Barometric formula for non-isothermal atmosphere

Abstract

Abstract A new barometric formula is derived for a non-isothermal atmosphere. It takes into account the dependence of the acceleration of gravity and gas temperature on the height z above the Earth’s surface. When deriving this formula, it was assumed that the dependence of the gas temperature on altitude is due to the heating of the Earth’s surface by the Sun and the subsequent heat transfer of energy from the Earth’s surface to the atmosphere. The proposed formula coincides with the classical barometric formula for an isothermal atmosphere at low altitudes z, takes into account the experimental linear decrease in the temperature of the atmosphere in its lower layers with increasing altitude z and gives a physically correct asymptotics for the pressure (and for concentration) of the gas as z -> oo, namely, the pressure (and concentration) of gas tends to zero faster than exponentially as z -> oo, which ensures the localization of a finite amount of gas near the Earth.