<p>As @RobJeffries <a href="https://astronomy.stackexchange.com/questions/25092/stars-magnitude#comment42948_25092">mentions</a>, you can calculate the difference from the equations which define magnitude and flux. But this particular case is even covered in the <a href="https://en.wikipedia.org/wiki/Apparent_magnitude#Standard_reference_values" rel="noreferrer">Wikipedia article on apparent magnitude</a>:</p>

<blockquote>
  <p>For objects within the Milky Way with a given absolute magnitude, 5 is added to the apparent magnitude for every tenfold increase in the distance to the object.</p>
</blockquote>

<p>So if the nearest star has magnitude 5, the farthest one has magnitude 5 + 5 = 10.</p>

CC BY-SA 3.0
2018-02-14T22:47:48.360Z
2018-02-14T22:47:48.360Z
Glorfindel
<p>I have a question: assume two identical stars, but one is 10 times farther than the other from the earth. If the nearest star has a relative magnitude of 5, what is the relative magnitude of the other?</p>

CC BY-SA 3.0
2018-02-14T20:25:51.547Z
Why can't you do this simple problem using the definition of the magnitude system and that received flux is proportional to the reciprocal of the square of the distance?
ProfRob
CC BY-SA 3.0
2018-02-15T14:29:06.230Z
This is a good question, but it's also one that's very easily answered by looking at any primary or secondary source.
Carl Witthoft
<magnitude>
Stars magnitude
gulraiz safdar
# Stars magnitude

(Asked by: username_0 on 2018-02-14)

I have a question: assume two identical stars, but one is 10 times farther than the other from the earth. If the nearest star has a relative magnitude of 5, what is the relative magnitude of the other?

**Tags:** magnitude
> **Comments:**
> **username_1**: Why can't you do this simple problem using the definition of the magnitude system and that received flux is proportional to the reciprocal of the square of the distance?  
> **username_2**: This is a good question, but it's also one that's very easily answered by looking at any primary or secondary source.  

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## 1 answers

### Answer by username_3 on 2018-02-14. Score: 6 | Accepted answer

As @RobJeffries [mentions](https://astronomy.stackexchange.com/questions/25092/stars-magnitude#comment42948_25092), you can calculate the difference from the equations which define magnitude and flux. But this particular case is even covered in the [Wikipedia article on apparent magnitude](https://en.wikipedia.org/wiki/Apparent_magnitude#Standard_reference_values):

> For objects within the Milky Way with a given absolute magnitude, 5 is added to the apparent magnitude for every tenfold increase in the distance to the object.

So if the nearest star has magnitude 5, the farthest one has magnitude 5 + 5 = 10.


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