# Apparent magnitude

1. ### luuurey

24
Hello everyone,
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

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

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:

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

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$I_M=0.12 I_S$, where I_M is the flux of light that comes from The Moon. So I get:

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

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?