CONTRIBUTIONS

ASTROPHYSICS

Volume 8, Number 9 (End of Volume)

Static Diffusion Models

of the Upper Atmosphere With Empirical Temperature

Profiles

by Luigi G. Jacchia

Smithsonian Institution Astrophysical Observatory Washington, D.C.

Smithsonian

Contributions to Astrophysics

Volume 8, Number 9 STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE

WITH EMPIRICAL TEMPERATURE PROFILES

by Luigi G. Jacchia

SMITHSONIAN INSTITUTION

Washington, D.C.

1965
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For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C, 20402 - Price 40 cents
Static Diffusion Models of the Upper Atmosphere with

Empirical Temperature Profiles'

Luigi G. Jacchia 2

1. Static and time-dependent models The first multitemperature models of the atmosphere above 120 km. based on diffusion equilib- rium were produced by Nicolet (1961, 1963). These models proceed from a fixed set of boundary conditions, temperature and partial densities, at 120 km. Above this height the partial densities vary according to diffusion theory, except for hydrogen for which diffusion equi- librium is reached only at greater heights (Kockarts and Nicolet, 1962, 1963); thermal

diffusion is taken into account for helium. The

vertical temperature distribution is computed

for the "hottest" model, i.e., the one with the highest exospheric temperature, assuming

thermal equilibrium; the other models are obtained from this model by conduction cooling

of the atmosphere in the absence of external energy sources. The temperatures which are obtained in this manner at the height of 150 km. (a nearly isopycnic layer) are linearly con- nected with the constant temperature at 120 km. Models can be computed by this pro- cedure for conveniently spaced values of the exospheric temperature. These quasistatic models have proved very practical as a back- ground for deriving and analyzing atmospheric

1 This work was supported in part by grant NsG

87-60 of the National Aeronautics and Space Administration. A preprint of this paper has appeared as Smithsonian Astrophysical Observatory Special Report

No. 170. Owing to an imperfection in the numericalintegration program, table 1 in that publication is affected by a small systematic error, whose maximum

value, 0.011 in log p, occurs at a height around 200 km. when T„ is large. For normal satellite heights and

temperatures the error amounts to only 0.006 in log p, so its practical effect can be considered to be negligible.

2 Physicist, Smithsonian Astrophysical Observatory.

densities from satellite drag (Jacchia and

Slowey, 1963). Atmospheric models can be constructed only

at the expense of oversimplifications. Such

are, for example, the invariance of the boundary

conditions at 120 km. and the constant temperature gradient between 120 and 150 km. found

in Nicolet's models. Another serious limitation

is the assumption of static equilibrium in an atmosphere which is subject to large day-to- night temperature variations, with a period which is not much longer than conduction time

in the lower thermosphere. Atmospheric models which attempt to take

into account the diurnal variation at low lati- tudes have been computed by Harris and

Priester (1962a, 1962b). They also assumed

fixed boundary conditions at 120 km. and dif- fusion above this height, but the hydrostatic equation and the heat-conduction equation were integrated simultaneously and the heat

input varied with a 24 hour cycle. Since the amount of solar EUV necessary to maintain

the heat balance gave diurnal density oscilla- tions much in excess of those observed, Harris and Priester (1962 a, b) were obliged to intro- duce a second source of heat with a maximum at a different hour. This device may perhaps have a counterpart in the actual heating process, but

doubts have been voiced that it may mostly re

fleet the inadequacy of an oversimplified theory. By suitably varying the "second heat source,"

the Harris-Priester models can be made to fit the densities from satellite drag with almost any

degree of accuracy, and their new version, pre- pared for the new C'OSPAR International Reference Atmosphere (CTRA 1965) to be

published shortly, is remarkably successful

in thii: respect. 215
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 boundary 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, CD =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 atmospheric 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(N2 )=4.0X10n

, n(O2 ) = 7.5X1010

, n(O) = 7.6X1010

, n(He) = 3.4X107

. 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

log10 7i(H) 500 = 73.13-39.40 log10 Ta + 5.5 (log10 T„Y (1) to their concentrations at 500 km., which were

used as boundary for the computation of concentrations at greater heights. Starting from the boundary conditions, the concentrations nt of each constituent i were computed as a function of the geometric height

z by integrating the diffusion equation dnt dz dT ,, , . (2) Here, T is the temperature, a the thermal-diffusion factor, and H, is the scale height of the individual constituent, defined as Hr

- kT ; ~m t g

(3) where k is the Boltzmann constant, mt the molecular (or atomic) mass of the constituent, and g the acceleration of gravity. For helium, following Nicolet, we used a = —0.38; for N2 , 2 , and O, a = 0.

3. Temperature profiles To compute the vertical distribution of temperature 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
STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 217

to abandon theory entirely in constructing our temperature profiles. A survey of Nicolet's and of the Harris-Priester temperature profiles showed at once that they can all be represented, with a remarkable degree of approximation, by exponential curves of the form T=Ta ~(Ta -T12 o) exp [-s(2 -120)], (4) where Tn is the temperature at 120 km. and T„ the asymptotic (exospheric) temperature; 04

03

02

01500°

\ 1
218 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

all the satellites analyzed in Jacchia and

Slowey, 1963) we obtain temperature variations which are, on the average, smaller by

6 percent.

