Question

The apparent magnitude of the sun is - 26.8. Determine its absolute magnitude. It is given that the distance between the sun and the earth is 1.5 x 10^11m.

Answer 1

The absolute magnitude $M$ of a star is the magnitude which the star would have if it were located $d_0=10\text{ pc}$ from the observer. If we know the apartment magnitude $m$, we can use the following equation to determine the absolute:

$$M=m-5\text{lg}\frac{d}{d_0}.$$

Convert the distance from the Earth to the sun from kilometers to parsecs:

$$1.5\cdot10^{-11}\text{ km}\rightarrow4.848\cdot10^{-6}\text{ pc}.$$

Then

$$M=-26.8-5\text{lg}\frac{4.85\cdot10^{-6}}{10}=+4.77.$$