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Orbital variations of satellite 1976-87a and a determination of the air density at heights of 205 – 220 km
Gamma Ray Event of 1979 March
32
[3] [e] [S] [6]
5
Arons, J. & Scharlemann, E. T. Ap. J. 231 (1979), 854. Basko, M. M. & Sunyev, R. A., M. N., 175 (1976), 395. Boldt, E. A., et al., A.0.p.. 50 (19761, 1.61. (Chinese Astrophysics" Ambarzumian V. A. et al., "TheGetical Chubanshe. 1956, p.468.
Chin.Astron.Astrophys.
2 (1982) 32-36
Pergamo
Act. Astron.Sin. -22 (19811 223-229
ORBITAL
VARIATIONS
OF
SATELLITE
translation)
Kexue
Press. Printed in Great Britain 0275-1062/82,'010032-04$07.50/O
1976-87A AND A DETERMINATION OF THE
AIR DENSITY AT HEIGHTS OF 205 - 220 KM LIU
Ya-ying,
Received
WANG Yong-bao,
1980 October
FENG Zhan-liang,
Purple Mountain Observatory
10
ABSTRACT We investigate the orbital changes of the satellite 1976-87A (the sixth Chinese satellite) during its lifetime and from its orbital decay rate determine the air density at heights 205-220km. The density we obtained is, on the average, over 20% greater than that in the CIRA 1972 model. We discuss in detail the correlation between changes in the density and in the geomagnetic activity, and the relationships between the geomagnetic effect and the latitude and the local solar time. on 1976 August 30, with an initial perigee height of about 195 Satellite 1976-87A wassentup km, an apogee height of 2145 km, an orbital inclination of 69.16" and a period of 108.7 The satellite lasted 816 days, and fell back on 1978 November 25. Its period minutes. changed at a rate of about 0.01-0.04 minfd and its latitude angle, at about 1 degld. As its life was short, its perigee height rather low, and its orbital changes fast especially in the period and the inclination, it is one of the best candidates for a study of the air density of the high atmosphere. 1.
ORBIT AND ITS VARIATIONS
During its life-time, the various satellite observing stations secured a total of more than 1700 theodolite readings spread over 144 revolutions, of which over 1200 readings were used in improving the orbits. When improving the orbits the calculated perturbation on the 128 sets of improved mean perigee distance rp was used as a constraint on the accuracy. elements were obtained based on data obtained within 3 days before and after each epoch. TABLE 1 shows the average standard error of each of the improved elements, the fit of the elements to the observed points has an accuracy of 2-3 arcmin. TABLE 1
Average
Standard
Deviation
of OrbitalElements
a~;,,
The variationsin the perigee distance, the orbital period and the inclination are shown In these the actual measured values are marked with small circles, and the in Figs. 1-3. calculated values in perturbation calculations, the continuous curves.
Air Density from Satellite 1976~G7A
~~~~~~~
,76cr
1976
Fig. 1
26M*r
25Mar
1978
1977
Time variation of the perigee distance rp=a(l-o)
1976
Fig. 2
-1T’. I
”
L
33
1977
1978
Time variations of the orbital period P (curve l? and of i (curve 2)
69.1OL.
.___-
nscp
f>:
-I-
IDCC
1SFrb
1976
Fig. 3
1977
lONay
29Jul
if&?-
$i ..A -MM, 1978
y
Measured values of the orbital inclination i and the theoretical time profile with n=l.l3
The perigee distance is affected by the odd harmonies of the Earth's field and shows a regular oscillation with an amplitude of about 10 km; the effect of air resistance is to decrease it by less than 3 km every half-year. The orbital period is decreased by the effect of air resistance by about 10 minutes over 2 years. In Fig. 2, the period P and its rate of change P are defined as P--, 1 &stni
' pm-.-
Gi-ti (& + A+
(1)
The measured i values agree well with the curve calculated from the CIRA 1972 model atmosphere Il./,after taking out their systematic difference. The daily variation rate of the orbital period may be as much as 0.04 min, sufficiently fast for an accurate determination of the air density. The variation in the orbital inclination is mainly caused by the rotation of the atmosphere /2/, while the luni-solar perturbation is negligibly small and the variation due to the JS term is an oscillation of 0.003". The measured values of inclination in Fig. 3 all have standard deviation less than 0.01' and the theoretical curve came from the perturbation theory of an oblate spheroid atmosphere, and was obtained by numerical integration at a steplength of 10 days, after allowing for the effects of a rotating atmosphere /3/ and of the Js term. The best fit was found for a rotation speed of A=l.l3 revolutions per day. 2.
