Air density at a height of 128 km, form visual observations of 1972-25g

Pbmet.

Space

Scf., Vol. 23, pp. 1405 to 1411.

AIR DENSITY

Pergamon

Press.

1975.

Printed

AT A HEIGHT OBSERVATIONS

in Northern

Ireland

OF 128 km, FORM OF 1972-256

VISUAL

D. M. BRIEBLEY Katanne Observatory,

Cockshot Road, Malvern, Worcestershire, England (Received 3 March

1975)

Abstract-655 visual observations of 1972-25G, Molniya 1V Rocket, were made when its perigee height was below 130 km, and have been used to determine its orbit at 17 epochs between 5 November 1973 and 24 February 1974 and obtain almost daily values of its rate of decay. These give 52 values of atmospheric density with a relative accuracy of 1% at a height of 128 km in latitudes 55-65”s. Dayto-day variations correlated with geomagnetic activity of up to 10% are found, plus an irregular semi-annual variation of amplitude 10%. The decrease in inclination has been measured accurately enough to enable the mean atmospheric rotation rate to be determined over the same time-span. 1. INTRODUCTION 1972-256, Molniya 1V Rocket, was launched on 4 April 1972, being the last-stage rocket that took Molniya 1V into its final 1Zhour orbit. The USSR have launched a long series of Molniya 1 communications satellites into very similar orbits with an initial inclination of 6S”, perigee height of about 500 km, and apogee height of about 39,000 km. The lifetimes of Molniya objects, satellites and rockets are measured in years only: luni-solar perturbations have an appreciable effect on an orbit with such a high apogee, causing the eccentricity to oscillate while the semi-major axis remains constant, so that at some stage the perigee height falls below 150 km and a very rapid orbital decay ensues. During the decay the perigee height remains relatively constant until re-entry is imminent. In February 1969 I made visual observations of the decaying Molniya lF, 1967-95A, and was able to use them to determine the atmospheric density at a height of 120 km. (l) It appeared that as successive Molniya objects decayed, there would be repeated opportunities for the determination of the atmospheric density at the rather inaccessible heights of 120-130 km; as the apogee has many thousands of km to fall, densities could be obtained daily for a period of weeks or even months. Additionally, since the perigee remains near southern apex throughout the lifetime of a Molniya object, densities would refer to a specific band of latitudes, 55-65’s. It now seems that most Molniya objects decay too fast for any systematic visual, or even radar tracking to be accomplished. In the early stages of the decay, luni-solar perturbations are still effective, and usually continue to push the perigee down. However in the case of two rockets, the perigee rose again, and

each was intensively observed from Britain during the later stages of the decay. They were 1970-l 14F, Molniya 1S Rocket, in February-March 1973 and 1972-25G in November 1973-February 1974. The combination of 65’ inclination and very high apogee near northern apex meant that British visual observers could obtain a very wide coverage of the orbit (for instance the Earth’s shadow was no problem even in mid-winter). As a result, accurate orbits could be obtained from observations made at a single site, in sharp contrast to the normal orbit determination situation in which observations from widely separated sites are required. This paper presents 17 orbits which werecomputed from 655 visual observations of 1972-256, and the 52 values of atmospheric density at a height of 128 km which were deduced from them. In principle the mean atmospheric rotation rate could be determined from the change in inclination, but there does not appear to be any development of the theory suitable for the high eccentricity and low perigee of the satellite. 2. OBSERVATION Molniya Rockets are cylinders with an approximate length and diameter of 2 rnt2) and have an apparent stellar magnitude of +35 to +4-5 at 1000 km range, and can be tracked visually to a range of about 15,000 km with the 120 mm refractor used to obtain the majority of the observations. 1972-25G was first seen on 5 November 1973, by which time its apogee height had fallen to 14,500 km. With a perigee height of 130 km, its orbital period was 266 min, decreasing by 0.2 min/rev. Two observers, D. J. Hopkins (at Cospar station 2414) and I (at 2421) attempted to obtain accurate observations

1405

1406

D. M. BRIERLEY

on at least one transit every night until the satellite became invisible on 1974 February by which time its orbital period had fallen to 124 min shortly before re-entry on 8 March. In the event, observations were obtained on 58 out of a possible 112 nights. Each observer made up to 6 observations per transit, spaced as widely across the sky as possible, using standard techniquesC3) to obtain an accuracy in position of better than %l’ arc. Although predictions (in the form of Spacetrack orbital elements) were supplied by telephone from the Appleton Laboratory, Slough, they could be in error by f15 min or more by the time the observer was

able to use them, and new techniques were developed t4) to enable such an unpredictable satellite to be acquired regularly. Two other observers(5) contributed to the final total of 705 observations of which all but 50 were used in orbit determination. 3. ORBIT DETERMINATION

