So, not surprisingly, a star's apparent brightness depends on both its luminosity and its distance.

A star's observed magnitude is called its **apparent
magnitude (m)**, since is not a true measure of a fundamental
property of the star.

Let's look at something which is a fundamental
property
of the star - its true brightness. We will define this as the
brightness
the star would have if it were 10 parsecs away from us. On the
magnitude
scale, we call this the star's **absolute
magnitude
(M)**. How do we do this?

Start by defining **f _{10}**
to be the flux you would receive from the star

Often if we know what kind of star it is, we can
estimate
its luminosity (and, thus, M). We can then measure its apparent
magnitude
(m) and solve for distance. Since m-M is a measure of distance, it is
called
the **distance modulus**.

**Question:** *what
is the
absolute magnitude of the Sun?***Answer:** *M=4.76
(this, technically, is the bolometric
absolute magnitue of the Sun -- more on that later)
*

We can use this in a nifty way to relate absolute magnitude to solar luminosity. Remember our definition of magnitude: