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I've been wondering if I can calculate the apparent magnitude of The Moon since I know the apparent magnitude of The Sun(say -27mag) and reflection coefficient of Moon's surface(say 0.12).

We know the equation

[itex]

\Delta m = -2.5 log_{10}(I/I_0)

[/itex]

Where I is the flux of the light that comes from source and I_0 is flux of a reference source. I know the magnitude of The Sun, so I can say:

[itex]

-27 = -2.5 log_{10}(I_S/I_0)

[/itex]

Where I_S is the flux that I can measure on the sunlight. I know that the flux of the light from The Moon is just reflected sunlight and hence[itex]I_M=0.12 I_S[/itex], where I_M is the flux of light that comes from The Moon. So I get:

[itex]

\Delta m_M = -2.5 log_{10}(I_M/I_0)= -2.5 log_{10}(0.12 I_S/I_0)= -2.5 log_{10}(I_S/I_0)-2.5 log_{10}(0.12) = -27 -(-2)=-25

[/itex]

I'm sure that the apparent magnitude of The Moon is definitely not 25mag. It's around -13mag. What's wrong with my idea? Where did I make mistake?

Thank you for your answer. I will be very thankful for your help!

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# Apparent magnitude

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