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}} $