Advanced Stellar Magnitudes
Calculating Absolute magnitude is useful for comparing stars brightness.
In the last article I introduced the Magnitude Scale and described how there are two scales, one for Apparent Magnitude and the other for Absolute Magnitude. Apparent magnitude is a logarithmic scale of the brightness of an object seen from Earth. Absolute Magnitude is the Apparent magnitude if the object was a standard distance away (10 parsecs).
Apparent Magnitude is observed and measured, while Absolute magnitude is calculated based on apparent magnitude and luminosity distance. For nearby astronomical objects the luminosity distance is almost exactly the same as the real distance to the object. This is because space-time within our galaxy is almost Euclidean. For much more distant objects the Euclidean approximation is not valid, and General Relativity must be taken into account.
The formula for calculating Absolute Magnitude within our galaxy is:
Absolute Magnitude (M) = Apparent Magnitude (m) - 5((log10D)-1)
Where D is the distance in parsecs. Distance can be calculated based on a few other factors, and will be covered in a future article.
Example
Barnard's Star lays 1.82 parsecs away and has an observed (apparent) magnitude of 9.54.
m - M = 5((log10 D)-1) M = 9.54 * 5((log10 1.82)-1) M = 9.54 - (-3.7) M = 13.24
If Barnard's Star were to be moved to a distance of 10 parsecs from the Earth it would then have a magnitude of 13.24.
If we already know both Apparent and Absolute magnitudes, it is possible to calculate the distance to the star:
d = 100.2(m - M + 5)Using Barnard's Star again,
d = 100.2(9.54-13.24+5) d = 100.26 d = 1.82 parsecs