It should be remembered, of course, that a comparison between temperatures becomes

impossible in atmospheric regions where the density is nearly independent of temperature. This situation occurs for heights lower than

+ 200°

+ 100'

AT

-100°
STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 219

nighttime temperature on the globe be T and

the maximum daytime temperature on the globe be RT . We shall assume that the daytime maxima TD and nighttime minima TN

at any point on the globe are given by the equations TD =7, (l +i?cos"! 7,), (10) TN =T (1 +Rsmm

d), where

v=2(<p—&o),

where <p is the geographic latitude and 5Q the

declination of the sun. The temperature T at this given point can

be expressed as a function of the hour angle H

of the sun (the local solar time). Let us write

with

and

T=TN (l+A cos" |\ (11) lp— -In R

cos"8 -q— sinm d l+R sinm

T=H+0+p sin (H+y) (- 7r<r<1r) (12) where /3, y, and p are constants, and H=0

corresponds to the sun's upper culmination. The constant determines the lag of the temperature maximum with respect to the sun's culmination, while p introduces in the temperature curve an asymmetry whose location is determined by y. Replacing TD and TN from

equation (10), we can write T=T (l+R sinm

0) (13) cosm

rj —sinm +R sinOT 6 A cos" -J

Although in these equations the exponents m and n, which determine the mode of the

longitudinal and the latitudinal temperature

variations respectively, are kept distinct, we

find that in practice we can take m=n. There

is a distinct possibility that the common value

of these coefficients might turn out to be a

little smaller than 2.5, the previously assumed

value, somewhere between 2.0 and 2.5. We

shall adopt the following constants: i?=0.28, m=«=2.5, /3= -45°, 2>=12°, 7= +45°.

e. Variation with geomagnetic activity.—After

the publication of Jacchia (1964), it was found

that the relation between the exospheric temperature and the 3 hour geomagnetic index av shows a strong departure from linearity for small values of av (Jacchia and Slowey, 1964a). The formula given in the last reference can be

used without alterations. The increase of temperature with av

is then AT=1°.0 ap +125° [1-exp (-0.08 a„)]. (14) AT represents the atmospheric heating above

the level corresponding to ap =0. During

1500'

To, (°K)

IOOO'

-
220 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

magnetic storms the temperature variations lag about 6 hours behind the variations in ap (Jacchia and Slowey, 1964b). There is evidence

that AT/ap is somewhat larger in high geo- magnetic latitudes (Jacchia and Slowey, 1964c).

6. Limitations of the present models

As we stated in section 1, atmospheric models must suffer from the oversimplified assumptions one is obliged to make to construct them. Our

models share with those of Nicolet the limitations imposed by the invariance of the temperature profiles and of the boundary conditions;

this latter limitation is common also to the

Harris-Priester models. A consequence of the fixed boundary conditions is a nearly isopycnic layer at 200 km. at times of moderate to high solar activity. At

such times, according to the models (ours, Nicolet's, and the Harris-Priester models), the

density at 200 km. should not show appreciable

variations when the exospheric temperature

varies. This condition is nearly fulfilled by the

diurnal variation which practically disappears

at heights lower than 200 km. On the other hand, density variations at the 200 km. level have been observed at times of high solar activity in correspondence with geomagnetic

storms, and also of the erratic ("27 day") component of the 10.7 cm. flux (Jacchia, 1959). The different response of the density at 200 km. to different types of heating could be ex- plained by assuming that the temperature at 120 km. is not subject to a diurnal variation, but increases in correspondence with geomagnetic storms and transient enhancements of

solar EUV radiation. If we increase the temperature at 120 km. by 50° without changing

the composition, the density at 200 km. will increase, according to our models, by a little over 30 percent when the exospheric temperature is about 1400° K. This is just about the order of magnitude of the erratic density changes observed in Sputnik 2 and 3. At

greater heights the density change is more or

less the same, decreasing only slightly with

height, but its relative importance becomes

smaller because of the increased response of the density to changes in the exospheric temperature (or, to be more accurate, to changes in the corresponding temperature gradient above 120 km.).

Satellites at heights as low as 160 km. have

recently shown that the density changes during magnetic storms are in phase with those at greater heights (Zirm, 1964). This indicates that most of the heating during these storms must occur at heights considerably lower than

160 km. It therefore looks highly probable

that the temperature at 120 km. must undergo

changes during a magnetic storm.

If we assume that also the erratic changes in solar EUV affect the temperature at 120 km.,

it is difficult to see how the much larger variations of EUV in the course of the 11 year solar cycle could leave the temperature at 120 km.

undisturbed. Perhaps there is such a change and the construction of better models will be

possible when this change becomes known.

7. Comparison with recent satellite-drag data at heights below 200 km. A valuable collection of drag data on satellites with low perigee heights has been recently presented by Small (1964). These data extend

in an unbroken series to heights as low as 160 km., and for one satellite (1962 pa) to 126 km.

