- Email: [email protected]
Atmospheric density from the low altitude satellite 1970-48A: Comparison of orbital decay measurements, accelerometer measurements and atmospheric models
Planet.
Space
Sci. 1975, Vol. 23, pp.
323 to 335.
Permttxm
Press.
Printed
in Northern
Ireland
ATMOSPHERIC DENSITY FROM THE LOW ALTITUDE SATELLITE 1970-48A : COMPARISON OF ORBITAL DECAY MEASUREMENTS, ACCELEROMETER MEASUREMENTS AND ATMOSPHERIC MODELS Space Physics Laboratory,
H. R. RUCGE and B. K. CHING The Aerospace Corporation, El Segundo, California 90245, U.S.A. (Received injinal form 26 June 1974)
Abstract-Atmospheric densities have been deduced from high resolution radardetermined orbital decay data and from data obtained from a uniaxial accelerometer flown onboard the low altitude satellite 197048A. Data were obtained during late June and early July, 1970. The orbital decay-deduced densities, having an effective 6 hr temporal resolution, were determined at an altitude of 143 km, essentially one-half scale height above perigee. The accelerometer deduced densities at the same altitude were obtained on both the approaching-perigee and leaving-perigee portions of each of fifty-nine orbits. A detailed comparison of the densities derived from both types of data is presented. In general, agreement is very good. A comparison of both types of data has also been made with the Jacchia 1970 and 1971 atmospheric models as well as the new OGO-6 atmospheric model. The Jacchia models display reasonable agreement with the data, but the OGO-6 model is unsuitable as a representation of atmospheric density at this altitude. 1. INTRODUCTION The great majority of all currently used atmospheric models (e.g. Jacchia, 1964, 1970, 1971; CIRA, 1965; U.S. Standard Atmosphere, 1962) have relied upon orbital decay measurements from heights above 200 km as the primary source of atmospheric density data. These density data necessarily represent temporal and spatial averages of truedensity, typically over a period of 848 hr in time and a minimum of tens of degrees in latitude and/or longitude. Accelerometers, on the other hand, can measure “instantaneous” orbital decay (i.e. deceleration); and hence “instantaneous” atmospheric densities can be deduced. A detailed comparison of these two types of density data is made in this paper. Such comparisons are important because the highly accurate accelerometer data can be used as a basis for checking the accuracy and consistency of the orbital decay data that were so often used as a basis for atmospheric models. In addition, the comparison of simultaneously obtained data can provide unambiguous information concerning the loss of spatial and temporal structure in the atmospheric density as inferred from orbital decay. Some comparisons of the density deduced from orbital decay and accelerometer measurements have been made for the OVl-15 and OVl-16 satellites by the group at the Air Force Cambridge Research Laboratories (Champion ef al., 1970a, b; Marcos et al., 1971) and for the LOGACS experiment by DeVries (1972). However, systematic comparisons have not been made using most of the AFCRL data, although the few examples of comparisons shown seem to give good agreement (4 per cent) between the two types of data. DeVries finds differences of between 10 and 30 per cent, dependent upon geomagnetic activity, for the two days for which he has presented data. It is significant to note that density measurements at heights below 200 km are extremely sparse. The major obstacle has been the environment itself, whose denseness severely limits the lifetime of a satellite. Very few satellites besides those cited above have provided density data, and consequently the spatial, diurnal, and seasonal coverage of the data are far from 323
324
H. R. RUGGE and B. K. CHING
complete. Furthermore, the bulk of the existing data was acquired only in the past few years and thus encompasses only a portion of a solar cycle. Because of the lack of data, the earlier atmospheric models had to rely on extrapolation in order to represent the regime between 100 and 200 km. As data became available some improvements were incorporated in the models (e.g. Jacchia, 1971), but there still exists the need for continued development and improvement based on observational data. The purpose of this paper is twofold: first, to systematically compare orbital decaydeduced densities obtained with highly accurate tracking radars and accelerometer-deduced densities obtained with a well calibrated instrument onboard a stabilized satellite; second, to compare the densities obtained by both methods with several recent atmospheric models (those of Jacchia (1970, 1971) and the atmospheric model based on recently acquired OGO-6 mass spectrometer data (Hedin et al., 1974)). 2. RADAR DE TERMINED ORBIT&
DECAY MEASURJZMENTS
The satellite used in this study was the U.S. Air Force vehicle 1970-48A. The satellite was launched on 25 June 1970 into an orbit of inclination 109” with perigee near 135 km and apogee near 400 km. The data used in this study were obtained from 25 June-5 July 1970. During this period the latitude of minimum altitude was 55”-65”N and the local time near 9 a.m. The orbit of the satellite was determined from high-precision radar tracking data. The atmospheric densities deduced near perigee from the orbital decay data used in this study were provided by Schusterman (1972) of The Aerospace Corporation. The method he employed is described in detail by DeVries et al. (1972). Briefly, the density was obtained by fitting a drag force model (i.e. density model) along with the orbital elements to the radar observations. The model used was the Jacchia-Walker density model (Jacchia, 1964; Walker, 1965) as modified by Bruce (1966) for low-altitude applications. The fitting procedure yields the appropriate integrated density around the orbit (which is heavily weighted by the density near perigee) but not necessarily the correct density at perigee due to possible errors in the scale height of the assumed model. King-Hele (1966) has shown that the error in the density related to the uncertainty in scale height is minimized at about half a scale height above perigee. Thus, in this study the density is evaluated at 143 km, which was the mean value of perigee plus half a scale height during the period under consideration. Owing to the geometry of the satellite, which was cylindrical with a large length to diameter ratio, and the departure from free molecular flow conditions at perigee, it was necessary to use a carefully evaluated height dependent drag coefficient in the orbital analysis. The drag coefficient was computed (Kainer, 1968) assuming perfect accommodation and diffuse reflection of atmospheric particles and taking into account the attitude of the satellite and the variable ratio of speeds of the satellite and the ambient particles. The resultant drag coefficient was dependent on both altitude and atmospheric temperature (as predicted by the atmospheric model). The orbital analysis was performed using 8 revolution (rev) fit spans and 8 fitting parameters. Six of the parameters which described the epoch vector (position and velocity) were fit over an entire g-rev span. The other two parameters were drag parameters, each fit over 4 rev of the span. This “splitting” technique is particularly useful and successful for low-altitude (high drag) orbits and increases the resolution of the derived density values.