DETERMINATION OF AIR DENSITY
Using the method used before /4/ in the determination of the air density from the data of the second Chinese satellite and rocket, and taking into consideration the effect of diurnal variation in the density, we first calculated 93 density values pi at heights zx= s+ XH~*, where z is the height of the perigee. We took the surface to mass ratio of the satellite to be 2.69X10-' m* kg-l, and we took the density scale height X from the CIRA 1972 model, The
Air Density
34
corrected
pi at z;\, corrected
density P1 -P:(I
From Satellite
for the diurnal
1976-878
variation
is then given by
+ Fcos&),
(2)
where F is the diurnal coefficient, and JI is the angle between the direction of the satellite and the diurnal peak density. The logarithms of the reduced density, reduced to a fixed height so, are shown in Fig. 4 alongside the solar flux ~10.7, daily mean geomagnetic index kP.and the local solar time L.T. at the perigee. We took so=220 and 205 km respectively for periods before and after 1977 This date also divides our subsequent reduction of o.zO into the standard outer November. layer temperature To =800 K and 1000 K. The theoretical log ozO curve shown in the figure is the CIKA 1972 model value.
12rcp
19Fcb 1977
1976 Fig.
4
Observed
ANALYSIS
26Dcc
19Jun
1OMay
and theoretical
geomagnetic
3.
31Mar
values
25Apr 1978
of air density,solar
flux
F,,,.,,
index KP and local solar time L.T.
OF RESULTS
Apart from showing fluctuations 1. The Mean Density Compared with the CIRA 1972 Model due to solar activity, geomagnetic activity, diurnal and semi-annual effects, the measured densities can be seen from Fig. 4 to be greater then the CIRA 1972 model values. Excluding 10 values around 1977 April 7 and April 20 when the density was particularly increased by geomagnetic activity, the averages of the remaining 83 values, divided into two height ranges, and the averages of the model values on the same days are: average
log ps,
1976.9-1977.6
observed model excess (O-C)
1977.12-1978.5
-9.877 -9.962 22%
-9.457 -9.561 27%
Fluctuations in the air density 2. Variation of the Density with Geomagnetic Activity. caused by geomagnetic activity are quite obvious. To investigate those variations, we must first correct the measured values for the diurnal variation, the variation in the solar activity and the semi-annual variations by means of the polynomial log p(z,~) given by numerical approximation of the CIRA 1972 model: 1ogPG- lOPP‘,- (AlogP, Alwm
-
Alwe
-
A log P, -
logp(zo,
T,) -
log P(ZO, TI,2> f(a)&+>.
+ Alogp,
+ Alwd, (3)
logP(zo>
TIJ,
1% P(ZO> Tll) 3 I
where T1, T,/, (=1.15 To), f(z) and g(t) are given by the formulae in the model and TV is the adopted standard outer layer temperature. The coErected densities log pi for the period 1977 March 3 - April 22 are in Fig. 5, alongside the KP curve. There is an overall
Air Density From Satellite 1976-87A
35
agreement between the two, with however, a time-lag in some instances. For example, on April 6, 7 and 8, kP was 5.04, 5.00 and 4.00, while log pG was the least on 6 and greatest on 7; again on April 18-21, kp was 2.17, 5.00, 4,OJ and 2.67, while log pG was least on 19 and greatest on 20. Unless these are caused by errors in the observations, they would suggest an occasional time-lag of 1 or 2 days between geomagnetic activity and density enhancement. The fluctuations due to this cause can at times be as much as 78%. 3. The CIRA 1972 CorrectionsforGeomagnetic Activity. These are mainly in the corrections for the outer layer temperature, i.e.,
Xg. 5
Variatio;:of Density with Geomagnetic Activity
Al;
-
AT6(1
AT6
-
14K,+ O.OZexp(K,),
AT,
-
ZSK, + O.O3exp(K,),
f -
-
f) + AT..f,
0.5{tanh[O.O4(z
-
(4)
35O)l+ l},I
In addition, there is a direct correction on the density, AlogpH-(1 -f)fO.O12& f 1.3x 10"e~~(&)~.