Apart from the assumed boundary conditions, our atmospheric models are based on drag data from satellites with perigee mainly above 250 km. and were completed before we had knowledge of Small's densities. It was gratifying to

find that the agreement of these densities with

our models is excellent, as can be seen from

figure 4. In this plot we divided the data into three groups according to the mean exospheric temperature prevalent at the pertinent time,

in addition we have separately marked the

points derived from Sputnik 3 (1958 52), which

are particularly numerous and may be affected by a small systematic error. According to our models log p (p= density)

at 180 km. varies by about 0.2 from sunspot maximum to sunspot minimum. Since the

residuals in log p for the three temperature

groups do not show any clear evidence of systematic differences, we must conclude that our models represent rather well not only the average densities, but also their variations. Since, however, the density variations below

200 km. are relatively small, the agreement with

observations in this region must be ascribed mainly to the boundary conditions, which are obviously satisfactory. The increase in scatter
STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 221

+ 2

+ I 00

-0.1

-0 2

1 • Too >l200

» I200<, >T„>I000°
222 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Cook, G. E.

1965. Private communication. Harris, I., and Priester, W.

1962a. Time-dependent structure of the upper

atmosphere. Journ. Atmosph. Sci., vol.

19, pp. 286-301.

1962b. Theoretical models for the solar-cycle vari- ations of the upper atmosphere. Journ. Geophys. Res., vol. 67, pp. 4585-4591. HlNTEREGGER, H. E.

1962. Absorption spectrometric analysis of the upper atmosphere in the E.U.V. region. Journ. Atmosph. Sci., vol. 19, pp. 351-368. Izakov, M. N.

1965. Some problems of investigating the structure

of the upper atmosphere and constructing

its model. In P. Muller, ed., Space Research V, North-Holland, Amsterdam,

pp. 1191-1213. Jacchia, L. G.

1959. Corpuscular radiation and the acceleration

of artificial satellites. Nature, vol. 183, pp. 1662-1663.

1964. The temperature above the thermopause. Smithsonian Astrophys. Obs. Spec. Rep.,

no. 150, 32 pp. Jacchia, L. G., and Slowey, J. 1963. Accurate drag determinations for eight artificial satellites; atmospheric densities and

temperatures. Smithsonian Contr. Astrophys., vol. 8, no. 1, pp. 1-99. 1964a. Temperature variations in the upper at- mosphere during geomagnetically quiet

intervals. Journ. Geophys. Res., vol. 69, pp. 4145-4148.

1964b. An analysis of the atmospheric drag of the Explorer IX satellite from precisely re- duced photographic observations. In P. Muller, ed., Space Research IV, NorthHolland, Amsterdam, pp. 257-270.

1964c. Atmospheric heating in the auroral zones: a preliminary analysis of the atmospheric drag of the Injun 3 satellite. Journ. Geophys. Res., vol. 69, pp. 905-910. Kockarts, G., and Nicolet, M.

1962. Le probleme aeronomique de l'h61ium et de

l'hydrogene neutres. Ann. de Geophys.,

vol. 18, pp. 269-290.

1963. L'helium et l'hydrogene atomique au cours d'un minimum d'activite' solaire. Ann.

de Geophys., vol. 19, pp. 370-385. Nicolet, M.

1961. Density of the heterosphere related to temperature. Smithsonian Astrophys. Obs.

Spec. Rep., no. 75, 30 pp.

1963. La constitution et la composition de 1 'at- mosphere superieure. In C. DeWitt,

J. Hieblot, and A. Lebean, eds., Geophysics, The Earth's Environment, Gordon

and Breach, Science Publishers, New York. Purcell, J. D.; Garrett, D. L. ; and Tottsey, R.

1964. Spectroheliograms in the extreme ultraviolet

(abstract). Astron. Journ., vol. 69, p. 147. Small, H. W.

1964. Atmospheric density between 70 and 200

nautical miles from satellite observations. Lockheed Missiles and Space Company,

Tracking Note no. 23. Zirm, R. R.

1964. Variations in decay rate of satellites. Journ. Geophys. Res., vol. 69, pp. 4696-4697.

Abstract

Tables of atmospheric density and composition are computed for a wide range of exospheric temperatures,

starting from a fixed set of boundary conditions at 120 km. The diffusion equation is integrated following empirical temperature profiles of exponential form capable of reproducing the densities derived from satellite drag over

the years. Formulae are given which relate the exospheric temperature to solar and geomagnetic activity and allow

for the diurnal and semiannual variations. The different response of the density at the 200 km. level to different types of heating is briefly discussed.
Tables
224 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature EXOSPHERIC TEMPERATURE = 2101 CEGREES

HEIGHT
STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 225

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 2053 DEGREES

HE IGHT
226 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Tabij; 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TcM^EKATURE = 2000 CEGXEES HEIGHT
N o. 9 STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 227

Tabi.e 1. —Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE - 1953 CEGREES HEIGHT
228 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 1900 OEGREES HEIGHT
no. s STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 229

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSCMERIC TEMPERATURE = 1350 CEGREES

HE ISHT

KM
230 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 1800 CEGREES

HEIGHT
so . g STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 231

Table 1. —Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 1750 CEGREES HEIGHT
232 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric date as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPER4TURE = 1733 DEGREES HEIGHT
no. 3 STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 233

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMDEFUrURE = 1650 CEGREES HEISHT
234 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 1600 DEGREES HEIGHT
no. 9 STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 235

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 1553 CEGREFS HEIGHT
236 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Tabu: 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHER1C TEMPERATURE = 1500 DEGREES HEIGHT
N0. 9 STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 237

