Air mass and its analytical derivation

Abstract

The light we receive from a celestial body has to cross the Earth atmosphere before to reach our eyes and telescopes. The path length of that light through the atmosphere is minimal when the celestial body is at zenith, equaling the atmosphere thickness itself, but it increases as the celestial body approaches horizon. In this article we will show how to derivate the quotient of the light path length and the atmosphere thickness (quantity usually known as "air mass"), as a function of the celestial body altitude.