An Analytic Solution for Density Distribution in a Planetary Exosphere

Abstract

An analytical expression ρ(r)=N₀[e^(1−R/r)E−(1−R²/r²)e^−(rE/r+R)], where E is a temperature dependent parameter and R is the radius of the base of exosphere, is derived for the density distribution in a planetary exosphere. The difference between this distribution and the barometric (Boltzmann) formula is small near the base of the exosphere but becomes significant at large r; at r=∞ the barometric formula gives a finite density where our distribution tends to zero. It is shown that according to a strict collisionless exosphere model the particles in the velocity space are confined in a region bounded by a hyperbola and a quarter circle. Outside this region there are no particles; inside, they are distributed by a Maxwellian law. The physical significance of this difference and its effect on the escape rate are discussed.