(5)
In Fig. 5, the log PO points are the values obtained after correcting the log pG points and the straight line (log p 0=-9.971) represents the model value in CIRA 1972. We see that the corrected points, apart from being some 20% greater than the model value, still contain certain fluctuation in phase with $, The clearest instances are on April 7 (i? =5) and on April 8 and 20 (zP=4), where the outstanding excesses are respectively, 55%, 39% and 38%. Obviously the corrections (4) and (5) given by the CIRA 1972 fail to remove the entire geomagnetic effect, with some exceptions eg. March 9. This could be due to the fact that the daily mean index ho may not represent the whole effect of magnetic storms in the upper atmosphere. 4. Relation between the Geomagnetic Effect in Density and Local Solar Time. In TABLE 2 we give 19 values of log pG, reduced to z0 and To with RI,>3.8, alongside the local solar time L.T. at the perigee, the latitude 15and the percentage deviation in density AP/P = [oG - P~~CIRA,Z)
1 /P
(C=bz).
For the three days, 1576 Sept 20, 21 and 1977 Mar 9, we find the mean values E =4.6, 191=57', L.T.=13h4lm(da time), and Ap/p=O.ZO, while for the 4 day April 7-29, we have ZP=4.5, 191=65O, L-T.=1 B 28m(night time) and Ap/p=O.56. The two sets have about the same mean En and \+I, but one refers to daytime, the other to night time, and their Apfp differ by 36%. This suggests that the geomagnetic effect is longer at night time than at daytime. A similar result was obtained by Bowman /5/, who using satellite 1967-31A found an increase of 40% from day to night, in the geomagnetic disturbance of the air density at heights 180-200 km. 5. Relation between the Geomagnetic Effect in Density and Latitude. The geomagnetic effect increases with increasing latitude, as may be seen in TABLE 2. For example, for the 9 measurements before 1977 April 20, we found the mean values, zp=4.5, lQI[ =63', Ap/o=O.37, while for the 10 measurements after 1978 April 10, we find 2 = 5.1, ]$I=15", Ap/p =0.19. While the E for the first set is even a little smaller thannfor the first set, Ap/p is actually grgater by 18% - apart from a difference in local time, the difference in latitude should be one of the main causes. Ching et al. 161, from densities measured from lowaltitude satellite accelerator and orbital decay rate found that the increase in density with the geomagnetic index is greater at higher latitudes and thought that the corrections given by the CIRA 1972 model are too small. Walker /7/ using Cosmso 462 also found that the model correction fail to eliminate completely the geomagnetic effect. Roemer in 1971 .78/has given a correction formula dependant on latitude: AT-
(21.4& I+1 + If9)~,+ O.O3exp(&)
and the formulae given in 1977 by Jacchia et al. are
(6)
Air Density From Satellite .976-878
36
TABLE 2
Relations between the Geomagnetic Effect and the Local Date M D
Y
13”
24”
55”7
-9.744
0.24
21
3.90
13
09
56.2
-9.758
0.29
3
9
4.62
14
30
-57.6
-9.824
0.06
4
4
3.80
05
03
-69.0
-9.809
0.15
6
5.04
04
12
-68.5
-9.715
0.33
7
5.00
03
50
-68.3
-9.599
0.74
8
4.00
03
22
-67.0
-9.667
0.58
19
5.00
23
30
-61.9
-9.730
0.29
20
4.07
23
08
-60.8
-9.655
0.61
10
4.52
16
07
-16.2
-9.491
0.13
4
5
A -
-
11
5.58
15
51
-15.0
-9.488
0.09
12
4.13
15
36
-14.0
-9.470
0.20
13
3.80
I5
22
-13.7
-9.466
0.23
14
5.12
15
OS
-11.6
-9.473
0.15
19
4.62
13
47
-5.7
-9.465
0.19
1
6.19
10
41
8.2
-9.452
0.15
2
6.33
10
26
8.9
-9.417
0.23
9
6.12
08
36
17.4
-9.429
0.21
11
4.70
0.3
05
19.0
-9.408
0.35
Asin%
i
57.5K,Il +
~.027~XP~U.4~~~1.
and Latitude
10s PC
5.z
9
1978
AT
Q,
20
1976 1977
L.T.
KY
Time
(7)
1
At high latitudes these formulae give larger corrections than (4) does, and in particular give somewhat better correction on 1977 April 7 and 20. However, (7) will give a zero correction for $=O", which is obviously inappropriate. For example, on 1978 April 18, May 1 and 2, $=O", yet the geomagnetic increase in density still reached some 17%, 21% and 33%; in these cases (4) gives rather reasonable corrections. The cause for incomplete elimination of the geomagnetic effect is manifold. Apart from the possible connections with local time and latitude just discussed, Trinks et al. /lo/, maintains that the global geomagnetic index may have little to do with locally limited data. It should be remembered that the density inferred from satellites pertains only to a limited arc interval about the perigee point. Summarizing, it seems that the relation between air density and geomagnetic activity is a complex one. Results of analysis of satellite data suggest that more satisfactory correction formula and the most plausible physical explanation still await further study. 4. PRELIMINARY CONCLUSIONS Our preliminary conclusions drawn from the above analysis of the satellite 1976-878 data are as follows: 1. Between September 1976 and June 1977, at heights around 220 km, the measured density ’ on the average, greater than the CIRA 1972 by about 22%; between December 1977 and May ;;;8, at heights around 20.5km it is greater by about 27%. 2. The rapid variation of the air density is closely related to geomagnetic activity. The geomagnetic effect is, at times, not completely eliminated with the correction formula given by the CIRA 1972 model. 3. The geomagnetic effect is gre_aterat higher latitudes: the density at $= 63" (7ip=4.5 is some 18% greater than at +=13' (K =5.1). 4. The geomagnetic effect is relae ed to the local solar time. For kP= 4.5, the density at night is about 36% greater than at daytime. REFERENCES 111 I21
t31
CIRA
1972, COSPAR
International
Group IV,
Akademie-Verlag,
Berlin.
King_Hela, Ring-Hole,
D.G.,Theorr
dellite D. W.,
D. Q. and S&t.
of
Refersme Atmosphere 1972, Compiied by COSTAR
Working
orbits in an atmosphere, Buttmworths, Pellet. SPOCS Sci., 14(lfi66), 1339,
(1964).
London
141
LIU Ya-ying, WANG Yong-bao, DING Yuan-jun, FENG Zan-liang. Chin. Astron. 4 (1980'113-120 Original Chinese version in Act. Astr. Sin. 20 (1979) 113-120. -, r51 Bowman, B. R.. P&net. SPOOS Sal., 25(1975), 1659. [sl Chin%, B. K. and Rugge, H. R.. Planet. Space Ski., f1(1975), 1801. 171 Walker. D. M. C., Pkmet. Space SOL. 26(1fi78). 291. [sl Roemer, af., spo08 ~CWC~, xI(1fi-n). 965. rfiiJa@chia, L.0..ales. 3.W. and !a~, u. VOW, 3. G~OP~YS.Bc~.. 82(le77), 684.
IIOJ
Trink*. Ii.,
Chandra, 8.. Spencer. N. w.
I&
Zahii, u. VOW, J. GeopLg(8. Rsi., 81(1e?%),
6~1s.
32
[3] [e] [S] [6]
5
Arons, J. & Scharlemann, E. T. Ap. J. 231 (1979), 854. Basko, M. M. & Sunyev, R. A., M. N., 175 (1976), 395. Boldt, E. A., et al., A.0.p.. 50 (19761, 1.61. (Chinese Astrophysics" Ambarzumian V. A. et al., "TheGetical Chubanshe. 1956, p.468.
Chin.Astron.Astrophys.
2 (1982) 32-36
Pergamo
Act. Astron.Sin. -22 (19811 223-229
ORBITAL
VARIATIONS
OF
SATELLITE
translation)
Kexue
Press. Printed in Great Britain 0275-1062/82,'010032-04$07.50/O
1976-87A AND A DETERMINATION OF THE
AIR DENSITY AT HEIGHTS OF 205 - 220 KM LIU
Ya-ying,
Received
WANG Yong-bao,
1980 October
FENG Zhan-liang,
Purple Mountain Observatory
10
ABSTRACT We investigate the orbital changes of the satellite 1976-87A (the sixth Chinese satellite) during its lifetime and from its orbital decay rate determine the air density at heights 205-220km. The density we obtained is, on the average, over 20% greater than that in the CIRA 1972 model. We discuss in detail the correlation between changes in the density and in the geomagnetic activity, and the relationships between the geomagnetic effect and the latitude and the local solar time. on 1976 August 30, with an initial perigee height of about 195 Satellite 1976-87A wassentup km, an apogee height of 2145 km, an orbital inclination of 69.16" and a period of 108.7 The satellite lasted 816 days, and fell back on 1978 November 25. Its period minutes. changed at a rate of about 0.01-0.04 minfd and its latitude angle, at about 1 degld. As its life was short, its perigee height rather low, and its orbital changes fast especially in the period and the inclination, it is one of the best candidates for a study of the air density of the high atmosphere. 1.
ORBIT AND ITS VARIATIONS
During its life-time, the various satellite observing stations secured a total of more than 1700 theodolite readings spread over 144 revolutions, of which over 1200 readings were used in improving the orbits. When improving the orbits the calculated perturbation on the 128 sets of improved mean perigee distance rp was used as a constraint on the accuracy. elements were obtained based on data obtained within 3 days before and after each epoch. TABLE 1 shows the average standard error of each of the improved elements, the fit of the elements to the observed points has an accuracy of 2-3 arcmin. TABLE 1
Average
Standard
Deviation
of OrbitalElements
a~;,,
The variationsin the perigee distance, the orbital period and the inclination are shown In these the actual measured values are marked with small circles, and the in Figs. 1-3. calculated values in perturbation calculations, the continuous curves.
Air Density from Satellite 1976~G7A
~~~~~~~
,76cr
1976
Fig. 1
26M*r
25Mar
1978
1977
Time variation of the perigee distance rp=a(l-o)
1976
Fig. 2
-1T’. I
”
L
33
1977
1978
Time variations of the orbital period P (curve l? and of i (curve 2)
69.1OL.
.___-
nscp
f>:
-I-
IDCC
1SFrb
1976
Fig. 3
1977
lONay
29Jul
if&?-
$i ..A -MM, 1978
y
Measured values of the orbital inclination i and the theoretical time profile with n=l.l3
The perigee distance is affected by the odd harmonies of the Earth's field and shows a regular oscillation with an amplitude of about 10 km; the effect of air resistance is to decrease it by less than 3 km every half-year. The orbital period is decreased by the effect of air resistance by about 10 minutes over 2 years. In Fig. 2, the period P and its rate of change P are defined as P--, 1 &stni
' pm-.-
Gi-ti (& + A+
(1)
The measured i values agree well with the curve calculated from the CIRA 1972 model atmosphere Il./,after taking out their systematic difference. The daily variation rate of the orbital period may be as much as 0.04 min, sufficiently fast for an accurate determination of the air density. The variation in the orbital inclination is mainly caused by the rotation of the atmosphere /2/, while the luni-solar perturbation is negligibly small and the variation due to the JS term is an oscillation of 0.003". The measured values of inclination in Fig. 3 all have standard deviation less than 0.01' and the theoretical curve came from the perturbation theory of an oblate spheroid atmosphere, and was obtained by numerical integration at a steplength of 10 days, after allowing for the effects of a rotating atmosphere /3/ and of the Js term. The best fit was found for a rotation speed of A=l.l3 revolutions per day. 2.
DETERMINATION OF AIR DENSITY
Using the method used before /4/ in the determination of the air density from the data of the second Chinese satellite and rocket, and taking into consideration the effect of diurnal variation in the density, we first calculated 93 density values pi at heights zx= s+ XH~*, where z is the height of the perigee. We took the surface to mass ratio of the satellite to be 2.69X10-' m* kg-l, and we took the density scale height X from the CIRA 1972 model, The
Air Density
34
corrected
pi at z;\, corrected
density P1 -P:(I
From Satellite
for the diurnal
1976-878
variation
is then given by
+ Fcos&),
(2)
where F is the diurnal coefficient, and JI is the angle between the direction of the satellite and the diurnal peak density. The logarithms of the reduced density, reduced to a fixed height so, are shown in Fig. 4 alongside the solar flux ~10.7, daily mean geomagnetic index kP.and the local solar time L.T. at the perigee. We took so=220 and 205 km respectively for periods before and after 1977 This date also divides our subsequent reduction of o.zO into the standard outer November. layer temperature To =800 K and 1000 K. The theoretical log ozO curve shown in the figure is the CIKA 1972 model value.
12rcp
19Fcb 1977
1976 Fig.
4
Observed
ANALYSIS
26Dcc
19Jun
1OMay
and theoretical
geomagnetic
3.
31Mar
values
25Apr 1978
of air density,solar
flux
F,,,.,,
index KP and local solar time L.T.
OF RESULTS
Apart from showing fluctuations 1. The Mean Density Compared with the CIRA 1972 Model due to solar activity, geomagnetic activity, diurnal and semi-annual effects, the measured densities can be seen from Fig. 4 to be greater then the CIRA 1972 model values. Excluding 10 values around 1977 April 7 and April 20 when the density was particularly increased by geomagnetic activity, the averages of the remaining 83 values, divided into two height ranges, and the averages of the model values on the same days are: average
log ps,
1976.9-1977.6
observed model excess (O-C)
1977.12-1978.5
-9.877 -9.962 22%
-9.457 -9.561 27%
Fluctuations in the air density 2. Variation of the Density with Geomagnetic Activity. caused by geomagnetic activity are quite obvious. To investigate those variations, we must first correct the measured values for the diurnal variation, the variation in the solar activity and the semi-annual variations by means of the polynomial log p(z,~) given by numerical approximation of the CIRA 1972 model: 1ogPG- lOPP‘,- (AlogP, Alwm
-
Alwe
-
A log P, -
logp(zo,
T,) -
log P(ZO, TI,2> f(a)&+>.
+ Alogp,
+ Alwd, (3)
logP(zo>
TIJ,
1% P(ZO> Tll) 3 I
where T1, T,/, (=1.15 To), f(z) and g(t) are given by the formulae in the model and TV is the adopted standard outer layer temperature. The coErected densities log pi for the period 1977 March 3 - April 22 are in Fig. 5, alongside the KP curve. There is an overall
Air Density From Satellite 1976-87A
35
agreement between the two, with however, a time-lag in some instances. For example, on April 6, 7 and 8, kP was 5.04, 5.00 and 4.00, while log pG was the least on 6 and greatest on 7; again on April 18-21, kp was 2.17, 5.00, 4,OJ and 2.67, while log pG was least on 19 and greatest on 20. Unless these are caused by errors in the observations, they would suggest an occasional time-lag of 1 or 2 days between geomagnetic activity and density enhancement. The fluctuations due to this cause can at times be as much as 78%. 3. The CIRA 1972 CorrectionsforGeomagnetic Activity. These are mainly in the corrections for the outer layer temperature, i.e.,
Xg. 5
Variatio;:of Density with Geomagnetic Activity
Al;
-
AT6(1
AT6
-
14K,+ O.OZexp(K,),
AT,
-
ZSK, + O.O3exp(K,),
f -
-
f) + AT..f,
0.5{tanh[O.O4(z
-
(4)
35O)l+ l},I
In addition, there is a direct correction on the density, AlogpH-(1 -f)fO.O12& f 1.3x 10"e~~(&)~.
