On the cooling of the upper atmosphere after sunset

The cooling of the “upper atmosphere” (region between the altitude h0 = 100 km and the altitude h1 = 380 km) after sunset was investigated under the assumptions that (a) the temperature at the altitude h0 is constant and equals 240°K, (b) the temperature gradient at the altitude h1 is equal to zero, and (c) the process of heat transfer takes place solely by conduction. Assumed initial temperature is that given by the Rocket Panel, ranging from 240°K at altitude h0 to 1250°K at altitude h1. For the sake of simplicity, thermal conductivity K and specific heat c were assumed constant and dependence of density ρ on temperature was ignored, the differential equation of heat conduction being solved numerically on the assumption that the density ρ and, therefore, the thermal diffusivity α = K/cρ varies with altitude but is independent of time, the variation of ρ with altitude being that given by the Rocket Panel. The computations revealed that after 2–1/2 hours the temperature has not changed at altitudes below 160 km, and that the maximum drop at altitude h1 is 440°K. From the computed temperatures at time t = 2h (2 hours), the densities were computed from formula (2) below. Computations revealed that a certain settling of the atmosphere takes place, the densities at time t = 2h being larger than at time t = 0 in some region, and correspondingly lower at altitudes above the upper limit of this region. Analysis of the ion density led to the conclusion that there is an appreciable increase of the ion density in the F-layer in spite of the recombination of ions which takes place after sunset.