ATMOSP~~C
DENSITY
FROM LOW ALT~DE
SATELLITE 1970-48A
325
The fitting spans were overlapped through the data in two rev increments, effectively giving a 4-rev running average (6 hr average) of the density every two rev. It should be noted that although the densities are assigned to time points at the middle of the fit spans, the values are really only averages over the 6-hr intervals of the fit spans. The major source of uncertainty in the density deduced from the orbital decay is that associated with the drag coefficient. This uncertainty results primarily from the necessity of making assumptions concerning the angular dependence of atmospheric particle reflectivity from the surface of the satellite (diffuse, specular or intermediate between the two) and the value of the accommodation coefficient, the ratio of energy change experienced by the impinging atmospheric particles to the maximum energy change that could take place. These assumptions are required because of the lack of adequate information concerning gas-surface interactions. These problems and the degree of uncertainty inherent in these assumptions are discussed in detail by Cook (1965). Using arguments similar to those of Cook and applying them to the present vehicle, we estimate that the uncertainty in the drag coefficient is fl &lo per cent. The error related to the uncertainty in scale height is estimated to be 1 per cent or less (see King-Hele, 1966); and that related to the uncertainty in perigee height is negligible, as the orbit was very well determined. 3. ACCELEROMETER
MElAS~~NTS
The accelerometer flown on 1970-48A was a single axis Bell MESA (miniature electrostatic accelerometer) similar to those flown on the LOGACS experiment (DeVries, 1972) and on the OVl-15, -16, -20 satellites (Champion et al., 1970a). The accelerometer measures the instantaneous deceleration, CI,along the orbital path. The deceleration is related to the atmospheric density by the relationship a=_-_
1 -GA 2
[ m 1 “a
(0
where p is the atmospheric density, A is the effective satellite frontal area, m is the satellite mass, v is the satellite velocity relative to the atmosphere, and C, is the drag coefficient discussed previously. The relationship between the output C (counts) of the accelerometer and the deceleration a is given by a=I;%+b (2) where the scale factor F was accurately determined from a ground calibration (in a l-g environment) and the bias b near apogee where the deceleration as a result of drag was essentially negligible. Determined in this way, a depends in no way on the orbital decaydeduced data; and hence the two measurements can be compared in a truly independent manner. The largest source of error in the accelerometer-deduced density is the ~10 per cent uncertainty in C, which has already been discussed. The scale factor and bias in the experiment were determined to better than 1 per cent. Another potential source of error is in the effective satellite velocity used in Equation (1). If neutral atmospheric winds are present, their components along or against the satellite velocity vector must be added or subtracted and hence will change the value of the effective satellite velocity used in Equation (1). Recent observations of winds in the lower ~ermosphere at high latitudes (Brekke, et al., 1973) have indicated speeds as high as 150 m/see. Even larger wind speeds have been reported, but only during intense geomagnetic disturbances flu, 2 7) and hence need not be
H. R. RUGGE
326
and B. K. CHING
considered here. A wind of ~200 m/set blowing along the satellite velocity vector would introduce an error of 5 per cent in the accelerometer-deduced density, which was computed assuming no wind. However, the data of Brekke et al. indicate that at a local time of our data (“9 a.m.) the high latitude winds are of order 20 m/set and not, on average, aligned with the satellite velocity vector, and thus would have an effect of less than 1 per cent. As for low latitude winds, there exist insticient data to define the normal global-scale circulatory system, but speeds of the order of 100 m/set have been observed on occasion (Bedinger, 1972). Considering all these factors we conclude that random errors of 5 f5 per cent due to “gusts” of wind may occur from time to time, but we do not believe there is any evidence that indicates there might be a comparable systematic error in our densities. The densities deduced from the accelerometer at 143 km were obtained for both the approaching-perigee and leaving-perigee portions of each of 59 rev. Data were available during two time periods, the first covering 25-28 June 1970 and the second from 3-4 July 1970. The densities were obtained from the measured accelerations by the use of Equations (1) and (2) with the drag coefficient appropriate to 143 km. It is of interest to examine the accelerometer data in order to obtain a better understanding of the variability of the atmosphere. The upper graph in Fig. 1 presents the ratio of the approaching-perigee density data, to the average of all approaching-perigee data in the time period 25 June-5 July. These densities were obtained at 143 km near 70”N geographic latitude. As can be seen in the figure, variations in the density from the average density can be as large as 30 per cent and can occur in time periods as short as a few hours. APPROACHING - PERIGEE LATITUDE . 7O’N
1.2 4. 3
1.0
0.8
I
26
1 I 1 r
I
27 JUNE
28 I
I
I
3
4 JULY I
’
LEh4G-PER;GEE 1.2 -
LATITUDE . 3S’N
-I s
‘.O-
f
by
0.8 I 26
I 27 JUNE
1 28
1.
DENSITY
UPPER
GRAPH-RATIO
OF
FOR APPROACHING-PERIGEE
1970
ACCELEROMETER-DEDUCED PASSES
I 4 JULY
DATE, FIG.
I 3
r
(Pi)
DATA
AT
143 km
DENSITIES FOR THE
(p)
TO
THE
TIME PERIODS
AVERAGE
FOR WHICH
EXIST.
The latitude at which these data were taken was -70”N. LOWER FOR
GRAPH-RATIO
OF ACCELEROMETER-DEDUCED
DENSITIES
(p)
TO THE
AVERAGE
km FOR THE TIME PERIODS FOR WHICH The latitude at which these data were taken was -35’N.
LEAVING-PERIGEE
PASSES
(pL)
AT
143
DATA
DENSITY EXIST.
ATMOSPHBRIC DENSITY FROM LOW ALTITUDE SATELLITE
1970-48A
327
The lower part of Fig. 1 contains similar data for the leaving-perigee portion of the orbit. The geographic latitude corresponding to these data was -35”N. Again, variations from the average density are fairly large and can occur in a matter of hours. 4. COMPARISON OF DEDUCED DENSITIES
The density inferred from the orbital decay applies at an altitude of 143 km (half a scale height above minimum altitude) and at the latitude of minimum altitude. The densities measured at 143 km by the accelerometer on the approaching- and leaving-perigee portions of an orbit were obtained at latitudes that were displaced from that of minimum altitude by about +18” and -18”, respectively. In order to obtain an accelerometer-deduced density value more representative of the density at the location of the minimum altitude, where the orbital decay value applies, the before- and after-perigee results from the accelerometer have been averaged to yield one density value per orbit of data. Averaged in this way, there are a total of 59 accelerometer density points that can be compared with the orbital-decay results. Figure 2 presents a direct comparison of the accelerometer-deduced density and the radar-determined orbital decay-deduced density at an altitude of 143 km. The accelerometer densities, as mentioned above, are averages of data points taken about 10 min apart on the approaching- and leaving-perigee portions of a given rev; the orbital decay-derived densities represent 4-rev averages of data. As a result, the accelerometer data have a much higher temporal resolution (data points every rev or 1.5 hr) than the radar data have (data points every 4 rev or 6 hr). An example of this can be seen in Fig. 2 at =I700 hr on June 26. Both types of data show a decrease in density at this time. The accelerometer data indicate a considerable decrease while the orbital decay data do not have the time resolution to show the full depth of the decrease, which has essentially vanished 6 hr later. In spite of this inherent difficulty the agreement is still rather good. The maximum deviation between the curves is 120 per cent. Deviations of this size usually occur during transient density variations for the reason mentioned above. Most of the variations are 15 per cent. The data display two major characteristics during the time period for which data exist : a generally increasing density with time and variations which to some extent seem to follow
JUNE 26
FIG. 2.
&biPARISON
OF
THE
JUNE27
JUNE28
ACCELEROMETER-DEDUCED
JULY 3
DENSITY
AND
THE
ORBITAL
143 km. KS for the time period of interest is presented at the bottom of the figure. DEDUCJID
DENSITY
AT AN ALTITUDE
OF
DECAY-
H. R. RUGGE
328
JUNE26
and B. K. CHING
JUNE27
JUNE28
JULY 3
FIG. 3. ACCELEROMETER AND ORBITALDECAY-DEDUCED DENSITIES TAKlNO
SLIDINff
FOUR
REV AVERAGES
EVERY
TWO
AT
143 km
OBTAINED
BY
REV.
K. for the time period of interest is presented at the bottom of the figure.
geomagnetic activity as indicated at the bottom of Fig. 2 by the KP index. The gradual increase in the average level of the density correlates rather well with the solar FIO., index, which increased monotonically from a value of 142 flux units on 25 June-195 flux units on 4 July. The 3-hourly K.. index appears to correlate considerably better with the longer-time averaged orbital decay-deduced density than with the “instantaneous” accelerometerdeduced density. The geomagnetic correlations are more obvious if the monotonic increase in density is first removed. A fairer comparison of the orbital decay and accelerometer data can be made if they are treated similarly. Figure 3 shows the radar data as they were in Fig. 2. The accelerometer data have been treated as the radar data were, i.e. the data have been averaged over 4-rev intervals with a 2-rev overlap between intervals. As can be seen from Fig. 3, the agreement is good everywhere, especially during the first span of data in late June. A consistent difference of the accelerometer data from the radar data of rc + 10 per cent is observed during the second span of data. There appear to be no systematic uncertainties in the analysis which could account for this, and it may, of course, be only coincidence. The difference exists for less than half a day and is not regarded as evidence of a serious discrepancy between the two types of data. A more quantitative comparison of the agreement of the two types of data can be. obtained by averaging both sets of data. The result obtained by averaging the 30 orbital decay measurements and the 59 accelerometer measurements during the time period under discussion at an altitude of 143 km is as follows: Accelerometer:
pIdS= 352 x XI-la g cm-s
Orbital Decay:
ljlrlJ = 3.43 x IO-lag cm-s,
5. COMPARISON OF DENSITY DATA WITH RECENT MODEL ATMOSPHERES The density data obtained at 143 km from both the orbital decay and accelerometer measurements are compared with three recent model atmospheres; the OGO-6 (Hedin et al., 1974), the Jacchia, 1970 (J70) and Jacchia, 1971 (571) models. For this comparison the accelerometer data obtained at 143 km on both the approaching-McGee and leavingperigee portions of each orbit are treated separately and evaluated at the latitudes at which the measurements were made.