Table 1.—Detailed atmospheric data as a function of height and exospherie temperature—Continued EXOSPHERIC TEMPERATURE = 1450 CEGREES

HE IGHT
238 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHtiUC TEMPERATURE = 1400 CEGREES

HE I3HT
N0, 9 STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 239

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 1350 DEGREES HEIGHT TEMP LOG NI02) LOG N(O) LOG N(NZ) LOG N ( HE ) LOG N1H) MEAN SCALE DENSITY LOG CEN

KM DEG K /CM3 /CM3 /CM3 /CM3 /CM3 MOL WT HT KM GM/CM3 GM/CM3

120.0 355.0 10.8751 10.8808 11.6021 7.5315 26.90 11.62 0.2461E-10 -10.609

130.0 559.5 10.3298 10.5094 11.1001 7.36!5 26.32 18.76 0.7851E-11 -11.105

1*0.0 721.9 9.9736 10.2759 10.7745 7.2661 25.85 24. T3 0.3769E-11 -11.424

150.0 851.0 9.7031 10.1050 10.5288 7.1969 25.43 29.72 0.2178E-11 -11.662

160.0 953.5 9.4807 9.9691 10.3279 7.1447 25.04 33.94 0.1398E-11 -11.855

170.0 1035.0 9.2887 9.8553 10.1553 7.1030 24.66 37.52 0.9589E-12 -12.018

180.0 1099.7 9.1170 9.7562 10.0018 7.0685 24.29 40.59 0.6882E-12 -12.162

190.0 1151.2 8.9597 9.6677 9.8616 7.0390 23.93 43.27 0.5103E-12 -12.292

200.0 1192.0 8.8129 9.5867 9.7312 7.0131 23.57 45.62 0.3877E-12 -12.412

210.0 1224.5 8.6740 9.5114 9.6081 6.99C0 23.22 47.72 0.3001E-12 -12.523

220.0 1250.3 8.5410 9.4404 9.49C6 6.9689 22.87 49.62 0.2357E-12 -12.628

230.0 1270.8 8.4127 9.3727 9.3774 6.9493 22.52 51.36 0.1874E-12 -12.727

240.0 1287.1 8.2880 9.3076 9.2675 6.9310 22.18 52.98 0.1504E-12 -12.823

250.0 1300.0 8.1662 9.2445 9.1603 6.9136 21.85 54.50 0.1218E-12 -12.914

260.0 1310.3 8.0467 9.1831 9.0553 6.896? 21.52 55.94 0.9929E-13 -13.003

270.0 1318.4 7.9291 9.1229 8.9520 6.88C9 21.19 57.32 0.8146E-13 -13.089 280.0 1324.9 7.8130 9.0638 8.8501 6.8653 20.88 58.64 0.6721E-13 -13.173

290.0 1330.1 7.6982 9.0056 8.7494 6.8501 20.57 59.93 0.5573E-13 -13.254

300.0 1334.2 7.5845 8.9480 8.6497 6.8352 20.28 61.18 0.4642E-13 -13.333

320.0 1340.0 7.3597 8.8347 8.4527 6.8062 19.71 63.59 0.3261E-13 -13.487

340.0 1343.7 7.1378 8.7231 8.2582 6.7778 19.19 65.90 0.2324E-13 -13.634

360.0 1346.0 6.9180 8.6129 8.0657 6.74?9 18.71 68.11 0.167BE-13 -13.775

380.0 1347.5 6.7002 8.5037 7.8749 6.7224 18.27 70.23 0.1226E-13 -13.911 400.0 1348.4 6.4840 8.3955 7.6856 6.6952 17.87 72.26 0.9054E-14 -14.043

420.0 1349.0 6.2693 8.28 80 7.4976 6.6683 17.52 74.21 0.6749E-14 -14.171

440.0 1349.4 6.0560 8.1813 7.3109 6.6415 17.19 76.09 0.5074E-14 -14.295 460.0 1349.6 5.8440 8.0753 7.1253 6.6150 16.89 77.91 0.3845E-14 -14.415