The 17 orbits obtained are listed in Table 1. They were fitted using a differential orbit correction process related to the one in regular use at the Royal Aircraft Establishment, Farnborough.@) Differences between the two spring from the need to represent an extremely high drag reasonably accurately-the

TABLE 1. ORBITALELEMENTS OF 1972-25G, MOLNIYA IV ROCKET,WITH STANDARDDEVIATIONS MJD 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

T

41991.78072 5 Nov 3 42001.74954 15 Nov 7 42005.783881 19Nov 6 42011.934502 25 Nov 12 42015.749627 29 Nov 8 42022.661960 6Dec 7 42027.624831 11 Dee 7 42032.744839 16Dec 4 42037.718065 21Dec 9 42046.698484 30Dec 11 42054.703908 7 Jan 10 42069.730892 22 Jan 7 42071.726501 24 Jan 5 42081.704779 3 Feb 4 42085.734746 7 Feb 5 42090.735217 12 Feb 6 421W745768 22 Feb 10

Key:

MJD

i

r,

65.872

6489

A

65.85; 13 65.8787 18 65.876 2 65.8689 19 65.8638 16 65.8651

647;

65.86:: 16 65.863 2 65.856 2 65.8575 13 65.8440 19 65.8403 18 65.828

6484.;

65.82: 4 65.810 4 65.803 14

648z.7 6484.: 1.3 6486.9 6484.: 6485.;

6488.; 6483.: 1.1 6484.1 6484.; 6485.: 8 6484.0 1.1 6486.7 648i.i 1.3 6486 3

R 2.257 6 356.692 18 354.410 4 350.711 348.29: 4 343.737 3 340.299 4 336.584 3 332.823 325.5784 6 318.594 4 303.916 5 301.783 4 290.276 5 285.166 6 278403 6 262.84 2

0 261.157 13 260.16 4 259.588 6 258.870 10 258.380 7 257.494 5 256.814 7 256.083 5 255.355 8 253.883 14 252.537 13 249.612 10 249.209 8 246.946 6 245.939 7 244.620 7 241.583 18

Modified Julian Day

Time of perigee passage, also epoch inclination (de& A rieht ascension of node (de& w a&ment of perigee (deg) P anomalistic veriod at evoch (min) Pl change in P’per revoluiion &in)’ P2 change in Pl per revolution (min) goodness of fit 0” time coverage of observations (days) N number of observations used.

T

P 266.476 19 254.991 5 250.0121 13 241.527 2 236.109 4 226.641 2 219.920 2 213.6443 13 207442

E

D

N

0.45

1.2

22

0.54

2.1

20

0.74

3.2

54

0.68

2.3

27

+ 0.0009

0.68

2.4

37

+o.w0:2

0.62

3.3

41

+0.000580 4

0.66

3.5

52

0.62

2.1

47

P2

Pl -0~188 7 -0.2217 8 -0.21991 14 -0.2480 4 -0.2278 15 -0.2213 5 -0.1950 4 -0.1821 -0.18083

+0@0037

0.78

3.3

58

-0.16584 15 -0.1376

+00006:

0.54

2.2

50

0,78

3.0

49

0.65

2.2

37

0.65

2.2

50

+0.00015”

0.76

2.2

35

+0.000182 2

0.85

2.1

37

0.67

1.1

31

0.96

2.0

16

n

19676; 18746:5 12 170.1150 18 167.8700 14 155.1252 9 150.1525 10 143.437 2 127.9986 7

