Absolute Magnitude and Distance
Once the apparent magnitude is known the absolute can be determined.
The absolute magnitude of an object is based on its parsec distance from Earth, i.e., 10 parsecs. In the table below, one can compare the apparent and absolute magnitudes of some stellar objects. The absolute magnitude determines the value of the intrinsic brightness of the star. This is important for astronomers to find because even if a star is very bright, it may be because of its nearness to Earth. It would not reflect its true luminosity. This moreover, is important in finding the distance to a star.
Here is a comparison of m (apparent magnitude) and M (absolute magitude) for five stars. If you know the apparent and absolute magnitude, you can determine its distance.
Here is what this table means:
The Distance function = m - M.
- If m-M is negative then the stars are closer than 10 parsecs.
- If m-M is positive then the stars are further than 10 parsecs.
- The size of the distance function determines the actual value of the distance, so that a star of distance function 1.5 is closer than one with a distance function of 8.7.
The formula to determine the parsec distance is: m - M = 5 log(d/10) where d is in parsecs.
Let us look at some of the elements of the table. First, just exactly how far away is GJ 75? Notice that the apparent and absolute magnitudes are the same. Why? Simply this: the star is actually 10 parsecs away from earth, so by definition its two, m and M, magnitudes must be the same.
Now look at Sirius. Its absolute magnitude is higher, and consequently dimmer, than its apparent magnitude. This means that distance wise it is closer than 10 parsecs to Earth. Betelgeuse's apparent magnitude is higher than its absolute magnitude so it would appear even brighter in the night sky if it were only 10 parsecs away.