216 



SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS 



To analyze or predict the motion of satellites 

 under the influence of drag, one requires models 

 which represent atmospheric variations above 

 all points of the globe in a continuous manner. 

 For this purpose, models of the Nicolet type 

 have a considerable advantage over those of 

 Harris and Priester, because with a suitable 

 model for the geographic temperature distribu- 

 tion above the thermopause they can yield 

 atmospheric densities at any given location 

 and height. The Harris-Priester model is 

 confined to low latitudes and does not account 

 for the seasonal migrations of the diurnal bulge; 

 its extension to higher latitudes would engender 

 gross errors and even a discontinuity at the 

 poles. For this reason, it was deemed advisable 

 to produce a set of atmospheric models pat- 

 terned after those of Nicolet, but based on the 

 most recent data on composition at the bound- 

 ary level and density at satellite heights. 

 The result is the present tables. 



2. Boundary conditions 



The boundary conditions selected for the 

 CIRA 1964 tables are the result of a careful 

 weighing of recent data from instrumented 

 rockets and satellites, and it would be difficult 

 to improve on them at this date. Therefore, 

 we have taken them as the basis for our tables 

 with only one change, namely, the helium 

 concentration which was increased by 40 

 percent to account for the densities derived 

 from satellites at heights greater than 600 km. 

 at times of low solar activity. There is a 

 distinct possibility that these densities, using a 

 constant value, C D =2.2, of the drag coefficient, 

 are actually overestimated by some 10 to 15 

 percent, since the drag coefficient should in- 

 crease as the molecular weight of the atmos- 

 pheric gas decreases (Izakov, 1965; Cook, 1965). 

 In such case the excess helium required to 

 account for these densities could be somewhat 

 reduced. 



At £=120 km. 



r=355° K, 



n(N 2 )=4.0X10 n , 

 n(O 2 ) = 7.5X10 10 , 

 n(O) = 7.6X10 10 , 

 n(He) = 3.4X10 7 . 



Argon was neglected since its contribution to 

 the total density is only 1 percent at 120 km. 



and becomes rapidly negligible at greater 

 heights. For hydrogen we have followed 

 Kockarts and Nicolet (1962) and fitted the 

 following equation 



log 10 7i(H) 500 = 73.13-39.40 log 10 T a 



+ 5.5 (log 10 T„Y (1) 



to their concentrations at 500 km., which were 

 used as boundary for the computation of con- 

 centrations at greater heights. 



Starting from the boundary conditions, the 

 concentrations n t of each constituent i were 

 computed as a function of the geometric height 

 z by integrating the diffusion equation 



dn t dz dT ,, , . 



(2) 



Here, T is the temperature, a the thermal-dif- 

 fusion factor, and H, is the scale height of the 

 individual constituent, defined as 



H r - 



kT ; 

 ~m t g 



(3) 



where k is the Boltzmann constant, m t the 

 molecular (or atomic) mass of the constituent, 

 and g the acceleration of gravity. 



For helium, following Nicolet, we used a = 

 — 0.38; for N 2 , 2 , and O, a = 0. 



3. Temperature profiles 



To compute the vertical distribution of tem- 

 perature on the basis of theory alone, we must 

 know, among many other things, how the 

 heating-energy input varies with height. Since 

 solar EUV is radiated in a discrete number of 

 spectral lines, each of which is absorbed at a 

 different height (Hinteregger, 1962) and each 

 of which varies in intensity with time in a 

 different manner (Purcell et al., 1964), the prob- 

 lem is complicated enough even when we 

 ignore energy sources other than solar EUV. 

 As to temperature and density observations, 

 the lower thermosphere, from 100 to 150 km., 

 is practically terra incognita (or, rather, aer 

 incognitus). Any present-day atmospheric 

 model must introduce a considerable degree of 

 empiricism in constructing temperature profiles 

 in that region; this is also the case of Nicolet's 

 profiles. 



Since an inadequate theory may be worse 

 than none when it must fit a great many ac- 

 curate observations, as is our case, we decided 



