000^th of a candela, the SI unit of luminous intensity.

In Leeds the sky brightness varies between 7.5 mcd/m² in the inner city to 0.74 mcd/m² in the countryside.

You might think that a truly dark night sky would have a brightness of 0 μcd/m², but there is a background brightness level of about 174 μcd/m². This is comprised of light from zodiacal light (sunlight scattering off interplanetary dust); scattered light from the Milky Way; and airglow, which is a faint emission caused by the reionisation of atoms which have been ionised during the daytime by the sunlight.

The artificial brightness can be used to calculate how many times more brighter the sky is compared to a normal dark sky using this formula:-

[sky brightness] = ([artificial brightness in μcd/m²] + 174)/174

In the Leeds City Council area the sky ranges between 4.25 and 43.11 × the brightness of a naturally dark sky.

The apparent magnitude of a star is a measure of how bright it appears from Earth. The scale was introduced over 2,000 years ago by the Greek astronomer Hipparchus, who grouped stars into six categories. The brightest 20 or so were deemed to be 'first magnitude', slightly dimmer stars 'second magnitude', and so on until the barely visible stars were classed as 'sixth magnitude'.

Later it was recognised that our eyesight, once it has been given time to get used to darkness, has a logarithmic response. i.e. a Mag. 1 star is actually 2.512 times brighter than a Mag. 2 star, or 6.310 times brighter than a Mag. 3 star (2.512 x 2.512 = 6.310).

The six Magnitudes thus corresponds to a 2.512⁶ difference in brightness or 100x.

Today the scale has now been extended, so that brighter objects can have an apparent magnitude of 0 or even negative. The brightest star Sirius, for example, has an apparent magnitude of -1.44 and the Sun is a whopping -26.74, due to it's close proximity to Earth.