-0.136; 5 -0.1372

18 -0WO42 2 +OGOO46 6 -0GO116

4 -0.1312 2 -0.1320 -0.141: -0.172:9 15

+OGOOO97 13

Air density at a height of 128 km change in orbital period at each perigee passage of 1972-256 was two orders of magnitude larger than the timing error in the obse~ations-and the ability to simplify the computation by ignoring effects small compared with that of drag. Some details follow : (a) Drag was taken to occur instantaneously at perigee, with a step reduction in orbital period and hence semi-major axis. The representation of mean anomaly M by a polynomial in time from epoch did not fit in with this “step” model. Parameters of the correction process were taken to be a perigee passage time T (also the epoch), the orbital (anomalistic) period P at epoch, and the step decrease PI in P at each subsequent perigee passage. There was also an optional P2, the change in P1 at each perigee passage. (b) The perigee radius r9 was used instead of the eccentricity e as one of the parameters; it was of direct interest in the calculation of atmospheric density, and could be assumed to be constant during the time-interval covered by one orbit determination. The inclination i was another parameter assumed to be constant. (c) Perturbations caused by deviations of the Earth’s gravitational field from spherical symmetry were ignored apart from the effect of the main flattening term Ja on the two other parameters R and w, averaged between successive perigee passages. Doing this was not expected to lead to errors of more than 1 km in the satellite’s position in space during one revolution, or less than 0.5’ arc as seen from the ground on most transits. Preliminary orbits were fitted to selected groups of at least 14 obse~ations made on two consecutive nights, i.e. covering about 1.2 days, including the parameter P2. The fits were excellent, with RMS residuals in position smaller than 1’ arc. Rejections due to mistakes in recording and reducing the observations occurred at the usual rate of 7-S%; however practically all the errors could be identified and corrected for use in subsequent orbit determinations. Most of the orbits had values of P2 much smaller than 1 S.D., indicating that longer time-intervals could be employed where the observations were plentiful enough, with a corresponding improvement in accuracy of all the parameters, so the observations were reassembled into groups covering up to 35 days, and fresh orbits determined. In a few cases P2 was still smaller than 3 SD., and these orbits were redetermined with P2 excluded (i.e. kept zero). This arbitrary procedure has been criticized,@) but is fully justified here by the way high correlation between Pl and P2 in each orbit, typically -0.99,

1407

making the inclusion of P2 an evil to be avoided if possible. In one case, a group of observations covering 3.2 days could not be fitted, and had to be split into two with an overlap of 1 day. These are orbits 12 and 13 in Table 1. Otherwise the orbits are completely independent, and satisfyingly accurate, apart from orbit 2 where the coverage of the orbit was known to be poor. The smallest SD. in inclination was 0+0013”, and in perigee height 0.3 km, corresponding to 0.~2 in eccentricity as shown in Table 2 of derived quantities. 4. ATMOSPHJ3RIC DENSITY

The atmospheric density above perigee (where H is atmosphere at perigee, and gives rise to only &h of the PA = 5

p, at a height YA, $H the scale height of the a fractional error in H error in pa) is given by: E(e),

where P is the rate of change of period with time, 6 incorporates the area/mass ratio and drag coefficient of the satellite and 1 2e

W

= 3 ; 0

“’ (1 - e)r’s (1 + c)3/2

for e > 0.2 and H < rp. It seems unlikely that the area/mass ratio of 1972-25G will ever be known to within a few per cent, and the expression simplifies for relative values of PA to

Af() PAKa9e or

The accuracy of P, Pl and P2 in the orbits suggested that Pl could be sampled daily with useful accuracy. A table of times of perigee passage, one for each night on which observations were used, was differenced to give 52 values of Pl. The formal S.D. was a fraction of 1 ‘A in all cases. Co~esponding values of PA were calculated using values of H taken from CfRQ 1972@)appropriate to the prevailing solar flux at 10.7 cm 5’ro.,, and geomagnetic index A, (the theoretical exospheric temperature ranged from 740-950 K). Seasonal and diurna1 effects for the appropriate latitudes (65” to 53% as given in Table 2) were also considered, but found to have a negligible effect.

D. M. BRIERLEY

1408

TABLE2. QUANTITIESDERIVEDFROMTHE ELEMENTS IN TASLE 1, WITH STANDARD DEVIATIONS e

YP

c

LT

128.7

- 64.4

13.9

13717.3 1.0

05269

2

13320.22 17

0.5141 7

Ill.4

-64.0

12.7

3

13146.25 5

0.50657 3

125.8

-63.8

12.2

4

12847.08 7

o-49527 10

123.4

-63.6

11.5

12654.23 13

0.48737 4

125.8

-63.4

Il.0

12313.67 8

0.47340 2

123.2

-63.0

10.1

12069.08 8

0.46259 3

124.6

-62.7

9,4

11838.28 5

0.45227 3

122.8

-62.3

8-7

9

11608-05 8

044101 5

127-3

-62.0

8.1

10

11206.09 19

121.6

-61.2

6.8

11

1085011 4

0.42145 10 0.40240 5

122.1

-60~5

5.6

12

10170.05 7

0.36241 8

121-8

-58.8

3.3

13

10080.37 6

0.35661 8

123.0

-58cY

3.0

14

9563.48 4

121.0

-57.1

1.3

15

9358.00 4

0.32200 II 0.30683 14

123.4

-56.4

0.6

16

9076.86 8

0.28574 15

119.6

-55c5

23.7

17

8413.27 3

0.2291 4

121.4

-53.3

21.8

Key :