480.0 1349.7 5.6334 7.9700 6.9409 6.5886 16.61 79.68 0.2934E-14 -14.533

500.0 1349.8 5.4240 7.8653 6.7576 6.5624 3.6895 16.35 81.43 0.2253E-14 -14.647

520.0 1349.9 5.2159 7.7612 6.5754 6.5363 3.6830 16.10 83.19 0.1739E-14 -14.760

540.0 1349.9 5.0089 7.6577 6.3942 6.5104 3.6764 15.85 84.98 0.1350E-14 -14.870

560.0 1350.0 4.8032 7.5548 6.2141 6.4847 3.6700 15.61 86.83 0.1053E-14 -14.978

580.0 1350.0 4.5987 7.4526 6.0350 6.4591 3.6635 15.35 88.77 0.8248E-15 -15.084

600.0 1350.0 4.3953 7.3509 5.8570 6.4336 3.6571 15.09 90.85 0.6488E-15 -15.188

620.0 1350.0 4.1931 7.2498 5.6800 6.4Ce3 3.6507 14.81 93.09 0.5123E-15 -15.290

640.0 1350.0 3.9921 7.1493 5.5040 6.3832 3.6444 14.51 95.55 0.4061E-15 -15.391

660.0 1350.0 3.7922 7.0494 5.3290 6.3582 3.6381 14.19 98.26 0.3231E-15 -15.491

680.0 1350.0 3.5935 6.9500 5.1550 6.3333 3.6318 13.85 101.27 0.2579E-15 -15.588

700.0 1350.0 3.3959 6.8512 4.9820 6.3C86 3.6256 13.48 104.65 0.2067E-15 -15.685

750.0 1350.0 2.9067 6.6066 4.5538 6.2474 3.61C2 12.44 114.99 0.1208F-15 -15.918

800.0 1350.0 2.4244 6.3654 4.1315 6.ie70 3.5950 11.27 128.77 0.7250E-16 -16.140

850.0 1350.0 1.9488 6.1276 3.7151 6.1275 3.5BC0 10.03 146.74 0.4481E-16 -16.349

900.0 1350.0 1.4797 5.8931 3.3044 6.0688 3.5652 8.81 169.31 0.2866E-16 -16.543

950.0 1350.0 1.0170 5.6617 2.8994 6.0109 3.5537 7.71 196.20 0.1905E-16 -16.720

1000.0 1350.0 0.5606 5.4335 2.4998 5.9538 3.5363 6.77 226.31 0.1321E-16 -16.879
240 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospherie temperature—Continued EXOSPHERIC TEMPERATURE = 1300 CEGREES

HEIGHT
no. 9 STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 241

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TE"PFR4TIIP.E = 1250 CEGREES HEIGHT TEMP LOG N I 02 1 LCG NIC) LCG NINZI LOG N(HE) LOG 'J ( H ) «6«N SC4LE DENSITY LOG CEN

KM nEG K /GM3 /CM3 /CM2 /CM? /CM? "01. WT HT KM GM/CM3 GM/CM3

120. J 355.3 10.3751 ID. 3808 11.6021 7.5315 26.90 11.62 0.2461E-10 -10.609

130.0 550.8 10.3337 13.514S 11. IT.'. 7.3693 26.32 18.43 0.7930E-11 -11.101

140.0 703.3 9.3767 13.2830 lu.7786 7.272C 25.84 24.12 0.3807E-11 -11.419

150.0 823.3 9.7036 13.1124 l.j.5313 7.2041 25.40 28.79 0.2193E-11 -11.659

163.0 916.6 9.4776 9.9761 13.3274 7.1528 24.99 32.69 0.1400F-11 -11.854

170.0 989.6 9.2812 9.8613 10.1512 7.1117 24.59 35.97 0.9535E-12 -12.021

180.0 1046.5 9.1345 9.7608 9.9935 7.0776 24.20 38.77 0.6791E-12 -12.168

190.0 1091.1 3.3417 9.6733 9.8487 7.0483 23.82 41.23 0.4992E-12 -12.302

200.0 1125.3 8.7889 9.5871 9.7133 7.3224 '3.43 43.33 0.3758E-12 -12.425

210.0 1153.0 8.6436 9.5093 9.5848 6.9991 23.06 45.24 3.2831E-12 -12.540

220.0 1174.2 8.5339 3.4355 9.4615 6 . 9 7 i 7 22.68 46.98 3.2241E-12 -12.650

230.0 1193.8 8.3686 9.3648 9.3423 6.9578 22.32 48.57 0.1763E-12 -12.754

243.0 1233.7 8.2366 9.2964 9.2261 6.9389 21.95 50.37 0.1401E-12 -12.854

250.0 1213.9 8.1073 9.2299 9.1124 6.9239 21.60 51.43 3.U22E-12 -12.950

260.0 1221.8 7.980O 9.1649 9.9097 6.9C36 21.25 52.33 0.9055E-13 -13.043

270. 1227.9 7.8545 9.1311 a. 3906 6.e868 23.90 54.12 C.7353C-13 -13.134

280.0 1232.8 7.7304 9.9382 8.7817 6.87C' 20.57 55.38 0.6095F-13 -13.221

290.0 1236.5 7.6375 3.9760 8.6739 6.8544 20.25 56.60 0.4929E-13 -13.307

300.0 1239.5 7.4355 8.9145 3.5679 6.8387 19.94 57.79 0.4366E-13 -13.391 320.0 1243.6 7.2441 8.7931 8.3554 6.8077 19.36 60.09 0.2802E-13 -13.553

340.0 1246.1 7.3352 8.6732 8.1462 6.7774 18.83 62.28 0.1961E-13 -13.708

360.0 1247.6 6.7685 8.5546 7.9389 6.7475 13.34 64.33 0.1392E-13 -13.856

380.0 1248.5 6.5336 9.4370 7.73''2 6.7183 17.91 66.39 0.9999F-14 -14.000 400.0 1249.1 6.3304 3.3203 7.5290 6.63e7 17.52 68.33 0.7265E-14 -14.139

420.0 1249.5 6.0687 3.2344 7.3261 6.6596 17.17 70.13 0.5331E-14 -14.273

440.0 1249.7 5.8334 8.0892 7.1246 6.63C8 16.85 71.89 0.3947E-14 -14.404 460.0 1249.3 5.6096 7.9748 6.9242 6.6C21 16.55 73.61 0.2946E-14 -14.531

