Only with the advent of the space era it was possible to gather reliable information about the density and composition of the Earth's upper atmosphere above 50 km. The information stems from analyzing the orbits of artificial satellites and from satellite missions carrying mass spectrometers and scat-terometers.

First reliable information was made available in the US Standard Atmosphere (1976). In parallel, several versions of the CIRA (COSPAR International Reference Atmosphere) were developed and made available in the years 1972, 1986, and 1992. One of the more elaborate models openly available is called MSIS (Mass Spectrometer and Incoherent Scatter), identifying the principal source of the data underlying the model. The version MSISe-90 (where e stands for extended) was developed by A. E. Hedin et al. from Nasa Goddard Space Flight Center. It is available over the internet (http://nssdc.gsfc.nasa.gov) and documented in [50] and [51]. It may be used as an a priori model for the density and temperature of the (constituents of the) upper atmosphere.

MSISe-90 gives the density of the atmosphere as a function of the height above the Earth's surface, of the DoY (Day of Year), of the geocentric latitude and longitude, of the time of day, and of true (local) solar time. The solar flux F(10.7 cm) at 10.7 cm (corresponding to 2800 MHz) and the magnetic index Ap are scaling factors of the model. When using realistic values for these parameters, the variations due to the 11 year solar cycle are therefore implicitly taken into account.

Figures 3.20 and 3.21 show that the solar flux F(10.7 cm) and the magnetic index Ap are subject to significant variations of several frequencies within one year. The two figures documenting the year 1999 stem from the series Solar-Geophysical Data, prompt reports [28]. The MSISe-90 computer programs allow it to specify mean values of these indicators over longer time periods or to use recent values. We do not address such details here and confine ourselves to present some prominent features of the upper atmosphere.

Figures 3.22-3.25 were produced using MSISe-90. They give an impression of the many variations that should be taken into account when implementing an a priori model for atmospheric drag. The most significant density variation is due to the height above the surface. Locally (i.e., over a few tens of km), this variation may be accounted for by the barometric formula p{h) = po e-^ , (3.121)

where p0 is the density at the reference height h0 and H0 is the scaling height at ho .

Figure 3.22 shows the logarithm (referring to base 10) of the density of the atmosphere (in units of kg/m3) for March 24, 10h UT for geographical longitude 7.5° and latitude 45.5° (corresponding to a location in Switzerland). A solar flux of F(10.7 cm) = 150 (in solar flux units) and an index of Ap = 4 were assumed. Figure 3.22 reveals, that MSISe-90 is a composed model. The homosphere, consisting of troposphere (0 — 15 km), stratosphere (15 — 50 km)

Fig. 3.22. Density of the atmosphere profile according to MSISe-90

Fig. 3.22. Density of the atmosphere profile according to MSISe-90

and mesosphere (50 — 90 km), the thermosphere (90 — 400 km) and the exo-sphere (400 — to km) obviously were dealt with separately.

Figure 3.22 shows that the density drops within the first 50 km by about a factor of 1000, at a height of 100 km the density is only of the order of 10~6 of the value at sea level. Between 100 km and 200 km and between 200 km and 1000 km the density is reduced by about a factor of ten thousand (in each case).

Figure 3.22 shows that even for orbits with small eccentricities the density at perigee is orders of magnitude higher than in apogee. For a satellite with an apogee height hapo « 200 km and a perigee height hper ~ 126 km , corresponding to a « 6541 km and e « 0.006, Figure 3.22 lets us expect « 40 . For close Earth satellites the velocity w.r.t. the rotating frame is of the order of 6 — 7 km/s . Using formula (3.118) one must expect significant accelerations due to drag up to heights of about 1000 km.

Figures 3.23 - 3.25 show the variations of the density in a height of 100 km as a function of latitude, of the time of the day, and of the day of the year. The longitudinal variations are not very pronounced and therefore not documented here. Four curves (corresponding to spring, summer, fall, and winter) are given in Figures 3.23 and 3.24. Figure 3.23 shows a pronounced latitudinal variation corresponding to a factor of about 3 in density. In spring and fall the density distribution is symmetric w.r.t the equator whereas strong asymmetries are observed in summer and winter (the seasons in Figures 3.23 -3.25 refer to the Northern hemisphere).

Figure 3.24 documents, that daily variations of the density of the atmosphere are significant and must be taken into account. Figure 3.25 shows the variation of the density as a function of the day of the year (for "Switzerland").

Latitude(Deg)

Fig. 3.23. Density of the atmosphere in a height of 100 km as a function of latitude

Latitude(Deg)

Fig. 3.23. Density of the atmosphere in a height of 100 km as a function of latitude

Density

Density

Fig. 3.24. Daily variations of the density of the atmosphere in a height of 100 km at mid-latitude h

Fig. 3.24. Daily variations of the density of the atmosphere in a height of 100 km at mid-latitude

At a height of 100 km the density is about a factor of 2 lower in summer than in winter. (Experience tells that, fortunately, effects of the same order of magnitude are not observed at "normal" altitudes in Switzerland!).

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