3

a semi-major axis (km)

found to reject it. The curve is a theoretical one, for a combination of two effects which each caused the perigee height to decrease by 4 km between the first and last orbits. The first effect combines changes caused by odd zonal harmonics of the Earth’s gravitational field, and luni-solar perturbations (the Moon causing the pronounced fortnightly oscillation), both of which can be calculated precisely. D. G. King-Hele kindly ran the computer program PRODtl”) at R.A.E. to do this for 1972-250. The second effect is a variable one caused by atmospheric drag; it is given, for an accompanying change in eccentricity from e,, to e by:(*) for

H’ < 2r,,

where H’ is the scale height at a height 3Hl2 above perigee, H being the scale height at perigee. The best fit to the observed values of rD after allowing for the first effect was obtained with H’ = 18 f 5 km at a height of 135 km, in reasonable agreement with CIRA 1972 which gives H = 12 rt 1 km for an exopheric temperature of 800 f 100 K. To derive a useful history of the atmospheric density between MJD 41995 and 42102, the values of pA for heights YA taken from the best-fitting curve were reduced to an average height (128 km was the most suitable) by using CIRA 1972 scale heights for a height of (ye + 128)/2 km appropriate to the prevailing solar flux, etc. Being relative values, it seemed sensible to scale them to the CIRA 1972 value for plze of 9.7 &g/m3 for an exospheric temperature of 800 K on MJD 42032, the date of a zerocrossing in the theoretical semi-annual variation, before plotting them in Fig. 2. The first and last few values of plzsr when (ya - 1281 was greater than H/4, should not be given much weight because a 10% error in the assumed vahte of H Ieads to an error of 3 ‘A or more in prse.

P eccentricitv J

yD height of perigee above local sea-level (km) 4 latitude of perigee (deg) LT local time at perigee (hr).

The values of perigee radius rs from TabIe 1 were converted to the perigee heights ys shown in Table 2 and plotted in Fig. 1 (except for orbit 2 which is of poor accuracy). The scatter is considerable, probably because with the particular distribution of observations available, rz, tended to absorb errors in the representation of drag. In particular, r2,from orbit 9 is 6 SD. from the fitted curve, but no reason can be

5. INFLUENCES ON DENSITY Figure 2 shows that, as expected, the changes in atmospheric density from day to day at a height of 128 km are very small compared with those higher in the atmosphere. The largest change in 24 hr is lo%, and many of the successive daily values agree to within 1%. The consistency of successive values confirms that the orbital decay rates were reliably determined, and suggests that errors in the relative densities may be of order 1%. The results therefore provide accurate observationa data at a lower height and over a longer time than any previously

I409

Air density at a height of 128 km

41990

42000

20

IO

30 Dale

40

60

50

80

70

90

and modifiedJulianday

FIG. 1. VALUES OF PERIGEE HEIGHT y, (WITH CD.)

WITHTHEORETICAL CURVE.

PO &o TE 100 g90

41993

42000

24

kc4

IO

20 Date

14 30 and

23

24 40

modified

60

50 Julian

70

Feb2 80

I2 90

IO0

110

day

FIG. 2. AIR DENSITY AT A HEIGHT OF 128 km , plzs WITH THEORETICAL SEMI-ANNUAL VARIATION; DAILY VALUES OF SOLAR FLUX ON 10.7cm (S,,.,) AND GEOMAGNETIC INDEX A,. published which refer to this rather inaccessible region of the atmosphere. The variations in density in Fig. 2 are apparently not dependent on solar activity, but there is a tendency for correlation with A,, with marked increases in density, of order 5-10 ‘A, at the times of the peaks in A, at MJD 42012, 42072, 42090 and 42101. (The 10% increase in density at MJD 42072 explains why an orbit could not be fitted to observations over the 3-day interval MJD 42070-42073). There is, however, no increase in density corresponding to the magnetic disturbance at MJD 42037, so this magnetic storm apparently had no appreciable influence at latitudes 55-65’s. Apart from these day-to-day variations, there is a longer-term trend apparent in Fig. 2. The density at the start, during November 1973, is 10.8 + 0.2 pg/m3; it then decreases to 9.9 + 0.2 pg/m3

ALSO

from 10 December 1973 to 25 January 1974, and afterwards rises again by about 5 %. The lower density between mid-December and mid-January, about 10 % lower than in November, may readily be ascribed to the semi-annual variation. The smooth curve in Fig. 2 shows the semi-annual variation as given by CIRA 1972 for a constant solar flux of 85 and zero geomagnetic activity. At greater heights the actual semi-annual variation is irregular, rather than smooth as given by the model, and Fig. 2 confirms that this irregularity persists down to 128 km. The amplitude of the variation is close to that given by the model. It should also be mentioned that the day-to-night variation would be in phase with the semi-annual variation; as Table 2 shows, the local time at perigee passed from 13.9 hr through midnight to 21.8 hr. However, although perigee passed into shadow at

D. M.

1410

BRIERLEY

Date and modified Julian day

FIQ. 3.

