## Absolute Magnitudes

The brightness of a star – as seen to the naked eye on Earth - depends on it's luminosity and it's distance from Earth. If two different stars have the same magnitude it does not mean they have the same absolute brightness or have the same size. To compare stars properly, the concept of absolute magnitude has been introduced.

The absolute magnitude of a star is the apparent magnitude it would have if it were observed from a distance of 10 parsecs. Since most stars are much further than 10 parsecs away, they would be brighter if observed at a distance of 10 parsecs. This means their absolute magnitudes are more negative than their apparent magnitudes.

The relationship between absolute magnitudeapparent magnitudeand distance away (measured in parsecs) is given by the formula

The apparent and absolute magnitudes of some stars, together with their distances from Earth, are given in the table below.

 Star Apparent Magnitude m Absolute Magnitude M Distance in parsecs Sirius -1.46 1.4 2.65 Canopus -0.72 -4.9 69 Alpha Centauri -0.10 4.3 1.32 Procyon 0.38 2.7 3.4 Betelbeuse 0.50 -7.0 320

The equation given above is illustrated here for Canopus.