ATMOSPHERIC
DENSITY
FROM LOW ALTITUDE
SATELLITE 1970-48A
329
The OGO-6 model is a global, empirical model of the atmosphere based on OGO-6 neutral mass spectrometer data obtained at altitudes between 400 and 600 km. The model extends to altitudes as low as 120 km by virtue of a method of extrapolation analogous to that employed by Jacchia (1964). Although the authors of the model have cautioned against its use under conditions dissimilar to the data base (in this case the altitude), we decided to compare the present data with the model because one of us (Ching and Carter, 1973) found excellent agreement between the model and density data obtained from an ion gauge experiment at heights between 200 and 300 km. The OGO-6 model does not include 02, but this omission is not expected to affect the comparison by more than about 10-20 per cent at a height of 143 km. The results of the comparison of our data with the OGO-6 model at 143 km indicated a poor fit of that model to the observed density. As an example, the average of the ratio of the accelerometer-deduced density to the OGO-6 model density (R) for all data taken at 143 km at a latitude of approximately 68”N is l-74. The standard deviation, defmed in the usual way, is 0.27, i.e.
where Nis the number of observations, R,(= pi/p,) is the ratio of the ith density measurement made with the accelerometer at 143 km to the model density at that altitude, and R is the average ratio. As will be seen shortly, these values are substantially larger than those obtained with the Jacchia models. As mentioned previously, the neglect of O2 in the model can account for only 10-20 per cent of the disagreement with the data. A major problem of the model encountered at low altitudes is similar to that encountered in other older models (e.g. CIRA-1965, Jacchia, 1964); namely that there is an isopycnic level near 150 km that results from the imposition of constant boundary conditions at too high an altitude. In the OGO-6 model only N2 (but not He and 0) is constrained to be constant at the lower boundary of 120 km, but since it is the dominant constituent until about 200 km, this lower boundary constraint is sufficient to cause the isopycnic problem in total density. Another problem may be that the average model density at 120 km is too low; e.g. it is about a factor of 1.3 lower than that of Jacchia (1971) even after adjustment for 0, is made. Thus, it appears that the OGO-6 model will not be very useful at altitudes below 200 km unless a Bruce (1966)~type modification of the model, which was specifically designed to avoid the isopycnic difficulty, is used. The relatively high standard deviation for the OGO-6 model can be attributed principally to two deficiencies in the modeling of the geomagnetic effect. First, 24 hr averages of q, are used, thus shorter period changes are smoothed out. Second, with increased heating (higher K,), the model density decreases at 143 km as a result of the isopycnic problem discussed above. Perhaps the most commonly used recent upper atmospheric models are those of Jacchia published in 1970 and 1971 (J70 and 571 respectively). The basic differences, at altitudes 5200 km, between the 571 model and the 570 model are: (1) the inclusion of a stronger dependence of density variations on geomagnetic activity, (2) a reduction in the seasonal/latitudinal effect at heights above about 115 km, (3) a larger semiannual effect, and (4) an increase in the relative abundance of atomic oxygen. Because of the sometimes substantial differences in these models and the present lack of definitive data
FIG. 4. RATIO OFTHE ORBITAL DECAY-DEDUCED DENSITYTOTHE AT 143 kill.
JACCHIA 1910 MODELDENSITY
The comparison is for a latitude -52”N. K, for the time oeriod of interest is presented at the bottom-of the figure. L 1.
I
I
I
I
I
1.3E
St.
55
P
1.
1.
oI
1
1
I
1
26
28
30
2
4
6
JULY
JUNE 1970 FIG. 5.
UXOOF THEORBITALDECAY-DJZDUCEDDENSITYTOTHEJACCHXA I~~~MODELDEN~~ AT 143 km. The comparison is for a latitude of -52”N. Ke for the time period of interest is presented at the bottom of the figure. 330
ATMOSPHERIC
DENSITY
FROM LOW ALTITUDE
SATELLITE 1970-48A
331
to differentiate between them at low altitudes, both models are compared with the orbital decay and the accelerometer data. The comparison of the orbital decay density data at 143 km fionrcao) with the 570 model density is shown in Fig. 4. The average ratio of drag density to model density is l-21. The standard deviation, defined above, is 0.058 A similar comparison is made for the J71 model in Fig 5. In this case the average drag to model density ratio is l-10, and the standard deviation is 0.066. The latitude for these data is e52”N. Assuming the drag coefficient, C,, has been correctly evaluated for this satellite, the indication is that both the 570 and 571 models give lower densities than actually existed at 143 km for the solar and geophysical conditions which prevailed during the time period of the observations. However, since the estimated uncertainty in CD is about 10 per cent, the 571 model cannot be considered in disagreement with orbital decay data. The discrepancy between the data and the 570 model cannot be reconciled by the uncertainty in C,. In any case, the 571 model does give a better fit to the data, and therefore the mo~fi~tions incorporated in that model appear to be substantiated by these data. Since the density variability of the two models with respect to geomagnetic activity is different, it is interesting to compare the results of the two models without the geomagnetic 1
26
28 JUNE
30
2
JUtY
6
1970
FIG. 6. THE RATIOS
OF ORBITAL
DECAY-DBDUCED
DENSITIES
To
THE
JACCHIA1970 AND 1971
143 km WlTHTHE MODEL &, SET EQUAL TO 0. Also shown are Kp and the solar F,,., index for the time period of interest. MODEL
ATMOSPHERES
AT
332
H. R. RUGGE
and B. K. CHING
activity dependence term included. This was done by setting K, = 0 in the density calculation for both models. The result of such a comparison is presented in Fig. 6. The ratios shown in the uppermost part of the figure may be thought of as “residual” density variations, presumably correlated with the KD index. Two phenomena are apparent. First the fits are not quite as good as those in Figs. 4 and 5. The average density ratio is now l-24 for the 570 model and l-18 for the J71 model. The standard deviations are, respectively, 0.058 and 0.055, much the same as with geomagnetic activity dependence included. However, major excursions of the ratios from 1 occur in Figs. 4 and 5, as well as 6 at times of large geomagnetic disturbances (K, > 4+) which occurred on 27 June and 4 July, indicating the models do not correctly take into account the effect of geomagnetic heating at this altitude at least for large KS. A comparison of the ratios in Fig. 6 with the 3-hourly K, index indicates that the residual density variations do not correlate with K, in a straightforward way, despite the fact that these observations were all obtained at the same latitude, altitude and local time. In this sample of data, the time lag of the density maximum following a peak in the K, index is not always the same, and furthermore the correspondence of peaks in the density and K, index is sometimes ambiguous if not impossible to identify. It seems that factors in addition to latitude, local time, and altitude play an important part in determining the atmospheric behavior associated with geomagnetic activity at least at this altitude. The possibility also exists that Kg is not 1 APPbOACHlNG
I
- PiRIGEE
LATITUDE
-
60”N
I
n
0.6 l7 L
f
LEAVING LATITUDE
- PERIGEE -
570
33’N
1.2
0.61
I 26
I 27
I 28 JUNE
FIG.
I 29
1
1970
7. RATIOSOPTHE ACCELEROMETER-DEDUC DENSITYTOTHE J71 AND J70 PHERESAT 143krn FORTHETIMEPERIOD 25_28Ju~~,15’70.
MODELATMOS-
ATMOSPHERIC
DENSITY
FROM
LOW ALTITUDE
SATELLITE
1970-48A
333
1 I
ii
/
J70
APPROACHING-PERIGEE LATITUDE - 70”N
1.0
eJ71 0.8 I
1.4
J70
1.2 Q? $
LEAVING- PERIGEE LATITUDE - 40’N
’
0.8 3
4 JULY,
FIG. 8.
RATIOS
OF THE
ACCE.LEROMETER-DEDUCED
PHERES
AT
143 km
FOR THE
1970 DENSITY
TIME PERIOD
J71 AND J70 3-4 JULY, 1970.
