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 / D2.
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 Lsun = 3.9 x 1033 erg s-1. We can calculate the absolute magnitude of the Sun Msun 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 Msun = +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 / Lsun).