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?
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2$\begingroup$ 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? $\endgroup$– ProfRobFeb 14, 2018 at 20:25
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$\begingroup$ This is a good question, but it's also one that's very easily answered by looking at any primary or secondary source. $\endgroup$– Carl WitthoftFeb 15, 2018 at 14:29
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1 Answer
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As @RobJeffries mentions, 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:
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.
answered Feb 14, 2018 at 22:47