## Apparent magnitude of two stars

1. The problem statement, all variables and given/known data

Two stars have apparent magnitudes of V = 5.1 and V = 4.6 but are too close together to be resolved with the naked eye and appear to be a single object. What is its apparent magnitude?

2. Relevant equations

I don't know what the relevant equations are if there are any.

3. The attempt at a solution

Apparent magnitude = the sum of the two magnitudes = 9.7 but i know that's probably wrong, any help would be appreciated thanks!

Sorry if this is in the wrong place by the way.
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 Recognitions: Homework Help Science Advisor Magnitudes don't add. Luminosities add. What's the relation between magnitude and luminosity?
 m = -2.5*log(L/4*pi*d^2) + c So L = 10^((m-c)/-2.5) * (4*pi*d^2) So errm i think i was given the c for the visual in another question i think it's -21.58... So L1+L2 = 10^((5.1+21.58)/-2.5)*(4*pi*d^2)+10^((4.6+21.58)/-2.5)*(4*pi*d^2) = 2.13*10^-11*(4*pi*d^2) + 3.37*10^-11*(4*pi*d^2) = 5.50*10^-11*(4*pi*d^2) m = -2.5*log(L/4*pi*d^2)+ c m = -2.5*log(5.50*10^-11*(4*pi*d^2)/4*pi*d^2) -21.58 m = -2.5*log(5.50*10^-11) -21.58 m = 4.07 Is that right? I just thought woohoo i have a number which is different from the others but i don't know if it's right?

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