Finding Magnitude

Now we know how to find the distance to a far off star by using its absolute and apparent magnitudes. What if we wanted to do the opposite? Given the distance to a star and how bright it is on earth, we can figure out its absolute magnitude.

This is the brightest star in the sky, bright enough to be seen even during the day under the right conditions. It has an impressive apparent magnitude of -1.47 and is one of the closer stars to the Earth at 2.63 parsecs. What is its absolute magnitude?

Solution:

This time, we know d=2.63 and m_app=-1.47, but we first have to take the log₁₀ of both sides:

and we see that Sirius' absolute magnitude is 1.43.

You may have noticed that for both of these stars, the absolute magnitude was less bright than the apparent magnitude (remember, bigger numbers of magnitude mean less light). Why is that?

The reason comes from our definition of absolute magnitude: how bright a star is at 10 parsecs away. Since these stars look brighter to us than they would look at a distance of 10 parsecs, they must be less than 10 parsecs away from the Earth (or because we already told you how far away they are).