# A double star consists of two stars of equal brightness at equal distance from the Earth. What is the apparent magnitude of the combined object?

The magnitude of each star in the V-band is mV= 8.34. If these stars are so close together that they appear as one object, what is the apparent magnitude of the combined object?

I just want someone to point me in a general direction of how to approach this problem. The magnitude is logarithmic so it won't be double when combined. Or at least that is what I think. How do I apply the formula

$$m=-2.75 \log_{10} F + C$$

• One star has magnitude mV=8.34 and flux F. Two identical stars have a total combined flux of 2F Oct 15, 2020 at 22:08
• I've changed the format of your equation to use MathJax and added base 10. But I think the number in front should be 2.5, not 2.75, can you check on that? Also, remember that $\log(ax) = \log(a) + \log(x)$
– uhoh
Oct 16, 2020 at 4:53

The magnitude formula is $$m = -2.5 \log_{10} \left(\frac {F}{F_{0}}\right)$$
Where $$F_0$$ is the flux of magnitude 0 star.
So if you have two stars of equal brightness, the flux is doubled, and you get $$m = -2.5 \log_{10} \left(\frac {2F}{F_{0}}\right)\\ = -2.5\log_{10}(2) -2.5 \log_{10} \left(\frac {F}{F_{0}}\right)$$