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

CC BY-SA 4.0
2020-10-17T16:40:12.527Z
2020-10-17T16:40:12.527Z
James K
<p>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?</p>
<p>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</p>
<p><span class="math-container">$$m=-2.75 \log_{10} F + C$$</span></p>

CC BY-SA 4.0
2020-10-15T22:08:42.510Z
One star has magnitude mV=8.34 and flux F. Two identical stars have a total combined flux of 2F
planetmaker
CC BY-SA 4.0
2020-10-16T04:53:28.187Z
I've changed the format of your equation to use [MathJax](https://math.meta.stackexchange.com/q/5020/284619) 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
<apparent-magnitude>
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?
Anupam Dhungana
# 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?

(Asked by: username_0 on 2020-10-15)

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

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

**Tags:** apparent-magnitude
> **Comments:**
> **username_1**: One star has magnitude mV=8.34 and flux F. Two identical stars have a total combined flux of 2F  
> **username_2**: I've changed the format of your equation to use [MathJax](https://math.meta.stackexchange.com/q/5020/284619) 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 $\log(ax) = \log(a) + \log(x)$  

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## 1 answers

### Answer by username_3 on 2020-10-17. Score: 2

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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