(5)
In Fig. 5, the log PO points are the values obtained after correcting the log pG points and the straight line (log p 0=-9.971) represents the model value in CIRA 1972. We see that the corrected points, apart from being some 20% greater than the model value, still contain certain fluctuation in phase with $, The clearest instances are on April 7 (i? =5) and on April 8 and 20 (zP=4), where the outstanding excesses are respectively, 55%, 39% and 38%. Obviously the corrections (4) and (5) given by the CIRA 1972 fail to remove the entire geomagnetic effect, with some exceptions eg. March 9. This could be due to the fact that the daily mean index ho may not represent the whole effect of magnetic storms in the upper atmosphere. 4. Relation between the Geomagnetic Effect in Density and Local Solar Time. In TABLE 2 we give 19 values of log pG, reduced to z0 and To with RI,>3.8, alongside the local solar time L.T. at the perigee, the latitude 15and the percentage deviation in density AP/P = [oG - P~~CIRA,Z)
1 /P
(C=bz).
For the three days, 1576 Sept 20, 21 and 1977 Mar 9, we find the mean values E =4.6, 191=57', L.T.=13h4lm(da time), and Ap/p=O.ZO, while for the 4 day April 7-29, we have ZP=4.5, 191=65O, L-T.=1 B 28m(night time) and Ap/p=O.56. The two sets have about the same mean En and \+I, but one refers to daytime, the other to night time, and their Apfp differ by 36%. This suggests that the geomagnetic effect is longer at night time than at daytime. A similar result was obtained by Bowman /5/, who using satellite 1967-31A found an increase of 40% from day to night, in the geomagnetic disturbance of the air density at heights 180-200 km. 5. Relation between the Geomagnetic Effect in Density and Latitude. The geomagnetic effect increases with increasing latitude, as may be seen in TABLE 2. For example, for the 9 measurements before 1977 April 20, we found the mean values, zp=4.5, lQI[ =63', Ap/o=O.37, while for the 10 measurements after 1978 April 10, we find 2 = 5.1, ]$I=15", Ap/p =0.19. While the E for the first set is even a little smaller thannfor the first set, Ap/p is actually grgater by 18% - apart from a difference in local time, the difference in latitude should be one of the main causes. Ching et al. 161, from densities measured from lowaltitude satellite accelerator and orbital decay rate found that the increase in density with the geomagnetic index is greater at higher latitudes and thought that the corrections given by the CIRA 1972 model are too small. Walker /7/ using Cosmso 462 also found that the model correction fail to eliminate completely the geomagnetic effect. Roemer in 1971 .78/has given a correction formula dependant on latitude: AT-
(21.4& I+1 + If9)~,+ O.O3exp(&)
and the formulae given in 1977 by Jacchia et al. are
(6)
Air Density From Satellite .976-878
36
TABLE 2
Relations between the Geomagnetic Effect and the Local Date M D
Y
13”
24”
55”7
-9.744
0.24
21
3.90
13
09
56.2
-9.758
0.29
3
9
4.62
14
30
-57.6
-9.824
0.06
4
4
3.80
05
03
-69.0
-9.809
0.15
6
5.04
04
12
-68.5
-9.715
0.33
7
5.00
03
50
-68.3
-9.599
0.74
8
4.00
03
22
-67.0
-9.667
0.58
19
5.00
23
30
-61.9
-9.730
0.29
20
4.07
23
08
-60.8
-9.655
0.61
10
4.52
16
07
-16.2
-9.491
0.13
4
5
A -
-
11
5.58
15
51
-15.0
-9.488
0.09
12
4.13
15
36
-14.0
-9.470
0.20
13
3.80
I5
22
-13.7
-9.466
0.23
14
5.12
15
OS
-11.6
-9.473
0.15
19
4.62
13
47
-5.7
-9.465
0.19
1
6.19
10
41
8.2
-9.452
0.15
2
6.33
10
26
8.9
-9.417
0.23
9
6.12
08
36
17.4
-9.429
0.21
11
4.70
0.3
05
19.0
-9.408
0.35
Asin%
i
57.5K,Il +
~.027~XP~U.4~~~1.