480.0 1249.9 5.3821 7.8613 6.7251 6.5737 16.28 75.31 0.2214E-14 -14.655

500.0 1249.9 5.1560 7.7480 6.5271 6.5454 3.8616 16. CI 77.02 0.1674E-14 -14.776

520.0 1250.? 4.9312 7.6356 6.3303 6.5172 3.e545 15.74 78.78 0.1274E-14 -14.895

540.0 1250.0 4.7378 7.5238 6.1347 6.4893 3.8474 15.47 89.61 0.9741F-15 -15.011

560.0 1250.0 4.4856 7.4127 5.9402 6.4615 3.8404 15.20 82.57 0.7436E-15 -15.126

580.0 1253.0 4.2647 7.3023 5.7468 6.4338 3.8335 14.90 84.69 0.5779F-15 -15.238

600.0 1250. 3 4.3451 7.1925 5.5546 6.4064 3.8265 14.58 87.03 0.4489E-15 -15.349

620.0 1250.3 3.3268 7.0833 5.3634 6.3790 3.8197 14.24 89.63 0.3489E-15 -15.457

640.0 1250.0 3.6096 6.9748 5.1733 6.3519 3.el28 13.87 92.56 0.27286-15 -15.564

660.0 1250.9 3.3938 6.8668 4.9843 6.3249 3.3C6C 13.47 95.87 0.2142E-15 -15.669 680.0 1250.0 3.1791 6.7595 4.7964 6.29e0 3.7993 13.03 99.63 0.1689E-15 -15.772

700.0 1250.0 2.9657 6.6528 4.6096 6.2713 3.7925 12.57 103.91 0.1338E-15 -15.874

750.0 1250.0 2.4374 6.3837 4.1471 6.2052 3.7759 11.29 117.23 0.7635E-16 -16.117

800.3 1250.3 1.9165 6.1282 3.6910 6.14CC 3.7595 9.93 135.22 0.4511E-16 -16.346

850.0 1250.0 1.4028 5.8713 3.2413 6.3758 3.7433 8.61 158.17 0.2776E-16 -16.557

900.0 1250.0 0.8962 5.6180 2.7978 6.0124 3.7273 7.44 185.71 0.1790E-16 -16.747

950.0 1250.0 3.3965 5.3682 2.3603 5.9498 3.7116 6.47 216.23 0.1214E-16 -16.916

1000.0 1250.0 -0.0964 5.1218 1.9288 5.8882 3.6961 5.73 247.55 0.8667E-17 -17.062
242 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospherie temperature—Continued EXOSPHERIC TEMPERATURE = 1200 DEGREES

HEIGHT
K0, 9 STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 243

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 1150 CEGREES HEIGHT
244 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature— Continued EXOSPHFRIC TEMPEftATUUF. = U03 CEGREES HEI3HT TEM" LOG NIG2) LOG NIG) LOG N(N2) LOG N(H6) LOG N(H) MEAN SCALE DENSITY LOG OFN

KM OEG K /CM3 /CM3 /CM3 /CM3 /CM3 MOL UT HT KM GM/C3 GM/CM3

120.0 355.3 13.3751 10.8803 11.6021 7.5315 26.90 11.62 0.2461E-19 -IP. 609

130. J 531. ID. 3427 ID. 5272 11. 1 1 A 2 7.3783 26.31 1 7 .

•> 2 0.8U5E-11 -11.091

140. J 665.4 9.9»22 10.2979 lj.7864 7.2847 25. 8C 22.84 0.38826-11 -11.411

150.0 768.1 9.7016 10.1265 10.5330 7.21J8 25.33 26.94 0.2210F-11 -11.656

160.0 846.5 9.4661 9.9876 lj.3216 7.1684 24.88 30.3? 3.13896-11 -11.857

170.0 906.4 9.2589 9.8692 1J.1365 7.1278 24.44 33.15 0.9300F-12 -12.032

180. J 952.1 9.0706 9.7644 9.9690 7.0937 24. CO 35.56 0.6501E-1? -12.187

190.0 937.0 8.8954 9.6690 9.8137 7.064C 23.57 37.66 0.4687E-12 -12.329

2O0.0 1013.7 8.7297 9.5803 9.6671 7.0375 23.14 39.51 0.3458E-12 -12.461

210.0 1034.1 8.5709 9.4966 9.5270 7.0134 22.72 41.18 0.2597F-12 -12.586

220.0 1049.7 8.4172 9.4165 9.3917 6.99C9 22.30 42.72 0.19796-12 -12.704 230.0 1061.6 8.2675 9.3392 9.2600 6.9698 21.89 44.15 0.15266-12 -12.817

240.0 1070.6 8.1209 9.2640 9.1311 6.9496 21.48 45.50 0.1188E-12 -12.925

250.0 1077.6 7.9766 9.1905 9.0045 6.93C2 21. C9 46.80 0.9328E-13 -13.030 260.0 1082.9 7.H342 9.1182 8.8796 6.9113 20.70 48.05 0.73816-13 -13.132

