Density and temperature distributions in non-uniform rotating planetary exospheres with applications to earth

Using an exosphere model which includes the effects of rotation and temperature and density variations at the exobase, we determine kinetic temperature and density distributions for planetary exospheres in general and terrestrial O, He and H in particular, the latter being based on empirical models for density and temperature variations at exobase altitudes. We examine the effects of energy flow and confirm Fahr's suggestion that the lateral energy flow at the exobase should be important for the temperature distributions above the base. Considering uniform density and sinusoidal temperature variations at the base, we find that temperatures decrease with altitude above the diurnal temperature maximum Tmax at the base. On the other hand, above the diurnal temperature minimum Tmin at the base, the temperatures increase from the base to peak values (except for low values of mMG/kT₀) and then decrease above the peaks, tending to approach the values above Tmax. The corresponding densities near the base, above Tmin, decrease with altitude more rapidly than above Tmax but exhibit considerable increases in their scale heights in the vicinity of their temperature peaks, at which points the densities begin to approach those above Tmax. In the converse case, with uniform base temperature and sinusoidal base density variations, the exospheric density and temperature distributions above the diurnal density maximum Nmax and minimum Nmin at the base result in similar characteristics to those above Tmax and Tmin, respectively. Applying the model to terrestrial O, He and H, we find that multiple exospheric temperatures should occur wherein temperatures above Tmax decrease less rapidly with altitude for increasing species mass. On the other hand, O and He temperatures increase with altitude above Tmin to peak values near 5000 km and then decrease above the peaks while H temperatures decrease with altitude throughout. We also examine the effects of the terrestrial exospheric H temperature distribution on optical depths for Lyman alpha absorption and find that such temperature variation may be important for radiative transfer calculations when the depths are greater than unity and satellite orbits are unimportant.