Relative optical mass in a nonisothermal atmosphere

Abstract

A closed-form expression is theoretically derived for the relative optical air mass as a function of zenith angle in an atmosphere with a temperature gradient. The effects of refraction are included, and the atmosphere is assumed to be in hydrostatic equilibrium. Due to the temperature gradient, the atmospheric density does not fall off exponentially with altitude but according to a power law. The radius of the earth is a factor in the expression; thus the relative air mass on other planets can also be calculated. The relative air mass is 1.0 for a vertical path and is around 40.0 for a horizontal path to space. A comparison is made to other expressions showing the effects of refraction and temperature at different altitudes in the atmosphere. Since refraction is much less at high altitudes in the atmosphere, the relative air mass is a definite function of altitude. The expressions presented here can be easily incorporated into computer programs. A similar expression can be derived for the equivalent pressure along an atmospheric path.