The **brightness** of a star of
a given luminosity **L**, radiated in all directions, falls off as
one over the distance to the object squared:, that is
b(D) is proportional to L / D^{2}.

Objects of the same luminosity that are located at different distances
from us will have different apparent magnitudes.
We therefore need to define the **absolute magnitude M** as the
apparent magnitude an object would have if it were at a certain distance
which we shall arbitrarily adopt to be **10 pc**.

*Remember:* A **parsec** is the distance at which a star
would have a parallax of one second of arc:

The basic formula relating the apparent (**m**) and absolute (**M}**
magnitudes then is

where D is the distance to the object in pc.

Consider that we already know that the Sun has m = -26.8, and it is
located at 1 A.U. (** astronomical unit**) from us.

The sun has a luminosity of 1 solar luminosity L_{sun}
= 3.9 x 10^{33} erg s^{-1}.
We can calculate the absolute magnitude of the Sun M_{sun} by
considering how much fainter the Sun would appear if it were located at 10 pc
from us instead of 1 A.U. For the Sun:

Thus, the absolute magnitude of the sun is M_{sun} = +4.77.
Similarly, for other stars, a star of a certain absolute magnitude M,
is more or less luminous than the sun according to:

M = +4.77 - 2.5 log (L / L_{sun}).