Apparent Magnitude

The equation for apparent magnitude is outlined below

$$m _{app} - m _{vega} = -2.5 log_{10}{\frac {F _{obj}}{F _{vega}}} $$

Total integrated magnitude of the night sky ("Ahad's constant") is below

$$ -2.5 log\sum_{i=1}^{\infty }10^{-0.4m_{i}} $$