The space-temporal variations of the upper atmosphere density derived from satellite drag data

Adv. Space Res. Vol. I I,No. 6, pp. (6)155

0273—I 177/91 $0.00 + .50 Copyright © 1991 COSPAR

(6)160, 1991

Printed inGreat Britain. All rights reserved.

THE SPACE-TEMPORAL VARIATIONS OF THE UPPER ATMOSPHERE DENSITY DERIVED FROM SATELLITE DRAG DATA A. I. Nazarenko, S. N. Kravchenko and S. K. Tatevian Astronomical Council of the USSR. Academy of Sciences, Pjatnirskaya Str. 48, Moscow 109017, USSR.

ABSTRACT

To improve our knowledge of the variations of the upper atmosphere density in 1989 experiments were made in the USSR using passive standard satellites of the shape of a sphere with the known weight and size. These satellites were set in pairs onboard spacecrafts “Recourse—F”, COSPAR identification No. 89038001. The above spacecrafte were put into orbit on May 25, 1989 and July 18, 1989. The separation of standard satellites from the first spacecraft took place on June 8 and 9 from the second one on August 6 and 7. These satellites as well as other 58 space objects chosen for the experiment were observed by radars. Improvement of the orbits was made by the trajectory measurements obtained. The movement of the satellites was under control up to their decay in the atmosphere. For the estimation of a satellite drag in the atmosphere, ballistic coefficient was used. It was determined in the process of improvement of orbital elements as acconiodation coefficient of the actual drag and the estimated atmosphere density. Besides the above mentioned satellites two more satellites (No.1 e 80037001 and 82121001) having the shape of a smooth sphere were used ~i ~andard ones. In the con— aidered altitude and time interval with 3 hours’ resolution relative variations of the atmosphere density/I/ are built in the form of normalized declinations of the actual density in the given point from those calculated by the dynamic model /2/ with the permanent level of solar and geomagnetic activity. Dependences of variations on indeces F107 and K~ built, confirm a possibility of applications of variations for the improvement of the atmosphere density. —

The values of the ballistic coefficients (K8 ) determined while improving the orbits contain considerable errors resulting from the errors of the atmosphere model and the influence of the measurement errors. The using of standard objects and the data on a drag of a great number of low—altitude satellites gives us an opportunity to determine the variations of the atmosphere density and to improve the accuracy of KS estimation by decreasing of the disturbing influence of the atmosphere model inaccuracy. Atmosphere density variations are determined on the basis of orbital data processing (orbital elements, K~ ) collected in a special data bank for all the satellites chosen for the experiment. In the process of investigation more than 25 000 sets of orbital elements in the period from June 4, 1989 to September 21, 1989 and in the altitude interval of 150—500 kms are accumulated. The data obtained are unique in time resolution (240 points per 24 hours) and altitude range. Main information on satellites is given in Table I. The distribution of the accumulated orbital data within the altitudes are shown in Table 2. It,issfen that 60% of the data are concentrated in the 3OO—40O1~srange.

(6)156

A.!. Nazarenko eta!.

K~1,(~mo~t(3j.~) = Xs’~p’~(:~.a.) Here ~b,nod(3 j,j ) and ~z (3 i.j~ ) are the model value /2/ and the real value of the density in perigee correspondingly. is the real estimated value K 6 It is also assumed that the difference of the real density value from the es1timated one can be approximated by square function of perigee altitude C n,~): ~ pm,d(fl~~j).. ~c~-~ = ii~ .L .\. A ,..~

~Q~gQ~

j~n~cd (h~) (I where errors.

p

(T4) are approximation parameters, ~ From ‘these relations we have A~.

j_

—

~U4.%

are approximation d’

(~(t~),h~)

~.

For the,~estim?tion of the real values K 8~ and density atmosphere variations ~‘‘ç~ ( ~q1 Ct,,,), h) a criterion of least squares of weighted variances is used ~..

~

~

Here ,~: is a weight factor whose value is inversely proportional to the dispersions of residuals for the i—th object:

/

=

2

Z~

=

7

While minimizing (...), let us consider ballistic coefficients of standard satellites to be fixed. Then it is possible to determine K S of the rest of the objects on the “background” of standard ones. Minimization iS done my means of approximations. Then values of K~ and of weight P. are improved and the process is repeated as long as K ~ stability is obtained. To explain the techniques described above, Fig. I gives values KS~4 obtained as accomodation coefficients for the smooth sphere (Nointern 80037001) in the inte~valfrom June 6 1989 to June 23, I9~9, atmosphere density variations 01/p (h—3oo kni~5 and the values of residuals ~ . The character of behaviour of the two upper curves is seen to be idenfical. It means that disregarding of atmosphere density variations when solving the problem of orbital improvement can lead to corresponding distortions of ballistic coefficients to be determined. Small values of residuals A~ confirm the reliability of the techniques. The diagrams are illustrati~nethe techniques of “filtration” of the estimated values apart from the component connected with the atmosphere changes. The values of itidices of solar and geomagnetic activity and atmosphere density variationsap/? (h~300ions) obtained for the same period are shown in Fig. 2. It can b~ seen that atmosplmre density variations are connected with changing of indices. This method was used for the determination of atmosphere density variations in the time period from June 5 to September 20, 1989 with time resolution of 3h~ The number of time mome-nts in which variations were deter~~c mined is 863. &eophysical conditions during the considered period are characterized by a high level of solar activity and average geomagnetic activity. The peculiarities of the period under analysis lie in the fact that in this period the maximum of the solar activity index reaches usualiy big values (335 June 15, 282 August 15, 1989, 312 September 9, 1989). Below statistic characteristics of.indices of geoma~eticand solar activities are given: mean value m, mean suqare deviation 0 , and its —

—

__,._..._

(,n...i..,...

—

Atmospheric Density Variations

(6)157

from these data that the best accuracy of the estimated variations is obtained in the altitude range of 300—400 kms. Errors of variations are to a considerable extent less than their values in the altitudes of 300—400 kms — 8—10 times and 200—500 kms 3 times less. —

A certain idea as to the accuracy 01’ the~timated atnio~phex’e density variations provides the analysis of mean square deviations OAI and of residuals for different objects as shown in Table 5. Figs. 3 and LI. present regressive dependence of the atmosphere density variations obtained for altitudes of 300 and 400 knls on the indices of gee— nagnetic or solar activity~

E\~,.~e.(t~12: K?(t-J-3~)/8] 3:0

E[.~(t)IF10,7(t—i,3d)j It is seen that increasing of these indices results in changing of the density of up to 30 and 50% at altitudes 300 and 400 knis respectively. A most objective way of testing reliability of the atmosphere density variations obtained is the estimation of the effectiveness of their use in density calculations in the process of the prediction of satellite motion. The predictions were made with the help of numerical analytical method described in /3/ . The accuracy of this method is the same as that of numerical integration and the time—spent is less by one order. As imitia]. data, a bs*k of orbital parameters of satellites (Table I) was used. The initial elements for predictions (including also a ballistic coefficient) were determined over the diurnal interval preceded the moment of their estimation. Witj~the use of the results predicted for I—6 days’ intervals discrepancies ~t of the time of crossing the equator were estimated. Since the absolute meaning of discrepancies bt are changing within very broad limits (by 2 or 3 orders) depending on the prediction interval, the values of the ballistic coefficients, of altitudes and other factors, errors were standardized in order to obtain a more homogeneous bank of accuracy parameters:

St Here tions,

2 is dispersion of ~(a,i.St~~) errors of time determination under initial condiSt~t~,,isdisturbing influence of the atmosphere.

~ ~

Mean suqare value (G~) of the standard error was taken as the indicator of the prediction quality. All these predictions were made with two variants of atmosphere density estimation availahle In the first one the atmosphere density ~ (I ~.) at the i—th moment of time and in the i—th point was estimated by the model /21 with permanent values of indices F 107 and K?.

~s(t~)~~?m~(’t~Fjo,r~ In the second variant relative atmosphere density variations were taken into accounct. Here

—

is the altitude of the j—th trajectory point.

For each of the variants of density variations 23467 predictions were made. As a result, the following was obtained: for the first variant 6’~ ~0.97, for the sec~ond nn~ c,. occ ~ ~ i~t~ ~ v~ tic~yt~teif —

A. I. Nazarenko eta!.

(6)158

prediction errors data obtained allow one to make a more detailed analysis, i.e. to find the dependences of indices from the main influencing factors, namely altitude b and the sum of indices of geomagnetic activity in the diurnal interval ~ preceding the fixation of the initial conditions. The dependence obtained are given in Figs. 5 and 6. Using the techniques described above one of the main sources of the prediction errors is inaccurate knowledge of the initial values of ballistic co.efficients and determined with the use of orbital data at the preceding interval. For illustration, 8 ball—shaped satellites were chosen differing from the rest of the satelli~esby the small values of the changing index of ballistic coefficients (bA.L3%). The prediction of the motion was carried out up to the moment of the decay of the satellite. The relative error of the determination of the moment of the decay was used as the accur~.cyparame~~. ter: C

I

v

t e~t where~t is the error of the living—time determination, texist is the time oi’ the existence of the satellite. By 337 determinatio~pthe following relative errors 6’.E~ were estimated: forthis the case firstwe variant O,~prediction .12.2%, for the Thus, in improve the accurasecond one as 2.4.5.4%. cy as many times. —

—

REFERENCES

I. Gorokhov Yu.P., Mazarenko A.I. Methodical questions of building the model of atmosphere parameters fluctuations., Nahlyudeniya Isk. Sputn. Astronomical Council of the USSR Acad. Sci., Moscow, N 80 (1982). 2. Model of density for ballistic provision of flights of satellites. Standards Editing Houae, GOST 2564.5—84. 3. Yurasov V.S. Applications of numerical—analytical method of the predicttion of satellite motion in the atmosphere. Nabliyud. Iskusstv.Sputn., Astronomical Council of the USSR Acad. Sci. Moscow, No 82 (1987).

