Pubs.GISS: Abstract of Shen 1963

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Shen 1963

Shen, C.S., 1963: An analytic solution for density distribution in a planetary exosphere. J. Atmos. Sci., 20, 69-72, doi:10.1175/1520-0469(1963)020<0069:AASFDD>2.0.CO;2.

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.}