STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 



221 



+ 2 



+ I 



00 



-0.1 



-0 2 



120 



130 



140 



150 



170 



180 



190 



200 



160 

 Z (km) 

 Figure 4. — Comparison of the Lockheed densities (Small, 1964) from the drag of low-orbiting satellites with the present tables. 

 The residuals in log p are taken in the sense Lockheed minus present models. 



that is observed in figure 4 as one proceeds to 

 greater heights is due to the increase in ampli- 

 tude of the various types of density variations, 

 which — for reasons stated in section 6 — we did 

 not attempt to remove Above 200 km. the 

 systematic density variations (diurnal, semian- 

 nual, geomagnetic, etc.) become so large that 

 no serious comparison can be made without 

 taking them into account, and a check on the 

 validity of the models is in the inner agreement 

 of temperatures derived from densities deter- 

 mined over a wide range of heights, such as in 

 figUT9 3. 



8. The tables 



Detailed data on composition and density are 

 given in table 1 for 30 temperature profiles 

 ending in exospheric temperatures 50° apart 

 and ranging from 650° K to 2100° K. Table 

 2 gives a summary of the density data only. 



The boundary conditions and the temperature 

 profiles are specified in section 3. For the 

 acceleration of gravity we used the formula 



#=980.665(1 +Z/#)- 2 cm/sec" 2 , 



with i?=6.35677X10 8 cm. 



Hydrogen concentrations are given only 

 above 500 km., as in the CIRA 1965 tables, 

 since hydrogen cannot be considered to be in 

 diffusion equilibrium at lower heights (Kockarts 

 and Nicolet, 1962). 



Although the tables extend to a height of 

 1000 km., the data above 800 km. must be 

 considered as theoretical extrapolations since 

 accurate satellite drag data are not available at 

 those heights. For high exospheric tempera- 



781-252 0—65 2 



tures (above, say, 1300°K) at which atomic 

 oxygen is still the major constituent between 

 800 and 1000 km., the densities should still be 

 reliable; however, the same cannot be said for 

 lower exospheric temperatures. 



The generation of individual densities for 

 given values of z and T„ from equations (4) 

 and (5) is so simple that prospective users of 

 these models may deem it preferable to use the 

 formulae rather than the tables to obtain 

 atmospheric densities in electronic-computer 

 programs. In such a case, the extrapolation of 

 the tables to heights above 1000 km., which 

 may be necessary for the sake of continuity in 

 numerical integrations along satellite orbits, is 

 automatic, and the density approaches zero 

 when z increases beyond any limit. If the 

 tables are used and it is desired to have the 

 density p approach a limiting value p„ rather 

 than zero, we can recommend the procedure we 

 have been using for some time in our numerical- 

 integration programs. Compute b = dln p/dz= 

 (In 10) d log 10 p/dz at 1000 km. from the tabular 

 values of log p and use 



p=p» + (piooo— P-)exp [6(2—1000)]. 



(15) 



(2>1000 km.) 



Acknowledgment 



The invaluable help of Mr. Jack Slowey in 

 preparing these tables for computation and for 

 publication is gratefully acknowledged. 



References 



CIRA 

 1965. 



COSPAR International Reference Atmos- 

 phere. North-Holland, Amsterdam (in 

 press) . 