TO THE
MODEL
ATMOS-
the best indicator of the physical processes that give rise to the transient density variations. We further note that these data show no evidence of daily periodic density perturbations as have been reported by DeVries et al. (1972) from an analysis of orbital decay data of satellites in orbital configurations very similar to 1970-48A. In order to identify such a periodicity with confidence, it is necessary to first remove all other known sources of density fluctuations, in particular the short-periodic variations associated with geomagnetic disturbances. As we have seen, however, it is difficult to correct for the latter quantitatively. Thus, we can only say that visual inspection of the data reveals no evidence of a daily periodicity distinct from geomagnetic-activity related fluctuations. The second readily noticeable phenomenon is the tendency of the ratios to increase monotonically with time. This behavior correlates better with the I;;,,.,index than K,, and is probably an indication that neither model correctly takes into account the heating effects which result from phenomena correlated with changesin the F,,., index at this low altitude. Comparisons of accelerometer data at 143 km with the Jacchia models can also be made. Figures 7 and 8 show such comparisons for both the approaching-perigee and leavingperigee passes. The two Jacchia models agree with each other reasonably well in the midlatitudes, but disagree by ~10 per cent at high latitudes. The average ratio of the accelerometer-deduced densities to the model densities at 143 km is l-16 f 0.175 (standard deviation) for the J70 model, and 1.06 f O-147for the 571 model. The difference in the average ratios
334
H. R. RUGGE
and 33. K. CHING
results almost entirely from the ~gh-latitude ~approac~ng-pe~gee) comparisons. In the 571 model, the magnitude of the seasonal-latitudinal effect (which increases with latitude) was decreased relative to 570. The modification is substantiated by these data. The standard deviations are, of course, an indication of the variability about the average value. They are twice as large for the accelerometer as for the orbital decay data primarily because of the faster time response of the accelerometer data and the short term changes in the atmosphere which cannot easily be incorporated into any model atmosphere. Table 1 summarizes the results from the comparison of the Jacchia model atmospheres with the orbital decay and accelerometer data. TABLE I
Model
J70 571 J7O(K, = 0) J71(& = 0)
Orbital decay Ave. ratio 1.21 l-10 1.24 1.18
Standard deviation 0.058 O-066 O-058 0.055
AcceIerometer Ave. ratio 1.16 1.06
Standard deviation 0.175 0.147
A comparison of accelerometer density measurements from the Cannon Ball II satellite (1971-67C) with the J71 model has recently been presented by Champion and Marcos (1973). At a height of 125 km, the average ratio obtained from 7 revs of data was about O-9, which is lower than our average value of 1.06 at 143 km. The difference in the height co~espon~ng to their data and ours probably plays only a small part in the apparent discrepancy. The more important factors are thought to be the level of solar activity and the latitudes and local times of the observations. The Cannon Ball II data were obtained when Fr*, was less than 110; the latitude of perigee was 12”-22”N and the local time ~16 hr. These conditions are quite different from those corresponding to the present data, and may explain the difference in data-to-model ratios obtained by the different satellites. 6. CONCLUSIONS
A comparison between densities deduced from an accelerometer and from orbital decay at 143 km has been made using results obtained from the low altitude satellite 1970-48A. The results indicate that under the conditions pertinent to this study, the densities inferred from the orbital decay measurements at Q scale height above perigee and averaged over a 4 rev fit span are in agreement with similarly averaged values of density at the same altitude deduced from accelerometer measurements. An average taken over 59 rev shows agreement to better than 3 per cent. Deviations as large as 30 per cent between the instantaneous accelerometer density and the averaged orbital-decay density are observed and attributed primarily to the much faster time response of the accelerometer data relative to the orbital decay data. Comparisons of both types of density data have been made with the 1970 and 1971 Jacchia model atmospheres as well as the OGO-6 model atmosphere. The measured density is found to be ~20 per cent higher than that predicted by the Jacchia 1970 model and ~10 per cent higher than that predicted by the Ja&.ia 1971 model. Density variations at 143 km associated with solar and geomagnetic activity appear to be underestimated in both 570 and 571. The OGO-6 atmosphere model does not agree with the data at this low altitude. Even after allowing for the fact that the model does not account for OS, the
ATMOSP~~C
DENSITY
FROM LOW ALTITUDE
SATEiLLITE 197048A
33s
predicted density is far below the observed value at 143 km. A further problem is that the model density near 140 km varies inversely with heating effects as a result of the tied boundary condition on N, at 120 km. Acknowledgemenfs-We would like to thank Mr. James Pearson for several helpful discussions concerning the orbital decay data and Mr. Ken Young for helping to get the accelerometer data into a usable format and for a number of discussions concerning the accelerometer and the satellite ballistic parameters. The work was funded under the Air Force Space and Missile Systems Organization (SAMSO) Contract No. FO4701-73-C-0074.
BREKKE, A., D~UPNX, J. R. and BANKS, P. M. (1973). A prehminary study of the neutral wind in the aurora1 E region. J. geophys. Res. 78,8235. BEDIN~ER, J. F. (1972). The~ospheric motions measured by chemical releases. S’ce Research XII (Eds. S. A. Bowhill, L. D. Jaffe and M. J. Rycroft) p. 919. Akademie, Berlin. ?~RUCE,R. W. (1966). An atmosphere density model recommended for the analyses of low altitude satellite orbits, TOR-1001(2110-01)-8, The Aerospace Corporation, El Segundo, California. CHAMPION,K. S. W. and MARCOS,F. A. (1973). Lower thermosphere density variations determined from accelerometers on the Cannon Ball II satellite. 5”ace Research XIZZ (Eds. M. J. Rycroft and S. K. Runcorn) p. 229. Akademie, Berlin. CHAMPION,K. S. W., MARCOS,F. A. and MCISAAC, J. P. (1970a). Atmospheric density measurements by research satellite OVl-15 Space Research X (Eds. T. M. Donahue, P. A. Smith and L. Thomas) p. 450. North Holland, Amsterdam. CHAMPION,K. S. W., MARCOS, F. A. and SCHWEINFURTH,R. A. (197Ob). Measurements by the low aItitude density satellite OVl-16. Space Research X (Eds. T. M. Donahue, P. A. Smith and L. Thomas) p. 459. North Holland, Amsterdam. CHING, B. K. and CARTER, V. L. (1973). Ion gauge measurements of latitudinal density variations at night. Trans. Am. geophys. Union 54,1146. CIRA (1965). COSPAR International Reference Atmosphere. North Holland, A~t~dam. COOK, G. E. (1965). Satellite drag coefficients. Planet. Space Sci. 13,929. DE VRIES, L. L. (1972). Analysis and interpretation of density data from the low-G accelerometer calibration system (LOGACS). Space Research XII (Eds. S. A. Bowhill, L. D. Jai&e and M. J. Rycroft) p. 777. Akademie, Berlin. DE Vatas, L. L., SCHUSTERMAN, L. and BRUCE, R. W. (1972). Atmospheric density variation at 140 kilometers deduced from precise satellite radar tracking data. J. geophys. Res. 77,1905. HEIXN, A. E., MAYR, H. G., REBER,C., SPENCER,N. W. and CARIGNAN,G. R. (1974). Empirical model of global thermospheric temperature and composition based on data from the OGO-6 quadrupole mass spectrometer. J. geophys. Res. 79,215. JACCHIA, L. G. (1964). Static diffusion models of the upper atmosphere with empirical temperature profiles, Rept. No. 170. Smithsonian Astrophysical Observatory, Cambridge, Mass. JACCHIA,L. G. (1970). New static models of the thermosphere and exosphere with empirical temperature profiles, Rep No. 313. Smithsonian Astrophysical Observatory, Cambridge, Mass. JACCHIA, L. G. (1971). Revised static models of the thermosphere and exosphere with empirical temperature profiles, Rept. No. 332. Smi~sonian Astrophysical Observatory, Cambridge, Mass. KAINER, J. (1968). Estimated variation of aerodynamic coefficients with altitude for an agena configuration, Rept. No. TOR-0158 (3110-Ol)-14. The Aerospace Corporation, El Segundo, California. KING-HELE, D. G. (1966). Methods for determining air density from satellite orbits. An& Geophys. 22,40. MARCOS,F. A., CHAMPION,K. S. W. and SCHWBINFURTH,R. A. (1971). More accelerometer and orbital drag results from the SPADES (OVl-15) and Cannon Ball 1 (OVl-16) satellites. Space Research XI (Eds. K. Ya. Kondratyev, M. J. Rycroft and C. Sagan) p. 941. Academic, Berlin. SCHUSTERMAN, L. (1972). Private communication. U. S. Standard Atmosphere (1962) and U. S. Standard Atmosphere Supplements (1966). U.S. Government Printing Office, Washington, D.C. WALKER, J. C. G. (1965). Analytical representation of upper atmosphere densities based on Jacchia’s static diffusion models. J. afmos. Sci. 22,462.
