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

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

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    $\begingroup$ One star has magnitude mV=8.34 and flux F. Two identical stars have a total combined flux of 2F $\endgroup$ Oct 15 '20 at 22:08
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    $\begingroup$ 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 $\log(ax) = \log(a) + \log(x)$ $\endgroup$
    – uhoh
    Oct 16 '20 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 $$m = -2.5 \log_{10} \left(\frac {2F}{F_{0}}\right)\\ = -2.5\log_{10}(2) -2.5 \log_{10} \left(\frac {F}{F_{0}}\right)$$

The first value is about -0.75, so the double star is 0.75 magnitudes brighter. If each object is 8.34 then the double star appears as a 7.59 object.


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