Apparent Magnitude - Calculations

Calculations

As the amount of light received actually depends on the thickness of the Earth's atmosphere in the line of sight to the object, the apparent magnitudes are adjusted to the value they would have in the absence of the atmosphere. The dimmer an object appears, the higher its apparent magnitude. Note that brightness varies with distance; an extremely bright object may appear quite dim, if it is far away. Brightness varies inversely with the square of the distance. The absolute magnitude, M, of a celestial body (outside the Solar System) is the apparent magnitude it would have if it were 10 parsecs (~32.6 light years) away; that of a planet (or other Solar System body) is the apparent magnitude it would have if it were 1 astronomical unit away from both the Sun and Earth. The absolute magnitude of the Sun is 4.83 in the V band (yellow) and 5.48 in the B band (blue).

The apparent magnitude, m, in the band, x, can be defined as,

,

where is the observed flux in the band x, and and are a reference magnitude, and reference flux in the same band x, such as that of Vega. An increase of 1 in the magnitude scale corresponds to a decrease in brightness by a factor of . Based on the properties of logarithms, a difference in magnitudes, can be converted to a variation in brightness as .