Space
Sci. 1975, Vol. 23, pp.
323 to 335.
Permttxm
Press.
Printed
in Northern
Ireland
ATMOSPHERIC DENSITY FROM THE LOW ALTITUDE SATELLITE 1970-48A : COMPARISON OF ORBITAL DECAY MEASUREMENTS, ACCELEROMETER MEASUREMENTS AND ATMOSPHERIC MODELS Space Physics Laboratory,
H. R. RUCGE and B. K. CHING The Aerospace Corporation, El Segundo, California 90245, U.S.A. (Received injinal form 26 June 1974)
Abstract-Atmospheric densities have been deduced from high resolution radardetermined orbital decay data and from data obtained from a uniaxial accelerometer flown onboard the low altitude satellite 197048A. Data were obtained during late June and early July, 1970. The orbital decay-deduced densities, having an effective 6 hr temporal resolution, were determined at an altitude of 143 km, essentially one-half scale height above perigee. The accelerometer deduced densities at the same altitude were obtained on both the approaching-perigee and leaving-perigee portions of each of fifty-nine orbits. A detailed comparison of the densities derived from both types of data is presented. In general, agreement is very good. A comparison of both types of data has also been made with the Jacchia 1970 and 1971 atmospheric models as well as the new OGO-6 atmospheric model. The Jacchia models display reasonable agreement with the data, but the OGO-6 model is unsuitable as a representation of atmospheric density at this altitude. 1. INTRODUCTION The great majority of all currently used atmospheric models (e.g. Jacchia, 1964, 1970, 1971; CIRA, 1965; U.S. Standard Atmosphere, 1962) have relied upon orbital decay measurements from heights above 200 km as the primary source of atmospheric density data. These density data necessarily represent temporal and spatial averages of truedensity, typically over a period of 848 hr in time and a minimum of tens of degrees in latitude and/or longitude. Accelerometers, on the other hand, can measure “instantaneous” orbital decay (i.e. deceleration); and hence “instantaneous” atmospheric densities can be deduced. A detailed comparison of these two types of density data is made in this paper. Such comparisons are important because the highly accurate accelerometer data can be used as a basis for checking the accuracy and consistency of the orbital decay data that were so often used as a basis for atmospheric models. In addition, the comparison of simultaneously obtained data can provide unambiguous information concerning the loss of spatial and temporal structure in the atmospheric density as inferred from orbital decay. Some comparisons of the density deduced from orbital decay and accelerometer measurements have been made for the OVl-15 and OVl-16 satellites by the group at the Air Force Cambridge Research Laboratories (Champion ef al., 1970a, b; Marcos et al., 1971) and for the LOGACS experiment by DeVries (1972). However, systematic comparisons have not been made using most of the AFCRL data, although the few examples of comparisons shown seem to give good agreement (4 per cent) between the two types of data. DeVries finds differences of between 10 and 30 per cent, dependent upon geomagnetic activity, for the two days for which he has presented data. It is significant to note that density measurements at heights below 200 km are extremely sparse. The major obstacle has been the environment itself, whose denseness severely limits the lifetime of a satellite. Very few satellites besides those cited above have provided density data, and consequently the spatial, diurnal, and seasonal coverage of the data are far from 323
324
H. R. RUGGE and B. K. CHING
complete. Furthermore, the bulk of the existing data was acquired only in the past few years and thus encompasses only a portion of a solar cycle. Because of the lack of data, the earlier atmospheric models had to rely on extrapolation in order to represent the regime between 100 and 200 km. As data became available some improvements were incorporated in the models (e.g. Jacchia, 1971), but there still exists the need for continued development and improvement based on observational data. The purpose of this paper is twofold: first, to systematically compare orbital decaydeduced densities obtained with highly accurate tracking radars and accelerometer-deduced densities obtained with a well calibrated instrument onboard a stabilized satellite; second, to compare the densities obtained by both methods with several recent atmospheric models (those of Jacchia (1970, 1971) and the atmospheric model based on recently acquired OGO-6 mass spectrometer data (Hedin et al., 1974)). 2. RADAR DE TERMINED ORBIT&
DECAY MEASURJZMENTS
The satellite used in this study was the U.S. Air Force vehicle 1970-48A. The satellite was launched on 25 June 1970 into an orbit of inclination 109” with perigee near 135 km and apogee near 400 km. The data used in this study were obtained from 25 June-5 July 1970. During this period the latitude of minimum altitude was 55”-65”N and the local time near 9 a.m. The orbit of the satellite was determined from high-precision radar tracking data. The atmospheric densities deduced near perigee from the orbital decay data used in this study were provided by Schusterman (1972) of The Aerospace Corporation. The method he employed is described in detail by DeVries et al. (1972). Briefly, the density was obtained by fitting a drag force model (i.e. density model) along with the orbital elements to the radar observations. The model used was the Jacchia-Walker density model (Jacchia, 1964; Walker, 1965) as modified by Bruce (1966) for low-altitude applications. The fitting procedure yields the appropriate integrated density around the orbit (which is heavily weighted by the density near perigee) but not necessarily the correct density at perigee due to possible errors in the scale height of the assumed model. King-Hele (1966) has shown that the error in the density related to the uncertainty in scale height is minimized at about half a scale height above perigee. Thus, in this study the density is evaluated at 143 km, which was the mean value of perigee plus half a scale height during the period under consideration. Owing to the geometry of the satellite, which was cylindrical with a large length to diameter ratio, and the departure from free molecular flow conditions at perigee, it was necessary to use a carefully evaluated height dependent drag coefficient in the orbital analysis. The drag coefficient was computed (Kainer, 1968) assuming perfect accommodation and diffuse reflection of atmospheric particles and taking into account the attitude of the satellite and the variable ratio of speeds of the satellite and the ambient particles. The resultant drag coefficient was dependent on both altitude and atmospheric temperature (as predicted by the atmospheric model). The orbital analysis was performed using 8 revolution (rev) fit spans and 8 fitting parameters. Six of the parameters which described the epoch vector (position and velocity) were fit over an entire g-rev span. The other two parameters were drag parameters, each fit over 4 rev of the span. This “splitting” technique is particularly useful and successful for low-altitude (high drag) orbits and increases the resolution of the derived density values.