TABLE I

COSPAR

I. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12. 13. 14. 15. 16. 17. 18.

65021001 80037001 81100002 89024001 65112001 66057001 67039001 70064001 76085001 89056001 82026001 82121001 78119001 84127001 80014001 84034002 71016001 84104001

Inclination

.

99.0 82.9 97.5 64.7 56.1 65.0 81.2 74.0 81.2 50.6 74.0 65.8 82.9 65.8 28.5 28.5 51.5 65.8 0

Hp max-mm

405—385 248—159 410—321 237—227 403—392 381—341 401—330 394—387 312—140 236—148 349—251 346—274 344—341

390—384 396—364 404—387 222—193 395—376 l,r,ri

~r,J.

•.

period 02.8—21.9 06.6—18.7 05.6—20.9 26.7—21.9 26.7—21.9 13.7—20.9 05.6—20.9 13.7—20.9 13.7—05.8 26.7—51 .~ 07.8—20.9 11.7—19.9 26.7—20.9 21.7—20.9 13.7—20.9 21.7—15.9 21.7-06.9 11.7—20.9 ‘rT

0

‘~‘i

0

Atmospheric Density Variations

I 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 4.2. 43. 44. 4.5. 46. 47. 48. 49. 50. 51. 52.

2 82026002 81115002 83046002 84007002 84068002 84104002 85018002 85050002 86067002 89022005 78026019 88113008 68097086 65039002 65082042 80089027 71012004 68091044 88113011 84015002 8950184.5 69082057 89051005 81028022 78026027 83044032 89056015 87012003 79017022

3 74.0 50,7 82.9 65.8 50.7 65.8 65.9 65.8 74.0 62.9 98.8 73.5 62.2 31.8 32.1 65.0 98.4 62.6 73.6 74.6 82.7 69.5 82.4 65.0 98.9 65.0 98.’l. 31.1

(6)159

4. 295—165 369—285

5 25.’LIO.B 05.6—20.9 05.6—20.9 04.6—27.6 04.6—20.9 11.7-08.9 05.6—20.9 13.7—20.9 18.8—20.9 05.6—25.8 o4.6—15.7 05.6—17.6 05.6—09.8 04.6-07.7 10.8—30.8 18.8-05.9 21.8—20.9 16.9—20.9 10.8—28.8 04.6—19.7 21.8—11.9 10.8-03.9 18.8—20.9 11.7—20.9 05.6—10.8 04.6—25.6 21.8—10.9 16.9—20.9 II .7—20.8

284—253 323—237 296—293 338—192 407—313 369—307 372—350 333—159 448—245 4.24—241 378—167 298—177 380—243 385—199 458—233 317_2711. 385—199 458—233 317—274 456—230 298—153 467—278 518—294 335—302 386—372 4.67—212 438—281

97.7

TABLE 2 A dlBtribution of the accumulated orbital

data

Heights km

150-200

200-250

250-300

300-350

350-400

400-450

450-500

Frequency

0. 007

0. 067

0. 169

0. 203

0. 398

0. 122

0. 014

TABLE 3,4

Statistic characteristics and estimated parameters

Index

m

F1O. 7

H

km M 0

0(~(dp)/p)

x

OA, X

geophysi.oal factors

max

mm

1.47

0

223. 9

42. 7

157. 5

-.019

300 -0.007

i~47

118

.

.052

.0i~4

TABLE 5 A distribution Range of

the

2.37

200

.

of

0. 0— -2, 5

2,5-5.0

.8 334. 7

350

400

500

.010

.036

.111

.

1~41

.0i~l

.

170

.

.019

30~I

.098

of errors of estimated density. variations

5. 0-7. 5

7. 5-10.0

10.0 -12. 5

12. 5 -15.0

>15.0

A. I. Nazarenko eta!.

(6)160

:::~______

250’

25T.0.1b~5.l.~

0.0040 6.0 4.0’

61.0000.00

‘5k)

‘

~id.o”i~.

t_ ~

06. GO.

Canon. 05.01.6G.

Fig. 1. Values

estimated for the spheri—

cal satellite, period 6 June—23 June, 1989.

00.00.00

Fig. 2. Indices of solar and geomagnetic activities, atmosphere density variations, period 6 June—23 June, 1989.

__

(~~P0F

0.0

~ob

0.0 r2-

-20

~°

28

)~,F2~4

~

P

-0:1

_:~:

1702

250

.290

Fioy