## Apparent & Absolute Magnitude

Some stars appear very bright but are actually fainter stars that lie closer to us. Similarly, we can see stars that appear to be faint, but are intrinsically very bright ones lying far away from Earth. The Greek astronomer Hipparchus was the first to categorise stars visible to the naked eye according to their brightness. Around 120 BC, he invented six different brightness classes, called magnitudes, where the brightest stars were magnitude 1 and the faintest were categorised as magnitude 6. Today, astronomers use a revised version of Hipparchus's magnitude scheme called 'apparent magnitudes', as well as 'absolute magnitudes' to compare different stars.

### Apparent Magnitude

The power radiated by a star is known as its luminosity. However, the apparent magnitude, m, is the power received by an observer on Earth. Since we now can see very faint stars using telescopes, the scale extends beyond the magnitude 6 that Hipparchus marked down as the faintest on his scale.

Figure 3.4: Apparent magnitude scale and observational limits

As you can see, the magnitude numbers are bigger for faint stars, and magnitudes are negative for very bright stars. Since the scale is logarithmic, a magnitude 1 star is 100 times brighter than a magnitude 6 star, i.e. the difference between each step on the scale is equal to a decrease in brightness of 2.512 and (2.512)5 = 100.

### Absolute Magnitude

Comparing apparent magnitudes is a useful reference for astronomers, and these often appear next to stars on star maps. Apparent magnitude, however, does not tell us about the intrinsic properties of the star, so it is necessary to use the concept of absolute magnitude.

The absolute magnitude, M, of a star is defined as what the apparent magnitude of that star would be if it were placed exactly 10 parsecs away from the Sun. Most stars are much further away than this, so the absolute magnitude of stars is usually brighter than their apparent magnitudes.

To calculate the absolute magnitude for stars, we use the following equation:

 M = m - 5 log (D/10)

The value m-M is known as the distance modulus and can be used to determine the distance to an object, often using the following equivalent form of the equation:

 D = 10 (m-M+5)/5

 Star(Bayer) Star(Proper) Parallax(arcseconds) Apparentmag. (m) Absolutemag. (M) α Canis Majoris Sirius 0.37921 -1.44 1.45 α Carinae Canopus 0.01043 -0.62 -5.53 α Boötis Arcturus 0.08885 -0.05 -0.31 α1 Cenaturi Rigel Kent 0.74212 -0.01 4.34 α Lyrae Vega 0.12893 0.03 0.58 α Aurigae Capella 0.07729 0.08 -0.48 β Orionis Rigel 0.00422 0.18 -6.69 α Canis Minoris Procyon 0.28593 0.40 2.68 α Orionis Betelgeuse 0.00763 0.45 -5.14 α Eriadani Achernar 0.02268 0.45 -2.77

Table 3.2: Apparent and Absolute Magnitudes for the ten brightest stars on the night sky

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Last Update: 14 May 2013