ATMOSP~~C
DENSITY
FROM LOW ALT~DE
SATELLITE 1970-48A
325
The fitting spans were overlapped through the data in two rev increments, effectively giving a 4-rev running average (6 hr average) of the density every two rev. It should be noted that although the densities are assigned to time points at the middle of the fit spans, the values are really only averages over the 6-hr intervals of the fit spans. The major source of uncertainty in the density deduced from the orbital decay is that associated with the drag coefficient. This uncertainty results primarily from the necessity of making assumptions concerning the angular dependence of atmospheric particle reflectivity from the surface of the satellite (diffuse, specular or intermediate between the two) and the value of the accommodation coefficient, the ratio of energy change experienced by the impinging atmospheric particles to the maximum energy change that could take place. These assumptions are required because of the lack of adequate information concerning gas-surface interactions. These problems and the degree of uncertainty inherent in these assumptions are discussed in detail by Cook (1965). Using arguments similar to those of Cook and applying them to the present vehicle, we estimate that the uncertainty in the drag coefficient is fl &lo per cent. The error related to the uncertainty in scale height is estimated to be 1 per cent or less (see King-Hele, 1966); and that related to the uncertainty in perigee height is negligible, as the orbit was very well determined. 3. ACCELEROMETER
MElAS~~NTS
The accelerometer flown on 1970-48A was a single axis Bell MESA (miniature electrostatic accelerometer) similar to those flown on the LOGACS experiment (DeVries, 1972) and on the OVl-15, -16, -20 satellites (Champion et al., 1970a). The accelerometer measures the instantaneous deceleration, CI,along the orbital path. The deceleration is related to the atmospheric density by the relationship a=_-_
1 -GA 2
[ m 1 “a
(0
where p is the atmospheric density, A is the effective satellite frontal area, m is the satellite mass, v is the satellite velocity relative to the atmosphere, and C, is the drag coefficient discussed previously. The relationship between the output C (counts) of the accelerometer and the deceleration a is given by a=I;%+b (2) where the scale factor F was accurately determined from a ground calibration (in a l-g environment) and the bias b near apogee where the deceleration as a result of drag was essentially negligible. Determined in this way, a depends in no way on the orbital decaydeduced data; and hence the two measurements can be compared in a truly independent manner. The largest source of error in the accelerometer-deduced density is the ~10 per cent uncertainty in C, which has already been discussed. The scale factor and bias in the experiment were determined to better than 1 per cent. Another potential source of error is in the effective satellite velocity used in Equation (1). If neutral atmospheric winds are present, their components along or against the satellite velocity vector must be added or subtracted and hence will change the value of the effective satellite velocity used in Equation (1). Recent observations of winds in the lower ~ermosphere at high latitudes (Brekke, et al., 1973) have indicated speeds as high as 150 m/see. Even larger wind speeds have been reported, but only during intense geomagnetic disturbances flu, 2 7) and hence need not be
H. R. RUGGE
326
and B. K. CHING
considered here. A wind of ~200 m/set blowing along the satellite velocity vector would introduce an error of 5 per cent in the accelerometer-deduced density, which was computed assuming no wind. However, the data of Brekke et al. indicate that at a local time of our data (“9 a.m.) the high latitude winds are of order 20 m/set and not, on average, aligned with the satellite velocity vector, and thus would have an effect of less than 1 per cent. As for low latitude winds, there exist insticient data to define the normal global-scale circulatory system, but speeds of the order of 100 m/set have been observed on occasion (Bedinger, 1972). Considering all these factors we conclude that random errors of 5 f5 per cent due to “gusts” of wind may occur from time to time, but we do not believe there is any evidence that indicates there might be a comparable systematic error in our densities. The densities deduced from the accelerometer at 143 km were obtained for both the approaching-perigee and leaving-perigee portions of each of 59 rev. Data were available during two time periods, the first covering 25-28 June 1970 and the second from 3-4 July 1970. The densities were obtained from the measured accelerations by the use of Equations (1) and (2) with the drag coefficient appropriate to 143 km. It is of interest to examine the accelerometer data in order to obtain a better understanding of the variability of the atmosphere. The upper graph in Fig. 1 presents the ratio of the approaching-perigee density data, to the average of all approaching-perigee data in the time period 25 June-5 July. These densities were obtained at 143 km near 70”N geographic latitude. As can be seen in the figure, variations in the density from the average density can be as large as 30 per cent and can occur in time periods as short as a few hours. APPROACHING - PERIGEE LATITUDE . 7O’N
1.2 4. 3
1.0
0.8
I
26
1 I 1 r
I
27 JUNE
28 I
I
I
3
4 JULY I
’
LEh4G-PER;GEE 1.2 -
LATITUDE . 3S’N
-I s
‘.O-
f
by
0.8 I 26
I 27 JUNE
1 28
1.
DENSITY
UPPER
GRAPH-RATIO
OF
FOR APPROACHING-PERIGEE
1970
ACCELEROMETER-DEDUCED PASSES
I 4 JULY
DATE, FIG.
I 3
r
(Pi)
DATA
AT
143 km
DENSITIES FOR THE
(p)
TO
THE
TIME PERIODS
AVERAGE
FOR WHICH
EXIST.
The latitude at which these data were taken was -70”N. LOWER FOR
GRAPH-RATIO
OF ACCELEROMETER-DEDUCED
DENSITIES
(p)
TO THE
AVERAGE
km FOR THE TIME PERIODS FOR WHICH The latitude at which these data were taken was -35’N.
LEAVING-PERIGEE
PASSES
(pL)
AT
143
DATA
DENSITY EXIST.
ATMOSPHBRIC DENSITY FROM LOW ALTITUDE SATELLITE
1970-48A
327
The lower part of Fig. 1 contains similar data for the leaving-perigee portion of the orbit. The geographic latitude corresponding to these data was -35”N. Again, variations from the average density are fairly large and can occur in a matter of hours. 4. COMPARISON OF DEDUCED DENSITIES
The density inferred from the orbital decay applies at an altitude of 143 km (half a scale height above minimum altitude) and at the latitude of minimum altitude. The densities measured at 143 km by the accelerometer on the approaching- and leaving-perigee portions of an orbit were obtained at latitudes that were displaced from that of minimum altitude by about +18” and -18”, respectively. In order to obtain an accelerometer-deduced density value more representative of the density at the location of the minimum altitude, where the orbital decay value applies, the before- and after-perigee results from the accelerometer have been averaged to yield one density value per orbit of data. Averaged in this way, there are a total of 59 accelerometer density points that can be compared with the orbital-decay results. Figure 2 presents a direct comparison of the accelerometer-deduced density and the radar-determined orbital decay-deduced density at an altitude of 143 km. The accelerometer densities, as mentioned above, are averages of data points taken about 10 min apart on the approaching- and leaving-perigee portions of a given rev; the orbital decay-derived densities represent 4-rev averages of data. As a result, the accelerometer data have a much higher temporal resolution (data points every rev or 1.5 hr) than the radar data have (data points every 4 rev or 6 hr). An example of this can be seen in Fig. 2 at =I700 hr on June 26. Both types of data show a decrease in density at this time. The accelerometer data indicate a considerable decrease while the orbital decay data do not have the time resolution to show the full depth of the decrease, which has essentially vanished 6 hr later. In spite of this inherent difficulty the agreement is still rather good. The maximum deviation between the curves is 120 per cent. Deviations of this size usually occur during transient density variations for the reason mentioned above. Most of the variations are 15 per cent. The data display two major characteristics during the time period for which data exist : a generally increasing density with time and variations which to some extent seem to follow
JUNE 26
FIG. 2.
&biPARISON
OF
THE
JUNE27
JUNE28
ACCELEROMETER-DEDUCED
JULY 3
DENSITY
AND
THE
ORBITAL
143 km. KS for the time period of interest is presented at the bottom of the figure. DEDUCJID
DENSITY
AT AN ALTITUDE
OF
DECAY-
H. R. RUGGE
328
JUNE26
and B. K. CHING
JUNE27
JUNE28
JULY 3
FIG. 3. ACCELEROMETER AND ORBITALDECAY-DEDUCED DENSITIES TAKlNO
SLIDINff
FOUR
REV AVERAGES
EVERY
TWO
AT
143 km
OBTAINED
BY
REV.
K. for the time period of interest is presented at the bottom of the figure.
geomagnetic activity as indicated at the bottom of Fig. 2 by the KP index. The gradual increase in the average level of the density correlates rather well with the solar FIO., index, which increased monotonically from a value of 142 flux units on 25 June-195 flux units on 4 July. The 3-hourly K.. index appears to correlate considerably better with the longer-time averaged orbital decay-deduced density than with the “instantaneous” accelerometerdeduced density. The geomagnetic correlations are more obvious if the monotonic increase in density is first removed. A fairer comparison of the orbital decay and accelerometer data can be made if they are treated similarly. Figure 3 shows the radar data as they were in Fig. 2. The accelerometer data have been treated as the radar data were, i.e. the data have been averaged over 4-rev intervals with a 2-rev overlap between intervals. As can be seen from Fig. 3, the agreement is good everywhere, especially during the first span of data in late June. A consistent difference of the accelerometer data from the radar data of rc + 10 per cent is observed during the second span of data. There appear to be no systematic uncertainties in the analysis which could account for this, and it may, of course, be only coincidence. The difference exists for less than half a day and is not regarded as evidence of a serious discrepancy between the two types of data. A more quantitative comparison of the agreement of the two types of data can be. obtained by averaging both sets of data. The result obtained by averaging the 30 orbital decay measurements and the 59 accelerometer measurements during the time period under discussion at an altitude of 143 km is as follows: Accelerometer:
pIdS= 352 x XI-la g cm-s
Orbital Decay:
ljlrlJ = 3.43 x IO-lag cm-s,
5. COMPARISON OF DENSITY DATA WITH RECENT MODEL ATMOSPHERES The density data obtained at 143 km from both the orbital decay and accelerometer measurements are compared with three recent model atmospheres; the OGO-6 (Hedin et al., 1974), the Jacchia, 1970 (J70) and Jacchia, 1971 (571) models. For this comparison the accelerometer data obtained at 143 km on both the approaching-McGee and leavingperigee portions of each orbit are treated separately and evaluated at the latitudes at which the measurements were made.
