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## The Magnitude Scale in Astronomy

March 7, 2010 6 comments

Astronomers describe how bright an object is using something called the magnitude scale. They might describe a bright star as being “first magnitude”, or the limit of human naked-eye observing as being “around 6.5 mag”. But what exactly do they mean?

The Greek astronomer Hipparcus, in the second century BCE, developed an early magnitude scale in which he grouped the stars in the night sky into six magnitude classes; the twenty brightest stars were given magnitude class of 1, the next brightest group a magnitude class of 2, all the way down to the faintest stars, at the limit of the human detection, which were given a magnitude class of 6.

This system is similar to that used today, except we have expanded the scale in both directions: for fainter objects, as our use of telescopes allows us to explore beyond the limit of the human eye; and for brighter objects such as the Moon and the Sun.

The faintest object detectable by the Hubble Space Telescope has a magnitude of around 32, whereas the Sun has a magnitude of around -27.

Our modern magnitude scale is logarithmic, meaning that for each unit you go up the scale, you get dimmer by a factor of 2.512 (this seemingly arbitrary number is chosen so that objects separated by 5 magnitudes – such as the brightest star in the night sky compared with the dimmest star visible to the naked eye – differ in brightness by a factor of 100, i.e. 2.512 to the power of 5).

So how much brighter is the Sun than the faintest star visible to the Hubble Space Telescope? The answer is 2.512 to the power of 60, or 10 million million million million times brighter. Those kind of astronomical numbers are impossible to visualise, and difficult to deal with, never mind to write out, and so astronomers opt for the much more manageable, if no more intuitive, magnitude scale.

Examples of magnitudes of astronomical objects

Full Moon: -12.6
Venus at its brightest: -4.6 (brightest planet)
Sirius -1.5 (brightest star in the night sky)
Vega 0 (Vega is part of the constellation Lyra the Harp, in the Summer Triangle)
Limit of an urban sky: 3 to 4
Limit of the human eye: 6.5 (depending on your eyesite of course

All of these numbers are apparent magnitude, that is the brightness as seen from Earth, and not a measure of an object’s intrinsic brightness.