Question

The apparent magnitude of Sun in V filter band is -26.7 mag. Please answer what's the absolute magnitude of the Sun in V-band? Suppose you are observing a globular cluster in the halo of the Milky Way, whose distance was 25 kiloparsecs, and you want to be able to detect stars like the Sun in this cluster. What would the apparent V magnitude be for a star identical to the Sun, if it were at that distance?

Answer 1

Let's start with definitions:

Apparent magnitude is a measure of how bright an object appears when seen from earth.

Absolute magnitude of an object is the value of apparent magnitude when we keep that object at a distance of 10 parsec (1 parsec = 3.26 Ly) from earth.

Now, all we have to use is this formula-

Where, m = apparent magnitude ; M = absolute magnitude; d = distance of an object in parsec

a) Here, and distance of the sun from earth in parsec is

So, the equation becomes-

b) In second part, we have to use the same formula. Just the trick here is that to know, if any star is identical to the Sun means its absolute magnitude is same as that of the Sun. Also the distance to be used is  .

Answers: Absolute magnitude of the Sun = and Apparent magnitude of the star identical to the Sun =