ATMOSPHERIC
DENSITY
FROM LOW ALTITUDE
SATELLITE 1970-48A
329
The OGO-6 model is a global, empirical model of the atmosphere based on OGO-6 neutral mass spectrometer data obtained at altitudes between 400 and 600 km. The model extends to altitudes as low as 120 km by virtue of a method of extrapolation analogous to that employed by Jacchia (1964). Although the authors of the model have cautioned against its use under conditions dissimilar to the data base (in this case the altitude), we decided to compare the present data with the model because one of us (Ching and Carter, 1973) found excellent agreement between the model and density data obtained from an ion gauge experiment at heights between 200 and 300 km. The OGO-6 model does not include 02, but this omission is not expected to affect the comparison by more than about 10-20 per cent at a height of 143 km. The results of the comparison of our data with the OGO-6 model at 143 km indicated a poor fit of that model to the observed density. As an example, the average of the ratio of the accelerometer-deduced density to the OGO-6 model density (R) for all data taken at 143 km at a latitude of approximately 68”N is l-74. The standard deviation, defmed in the usual way, is 0.27, i.e.
where Nis the number of observations, R,(= pi/p,) is the ratio of the ith density measurement made with the accelerometer at 143 km to the model density at that altitude, and R is the average ratio. As will be seen shortly, these values are substantially larger than those obtained with the Jacchia models. As mentioned previously, the neglect of O2 in the model can account for only 10-20 per cent of the disagreement with the data. A major problem of the model encountered at low altitudes is similar to that encountered in other older models (e.g. CIRA-1965, Jacchia, 1964); namely that there is an isopycnic level near 150 km that results from the imposition of constant boundary conditions at too high an altitude. In the OGO-6 model only N2 (but not He and 0) is constrained to be constant at the lower boundary of 120 km, but since it is the dominant constituent until about 200 km, this lower boundary constraint is sufficient to cause the isopycnic problem in total density. Another problem may be that the average model density at 120 km is too low; e.g. it is about a factor of 1.3 lower than that of Jacchia (1971) even after adjustment for 0, is made. Thus, it appears that the OGO-6 model will not be very useful at altitudes below 200 km unless a Bruce (1966)~type modification of the model, which was specifically designed to avoid the isopycnic difficulty, is used. The relatively high standard deviation for the OGO-6 model can be attributed principally to two deficiencies in the modeling of the geomagnetic effect. First, 24 hr averages of q, are used, thus shorter period changes are smoothed out. Second, with increased heating (higher K,), the model density decreases at 143 km as a result of the isopycnic problem discussed above. Perhaps the most commonly used recent upper atmospheric models are those of Jacchia published in 1970 and 1971 (J70 and 571 respectively). The basic differences, at altitudes 5200 km, between the 571 model and the 570 model are: (1) the inclusion of a stronger dependence of density variations on geomagnetic activity, (2) a reduction in the seasonal/latitudinal effect at heights above about 115 km, (3) a larger semiannual effect, and (4) an increase in the relative abundance of atomic oxygen. Because of the sometimes substantial differences in these models and the present lack of definitive data
FIG. 4. RATIO OFTHE ORBITAL DECAY-DEDUCED DENSITYTOTHE AT 143 kill.
JACCHIA 1910 MODELDENSITY
The comparison is for a latitude -52”N. K, for the time oeriod of interest is presented at the bottom-of the figure. L 1.
I
I
I
I
I
1.3E
St.
55
P
1.
1.
oI
1
1
I
1
26
28
30
2
4
6
JULY
JUNE 1970 FIG. 5.
UXOOF THEORBITALDECAY-DJZDUCEDDENSITYTOTHEJACCHXA I~~~MODELDEN~~ AT 143 km. The comparison is for a latitude of -52”N. Ke for the time period of interest is presented at the bottom of the figure. 330
ATMOSPHERIC
DENSITY
FROM LOW ALTITUDE
SATELLITE 1970-48A
331
to differentiate between them at low altitudes, both models are compared with the orbital decay and the accelerometer data. The comparison of the orbital decay density data at 143 km fionrcao) with the 570 model density is shown in Fig. 4. The average ratio of drag density to model density is l-21. The standard deviation, defined above, is 0.058 A similar comparison is made for the J71 model in Fig 5. In this case the average drag to model density ratio is l-10, and the standard deviation is 0.066. The latitude for these data is e52”N. Assuming the drag coefficient, C,, has been correctly evaluated for this satellite, the indication is that both the 570 and 571 models give lower densities than actually existed at 143 km for the solar and geophysical conditions which prevailed during the time period of the observations. However, since the estimated uncertainty in CD is about 10 per cent, the 571 model cannot be considered in disagreement with orbital decay data. The discrepancy between the data and the 570 model cannot be reconciled by the uncertainty in C,. In any case, the 571 model does give a better fit to the data, and therefore the mo~fi~tions incorporated in that model appear to be substantiated by these data. Since the density variability of the two models with respect to geomagnetic activity is different, it is interesting to compare the results of the two models without the geomagnetic 1
26
28 JUNE
30
2
JUtY
6
1970
FIG. 6. THE RATIOS
OF ORBITAL
DECAY-DBDUCED
DENSITIES
To
THE
JACCHIA1970 AND 1971
143 km WlTHTHE MODEL &, SET EQUAL TO 0. Also shown are Kp and the solar F,,., index for the time period of interest. MODEL
ATMOSPHERES
AT
332
H. R. RUGGE
and B. K. CHING
activity dependence term included. This was done by setting K, = 0 in the density calculation for both models. The result of such a comparison is presented in Fig. 6. The ratios shown in the uppermost part of the figure may be thought of as “residual” density variations, presumably correlated with the KD index. Two phenomena are apparent. First the fits are not quite as good as those in Figs. 4 and 5. The average density ratio is now l-24 for the 570 model and l-18 for the J71 model. The standard deviations are, respectively, 0.058 and 0.055, much the same as with geomagnetic activity dependence included. However, major excursions of the ratios from 1 occur in Figs. 4 and 5, as well as 6 at times of large geomagnetic disturbances (K, > 4+) which occurred on 27 June and 4 July, indicating the models do not correctly take into account the effect of geomagnetic heating at this altitude at least for large KS. A comparison of the ratios in Fig. 6 with the 3-hourly K, index indicates that the residual density variations do not correlate with K, in a straightforward way, despite the fact that these observations were all obtained at the same latitude, altitude and local time. In this sample of data, the time lag of the density maximum following a peak in the K, index is not always the same, and furthermore the correspondence of peaks in the density and K, index is sometimes ambiguous if not impossible to identify. It seems that factors in addition to latitude, local time, and altitude play an important part in determining the atmospheric behavior associated with geomagnetic activity at least at this altitude. The possibility also exists that Kg is not 1 APPbOACHlNG
I
- PiRIGEE
LATITUDE
-
60”N
I
n
0.6 l7 L
f
LEAVING LATITUDE
- PERIGEE -
570
33’N
1.2
0.61
I 26
I 27
I 28 JUNE
FIG.
I 29
1
1970
7. RATIOSOPTHE ACCELEROMETER-DEDUC DENSITYTOTHE J71 AND J70 PHERESAT 143krn FORTHETIMEPERIOD 25_28Ju~~,15’70.
MODELATMOS-
ATMOSPHERIC
DENSITY
FROM
LOW ALTITUDE
SATELLITE
1970-48A
333
1 I
ii
/
J70
APPROACHING-PERIGEE LATITUDE - 70”N
1.0
eJ71 0.8 I
1.4
J70
1.2 Q? $
LEAVING- PERIGEE LATITUDE - 40’N
’
0.8 3
4 JULY,
FIG. 8.
RATIOS
OF THE
ACCE.LEROMETER-DEDUCED
PHERES
AT
143 km
FOR THE
1970 DENSITY
TIME PERIOD
J71 AND J70 3-4 JULY, 1970.