VALUES OF INCLINATION

i

(WITH

MJD 42076, it was never more than 300 km below sunlit atmosphere. Since the diurnal variation predicted by the C&4 1972 model is small, it can probably be neglected. There seem to be no effects specfiic to high southern latitudes in summer. 6.

ATMOSPIIERIC

ROTATION

RATE

The ratio A of the mean atmospheric rotation rate to the rotation rate of the Earth at heights a little above perigee can normally be obtained from the secular decrease in inclination of satellites which suffer a marked decrease in orbital period during their lifetimes.t8) A satellite showing as great a decrease in period as 1972-250 should be ideal, especially as resonance effects are negligible at such a high rate of decay, although perigee was rather close to an apex where the effect on the inclination becomes zero or can even reverse slightly. Luni-soIar perturbations were evaluated in the run of PROD already described; there was a fortnightly oscillation su~rimposed on an overall decrease in inclination of 0.02S0. Figure 3 shows the observed values of inclination after removal of the perturbations. They are fitted satisfactorily by a curve descending increasingly steeply by a total of about 0.06“. Unfortunately present theory has not been developed to cater for a combination of very high eccentricity (e > 0.3) and very low perigee (such that H < 20 km). Expressions used to dateol) are expansions in powers of e and of c, with some cross-products, where c = (~r,/2H) sin2 i. Here E, the ellipticity of the atmosphere, can be taken to be @00335, and so c starts at a value of O-9 and expansions in powers of c are quite inappropriate.

S.D.)

AFTER REMOVAL OF PERTURBATIONS.

7.

CONCLUSIONS

Visual observations of a decaying Molniya Rocket made by 4 British observers have proved sufficientIy numerous and precise for the successful determination of 17 orbits, and as a result the density of the atmosphere at a height of 128 km and latitudes 55-65% has been determined at frequent intervals, sometimes daily, for a period of 112 days. An irregular semi-annual variation is found at this low height, of about 10%. Typical peaks in the geomagnetic index A, to 50 are generally (but not always) accompanied by a sharp increase of 10% in the density, which takes several days to subside. When a suitable theory has been developed it should be possible to deduce the mean atmospheric rotation rate at a height of 128 km in summer at high southern latitudes. 1t remains true that the work presented in this paper will be repeatable as further Molniya objects decay; they are still being launched at a greater rate than they reenter. A possible candidate is 1972-81 E, Molniya 1W Rocket. Acknowledgement.v--I should like to express my sincere thanks to D. G. King-Hele for his help and encouragement during the preparation of this paper, and to P. Neirinck of the Appleton Laboratory who ensured that Spacetrack elements were made availabIe to the observers as quickly as possible. REFERENCES 3. D. M. Brierley, Planet. Space Sci. 18, 309 (1970). 2. J. A. Pilkington, D. G. King-Hele and H. Hiller, Table of Earth Satellites, VoI. 2: 1969-l 973. Royal Aircraft ~tablishment, Farnborough (R.A.E.) Tech. Rept. 74105 (1974).

Air density at a height of 128 km

1411

8. D. G. King-Hele, Theory of Satellite Orbits in an 3. D. G. King-Hele, Observing Eurth Satellites. MacAtmosphere, Chapter 8. Butterworths, London millan, New York (1966). (1964). 4. D. M. Brierley, in Satellite Observing Notes 482114. 9. Cospar Working Group 4, CIRA 1912 (Cospar Appleton Laboratory, Slough (1974). International Reference Atmosphere). Akademie, 5. R. D. Eberst, STS Rep. 168 and 171, Royal ObservaBerlin (1972). tory, Edinburgh (1974). 6. R. H. Gooding, R.A.E. Tech. Memo Space 156 10. G. E. Cook, Gel. Mech. 7, 301 (1973). (1970). 11. D. G. King-Hele and D. W. Scott, Planet. Space Sci. 14, 1339 (1966). 7. R. H. Gooding, R.A.E. Tech. Rept. 74164 (1974).