270.0 1086.9 7.6934 9.0470 8.7561 6.8929 20.33 49.25 0.5880E-13 -13.231

280. J 1090.0 7.5538 8.9766 8.6337 6.8748 19.98 50.4? 0. 47136-13 -13.327

290.0 1092.4 7.4152 3.9068 8.5123 6.8570 19.64 51.57 0.38006-13 -13.420

300.0 1094.2 7.2776 8.8377 8.3917 6.8394 19.31 52.68 3.308CE-13 -13.512

320.0 1096.6 7.0046 8.7007 8.1526 6.8048 18.71 54.31 0. 20576-13 -13.688

340.0 1098. 6.7340 3.5651 7.9156 6.7707 18.18 56.83 0.13926-13 -13.856

360.0 1098.8 6.4656 8.4307 7.6806 6.7369 17.71 58.74 0.95836-14 -14.019

380.0 1099.3 6.1990 3.2973 7.4472 6.7035 17. ?9 60.54 0.66886-14 -14.175

400.0 1099.6 5.9342 8.1649 7.2153 6.67C3 16.92 62.25 0.47246-14 -14.326

420.0 1099.8 5.6711 8.0333 6.9850 6.6373 16.58 63.91 0.33716-14 -14.472 440.0 1099.9 5.4095 7.9025 6.7560 6.6046 16.27 65.53 0.24236-14 -14.615

460.0 1099.9 5.1495 7.7725 6.5284 6.572C 15.97 67.16 0.17636-14 -14.754

480.0 1100.0 4.8911 7.6433 6.3021 6.5397 15.67 68.85 0.12896-14 -14.890

500.0 1100.0 4.6342 7.5148 6.0772 6.5075 4.1746 15.36 70.64 0.94856-15 -15.023

520.0 1100.0 4.3788 7.1871 5.8536 6.4756 4.1665 15.04 72.59 0.70216-15 -15.154

540.0 1100.0 4.1248 7.2601 5.6213 6.443e 4.1585 14.68 74.76 0.52276-15 -15.282

560.0 1100.0 3.8724 7.1339 5.4103 6.4122 4.1506 14.30 77.21 0.39116-15 -15.408

580.0 1130.0 3.6214 7.0084 5. 1905 6.3808 4.1427 13.88 80.03 0.29436-15 -15.531

600.0 UOO.O 3.3718 6.8836 4.9720 6.3496 4.1348 13.41 83.28 0.22266-15 -15.653

620.0 1100.0 3.1237 6.7595 4.7548 6.3185 4.1270 12.90 87.07 0.16936-15 -15.771

640.0 1100.0 2.3770 6.6362 4.5388 6.2e77 4.1192 12.35 91.47 0. 12956-15 -15.888

660.0 110O.O 2.6317 6.5135 4.3241 6.257C 4.1115 11.77 96.53 0.9971E-16 -16.001

680.0 1100.0 2.3878 6.3916 4.1105 6.2265 4.1033 11.15 102.48 0.77286-16 -16.112

700.0 1100.0 2.1452 6.2703 3.8982 6.1961 4.0962 10.52 109.25 0.60346-16 -16.219

750.3 1100. 1.5449 5.9702 3.3726 6.121C 4.0772 8.95 130.26 0.33726-16 -16.472

800.0 11OO.0 0.9530 5.6742 2.8544 6.0469 4.0586 7.54 156.84 0.20016-16 -16.699

850.0 1100.0 0.3692 5.3823 2.3433 5.9739 4.0402 6.40 187.19 3.12706-16 -16.896

900.0 1100. -0.2065 5.0945 1.8393 5.9019 4.0221 5.57 218.13 0.86266-17 -17.064

950.3 1100.0 -3.7743 4.8106 1.3422 5.8308 4.0042 5. CO 246.66 0.62386-17 -17.205

1000.0 1100.0 -1.3344 4.5305 0.8519 5.76C7 3.9865 4.61 270.74 0.47506-17 -17.323
N0. 9 STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 245

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 1050 DEGREES HEIGHT
246 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 1000 CEGREES HEIGHT
STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 247

Tabi-e 1. —Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 950 DEGREES HEIGHT
248 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EX0SPHEP.1C TEMPERATURE = 930 CEGREES HEIGHT
STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 249

Tabuj 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXQSPHERIC TEMPERATURE = 850 CEGREES HEISHT

KM TEMP DEG K LCG NI02) /CM3

LOG N(O) LOG NIN2) LOG N(HE) /CM3 /CM3 /CM3 LOG N(H)