TO THE
MODEL
ATMOS-
the best indicator of the physical processes that give rise to the transient density variations. We further note that these data show no evidence of daily periodic density perturbations as have been reported by DeVries et al. (1972) from an analysis of orbital decay data of satellites in orbital configurations very similar to 1970-48A. In order to identify such a periodicity with confidence, it is necessary to first remove all other known sources of density fluctuations, in particular the short-periodic variations associated with geomagnetic disturbances. As we have seen, however, it is difficult to correct for the latter quantitatively. Thus, we can only say that visual inspection of the data reveals no evidence of a daily periodicity distinct from geomagnetic-activity related fluctuations. The second readily noticeable phenomenon is the tendency of the ratios to increase monotonically with time. This behavior correlates better with the I;;,,.,index than K,, and is probably an indication that neither model correctly takes into account the heating effects which result from phenomena correlated with changesin the F,,., index at this low altitude. Comparisons of accelerometer data at 143 km with the Jacchia models can also be made. Figures 7 and 8 show such comparisons for both the approaching-perigee and leavingperigee passes. The two Jacchia models agree with each other reasonably well in the midlatitudes, but disagree by ~10 per cent at high latitudes. The average ratio of the accelerometer-deduced densities to the model densities at 143 km is l-16 f 0.175 (standard deviation) for the J70 model, and 1.06 f O-147for the 571 model. The difference in the average ratios
334
H. R. RUGGE
and 33. K. CHING
results almost entirely from the ~gh-latitude ~approac~ng-pe~gee) comparisons. In the 571 model, the magnitude of the seasonal-latitudinal effect (which increases with latitude) was decreased relative to 570. The modification is substantiated by these data. The standard deviations are, of course, an indication of the variability about the average value. They are twice as large for the accelerometer as for the orbital decay data primarily because of the faster time response of the accelerometer data and the short term changes in the atmosphere which cannot easily be incorporated into any model atmosphere. Table 1 summarizes the results from the comparison of the Jacchia model atmospheres with the orbital decay and accelerometer data. TABLE I
Model
J70 571 J7O(K, = 0) J71(& = 0)
Orbital decay Ave. ratio 1.21 l-10 1.24 1.18
Standard deviation 0.058 O-066 O-058 0.055
AcceIerometer Ave. ratio 1.16 1.06
Standard deviation 0.175 0.147
A comparison of accelerometer density measurements from the Cannon Ball II satellite (1971-67C) with the J71 model has recently been presented by Champion and Marcos (1973). At a height of 125 km, the average ratio obtained from 7 revs of data was about O-9, which is lower than our average value of 1.06 at 143 km. The difference in the height co~espon~ng to their data and ours probably plays only a small part in the apparent discrepancy. The more important factors are thought to be the level of solar activity and the latitudes and local times of the observations. The Cannon Ball II data were obtained when Fr*, was less than 110; the latitude of perigee was 12”-22”N and the local time ~16 hr. These conditions are quite different from those corresponding to the present data, and may explain the difference in data-to-model ratios obtained by the different satellites. 6. CONCLUSIONS
A comparison between densities deduced from an accelerometer and from orbital decay at 143 km has been made using results obtained from the low altitude satellite 1970-48A. The results indicate that under the conditions pertinent to this study, the densities inferred from the orbital decay measurements at Q scale height above perigee and averaged over a 4 rev fit span are in agreement with similarly averaged values of density at the same altitude deduced from accelerometer measurements. An average taken over 59 rev shows agreement to better than 3 per cent. Deviations as large as 30 per cent between the instantaneous accelerometer density and the averaged orbital-decay density are observed and attributed primarily to the much faster time response of the accelerometer data relative to the orbital decay data. Comparisons of both types of density data have been made with the 1970 and 1971 Jacchia model atmospheres as well as the OGO-6 model atmosphere. The measured density is found to be ~20 per cent higher than that predicted by the Jacchia 1970 model and ~10 per cent higher than that predicted by the Ja&.ia 1971 model. Density variations at 143 km associated with solar and geomagnetic activity appear to be underestimated in both 570 and 571. The OGO-6 atmosphere model does not agree with the data at this low altitude. Even after allowing for the fact that the model does not account for OS, the
ATMOSP~~C
DENSITY
FROM LOW ALTITUDE
SATEiLLITE 197048A
33s
predicted density is far below the observed value at 143 km. A further problem is that the model density near 140 km varies inversely with heating effects as a result of the tied boundary condition on N, at 120 km. Acknowledgemenfs-We would like to thank Mr. James Pearson for several helpful discussions concerning the orbital decay data and Mr. Ken Young for helping to get the accelerometer data into a usable format and for a number of discussions concerning the accelerometer and the satellite ballistic parameters. The work was funded under the Air Force Space and Missile Systems Organization (SAMSO) Contract No. FO4701-73-C-0074.
BREKKE, A., D~UPNX, J. R. and BANKS, P. M. (1973). A prehminary study of the neutral wind in the aurora1 E region. J. geophys. Res. 78,8235. BEDIN~ER, J. F. (1972). The~ospheric motions measured by chemical releases. S’ce Research XII (Eds. S. A. Bowhill, L. D. Jaffe and M. J. Rycroft) p. 919. Akademie, Berlin. ?~RUCE,R. W. (1966). An atmosphere density model recommended for the analyses of low altitude satellite orbits, TOR-1001(2110-01)-8, The Aerospace Corporation, El Segundo, California. CHAMPION,K. S. W. and MARCOS,F. A. (1973). Lower thermosphere density variations determined from accelerometers on the Cannon Ball II satellite. 5”ace Research XIZZ (Eds. M. J. Rycroft and S. K. Runcorn) p. 229. Akademie, Berlin. CHAMPION,K. S. W., MARCOS,F. A. and MCISAAC, J. P. (1970a). Atmospheric density measurements by research satellite OVl-15 Space Research X (Eds. T. M. Donahue, P. A. Smith and L. Thomas) p. 450. North Holland, Amsterdam. CHAMPION,K. S. W., MARCOS, F. A. and SCHWEINFURTH,R. A. (197Ob). Measurements by the low aItitude density satellite OVl-16. Space Research X (Eds. T. M. Donahue, P. A. Smith and L. Thomas) p. 459. North Holland, Amsterdam. CHING, B. K. and CARTER, V. L. (1973). Ion gauge measurements of latitudinal density variations at night. Trans. Am. geophys. Union 54,1146. CIRA (1965). COSPAR International Reference Atmosphere. North Holland, A~t~dam. COOK, G. E. (1965). Satellite drag coefficients. Planet. Space Sci. 13,929. DE VRIES, L. L. (1972). Analysis and interpretation of density data from the low-G accelerometer calibration system (LOGACS). Space Research XII (Eds. S. A. Bowhill, L. D. Jai&e and M. J. Rycroft) p. 777. Akademie, Berlin. DE Vatas, L. L., SCHUSTERMAN, L. and BRUCE, R. W. (1972). Atmospheric density variation at 140 kilometers deduced from precise satellite radar tracking data. J. geophys. Res. 77,1905. HEIXN, A. E., MAYR, H. G., REBER,C., SPENCER,N. W. and CARIGNAN,G. R. (1974). Empirical model of global thermospheric temperature and composition based on data from the OGO-6 quadrupole mass spectrometer. J. geophys. Res. 79,215. JACCHIA, L. G. (1964). Static diffusion models of the upper atmosphere with empirical temperature profiles, Rept. No. 170. Smithsonian Astrophysical Observatory, Cambridge, Mass. JACCHIA,L. G. (1970). New static models of the thermosphere and exosphere with empirical temperature profiles, Rep No. 313. Smithsonian Astrophysical Observatory, Cambridge, Mass. JACCHIA, L. G. (1971). Revised static models of the thermosphere and exosphere with empirical temperature profiles, Rept. No. 332. Smi~sonian Astrophysical Observatory, Cambridge, Mass. KAINER, J. (1968). Estimated variation of aerodynamic coefficients with altitude for an agena configuration, Rept. No. TOR-0158 (3110-Ol)-14. The Aerospace Corporation, El Segundo, California. KING-HELE, D. G. (1966). Methods for determining air density from satellite orbits. An& Geophys. 22,40. MARCOS,F. A., CHAMPION,K. S. W. and SCHWBINFURTH,R. A. (1971). More accelerometer and orbital drag results from the SPADES (OVl-15) and Cannon Ball 1 (OVl-16) satellites. Space Research XI (Eds. K. Ya. Kondratyev, M. J. Rycroft and C. Sagan) p. 941. Academic, Berlin. SCHUSTERMAN, L. (1972). Private communication. U. S. Standard Atmosphere (1962) and U. S. Standard Atmosphere Supplements (1966). U.S. Government Printing Office, Washington, D.C. WALKER, J. C. G. (1965). Analytical representation of upper atmosphere densities based on Jacchia’s static diffusion models. J. afmos. Sci. 22,462.