and Latitude
10s PC
5.z
9
1978
AT
Q,
20
1976 1977
L.T.
KY
Time
(7)
1
At high latitudes these formulae give larger corrections than (4) does, and in particular give somewhat better correction on 1977 April 7 and 20. However, (7) will give a zero correction for $=O", which is obviously inappropriate. For example, on 1978 April 18, May 1 and 2, $=O", yet the geomagnetic increase in density still reached some 17%, 21% and 33%; in these cases (4) gives rather reasonable corrections. The cause for incomplete elimination of the geomagnetic effect is manifold. Apart from the possible connections with local time and latitude just discussed, Trinks et al. /lo/, maintains that the global geomagnetic index may have little to do with locally limited data. It should be remembered that the density inferred from satellites pertains only to a limited arc interval about the perigee point. Summarizing, it seems that the relation between air density and geomagnetic activity is a complex one. Results of analysis of satellite data suggest that more satisfactory correction formula and the most plausible physical explanation still await further study. 4. PRELIMINARY CONCLUSIONS Our preliminary conclusions drawn from the above analysis of the satellite 1976-878 data are as follows: 1. Between September 1976 and June 1977, at heights around 220 km, the measured density ’ on the average, greater than the CIRA 1972 by about 22%; between December 1977 and May ;;;8, at heights around 20.5km it is greater by about 27%. 2. The rapid variation of the air density is closely related to geomagnetic activity. The geomagnetic effect is, at times, not completely eliminated with the correction formula given by the CIRA 1972 model. 3. The geomagnetic effect is gre_aterat higher latitudes: the density at $= 63" (7ip=4.5 is some 18% greater than at +=13' (K =5.1). 4. The geomagnetic effect is relae ed to the local solar time. For kP= 4.5, the density at night is about 36% greater than at daytime. REFERENCES 111 I21
t31
CIRA
1972, COSPAR
International
Group IV,
Akademie-Verlag,
Berlin.
King_Hela, Ring-Hole,
D.G.,Theorr
dellite D. W.,
D. Q. and S&t.
of
Refersme Atmosphere 1972, Compiied by COSTAR
Working
orbits in an atmosphere, Buttmworths, Pellet. SPOCS Sci., 14(lfi66), 1339,
(1964).
London
141
LIU Ya-ying, WANG Yong-bao, DING Yuan-jun, FENG Zan-liang. Chin. Astron. 4 (1980'113-120 Original Chinese version in Act. Astr. Sin. 20 (1979) 113-120. -, r51 Bowman, B. R.. P&net. SPOOS Sal., 25(1975), 1659. [sl Chin%, B. K. and Rugge, H. R.. Planet. Space Ski., f1(1975), 1801. 171 Walker. D. M. C., Pkmet. Space SOL. 26(1fi78). 291. [sl Roemer, af., spo08 ~CWC~, xI(1fi-n). 965. rfiiJa@chia, L.0..ales. 3.W. and !a~, u. VOW, 3. G~OP~YS.Bc~.. 82(le77), 684.
IIOJ
Trink*. Ii.,
Chandra, 8.. Spencer. N. w.
I&
Zahii, u. VOW, J. GeopLg(8. Rsi., 81(1e?%),
6~1s.