/CM3 MEANMOL taT SCALE DENSITYGM/CM3

LOG DEN GM/CM3

120.0 355.0 10.3751 10.8808 11.6021 7.5315

130.0 479.7 10.3664 13.5611 11.1405 7.4031

140.0 573.0 9. 9911 13.3349 10.8023 7.3180

150.0 642.8 9.6839 10.1563 10.5271 7.2548

26.90 11.62 0.2461E-10 -10.609

26.27 16.1? 0.8630E-11 -11.064

25.68 19.76 0.4046E-11 -11.393

25.11 22.74 0.2203E-11 -11.657

160.0 170.0

180.0

190.0 200.0

695.0

734.1 763.3

785.2

801.5

9.4168 9.1754

8.9512

8.7392

8.5358

13.0058 9.8732 9.7527

9.6405 9.5343

10.2891 10.0747 9.8764

9.6892

9.5101

7.2C46

7. 1627 7.1262

7.0936

7.0638

24.55

23.98

23.42 22.86

22.31

25.23 27.36

29.22 30.89

32.41

1313E-11 8305E-12

5478E-12 3727E-12

2598F-12

-11.882

-12.081

-12.261 -12.429

-12.535 210.0 220.0

230.0

240.0

250.0

813.7 822.9

829.7

834.8 838.6

8.3388 8.1466

7.9580

7.7722

7.5886

9.4326

9.3340

9.2379

9.1437 9.0509

9.3368 9.1679

9.0023

8.8393 8.6783

7.0359

7.0094

6.9840 6.9595

6.9355

21.77 33.83 0.1846E-12 -12.734

21.24 35.16 0.1333E-12 -12.875

20.73 36.43 0.9760E-13 -13.011

20.25 37.65 0.7232E-13 -13.141

19.79 38.81 0.5416E-13 -13.266

260. D 270.0

280.0 290.0

300.0

841 .5 843.6 845.2 846.4

847.3

7.4067

7.2 2 64 7.0472

6.8691

6.6918

8.9592

8.8685

8.7785

8.6891

8.6003

8.5190

8.3609 8.2040 8.0479

7.8927

6.9120

6.8889

6.8661 6.8435

6.8211

19.36

18.95

18.58 18.24

17.92

39.94

41.01 42.04

•43.03 43.97

0.4096E-13 0.3125E-13

0.2403E-13 0.1862E-13

0.1452E-13

-13.388 -13.505

-13.619

-13.730

-13.838

320.0

340.0 360.0

380.0

400.0

848.5

849.2

849.5 849.7

849.9

6.3398 5.9904

5.6435

5.2988 4.9563

3.4239

8.2491

8.0755

7.9031 7.7319

7.5844 7.2785

6.9748 6.6730

6.3731

6.7767 6.7329

6.6894

6.6462

6.6033

17. 36 16.87

16.45 16.06

15.67

45.73 47.35 48.88

50.39

51.93

0.8994E-14

3.5686E-14 0.3656E-14

0.2385E-14

0. 1574E-14

-14.046

-14.245

-14.437 -14.623

-14.803 420.0

440.0

460.0

480.0

500.

849.9 850.0

850.0 850.0

850.0

4.6158 4.2774

3.9410 3.6066

3.2741

7.5616 7.3924

7.2242

7.0570

6.8907

6.0751

5.7788 5.4843

5.1915

4.9004

6.5607

6.5183

6.4742

6.4344

6. 3928 4.9C91

15.27 14.84

14. 34 13.78

13.13

53.61 55.52 57.78

60.51 63.86

0. 1050E-14 0.7068E-15

0.4799E-15

0.3286E-15 0.2269E-15

-14.979

-15.151

-15.319

-15.483 -15.644

520.0

540. 560.0

580.0

600.0

850.0

850.0

850.0

850.0

850.0

2.9436

2.6150

2.2883

1.9634

1.6405

6.7255

6.56 12 6.3978

6.2354

6.0739

4.6111 4.3234

4.0373

3.7530

3.4702

6.3514

6.3103

6.2694 6.2268

6.1884

4.8987 4.8884

4.8781

4.8679 4.8577

12.40

11.61 1C.76 9.89

9.03

67.99

73.09

79.32 86.80

95.63

0. 1582E-15 0.1114E-15

0.7940E-16 0.5733E-16

0.4201E-16

-15.801 -15.953 -16.100

-16.242

-16.377 620.0 640.0

660.0

680.0

700.0

850.0 850.0

850.0 850.0

850. J

1.3194

1.0001 3.6826

0.3670

0.0531

5.9134 5.7537

5.59 50 5.4372

5.2803

3.1891 2.9096

2.6317

2.3553 2.0806

6. 1482 6.1083 6.0685

6.0290

5.9898

4. 8476 4.8375

4.8275

4.3176

4.8077

8.21 7.45 6.78 6.20

5.71

105.80

117.18

129.52 142.47

155.62

0.3130E-16 0.2375E-16

0.1837E-16 0.1450E-16

0.1167E-16

-16.504 -16.624

-16.736

-16.839

-16.933

750.0 800.0

850.0

900.0 950.0

850.0

850.0

850.0

850.0

850.0

-0.7238

-1.4898

-2.2453 -2.9903

-3.7251

4.8918

4.5088 4.1311

3.7586

3.39 11

1.4004

J. 7297 0.0684

-0.5839 -1.2272

5.8926

5.7967

5.70 2 2 5.609C 5.5170

4.7832

4.7591

4.7353

4. 7118 4.6886

4.82

4. 30

4. CO 3.82

3. 70

186.73 0.7364E-17

212.21 231.40 245.88

257.56

0.5116E-17

0.3799E-17

0.2940E-17

0.2333E-17

-17.133

-17.291

-17.420 -17.532

-17.632 1000.0 850.0 3.0287 •1.8617 5.4263 4.6658 3.6C 267.89 0.1880E-17 -17.726
250 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 830 DEGREES

HEIGHT
STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 251

Table 1. —Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 750 DEGREES HEIGHT
252 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC TEMPERATURE = 700 DEGREES HEIGHT
STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 253

Table 1.—Detailed atmospheric data as a function of height and exospheric temperature—Continued EXOSPHERIC T6MP6R4TURE = 650 DEGREES

HEIGHT
254 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

J

6,£

o o

43 -<
STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 255
256 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS
STATIC DIFFUSION MODELS OF THE UPPER ATMOSPHERE 257

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U S GOVERNMENT PRINTING OFFICE 1965 —781-252