Variations in exospheric density at heights near 1100km, derived from satellite orbits

Planet.

Space

Sci. 1967.

Vol.

15. pp. 1933 to 1956.

Pergamon

Press Ltd.

Printed

in Northern

Ireland

VARIATIONS IN EXOSPHERIC DENSITY AT HEIGHTS NEAR 1100 km, DERIVED FROM SATELLITE ORBITS G. E. COOK and DIANA W. SCOTT Royal Aircraft Establishment, Famborough, Hams, England (Received 7 August 1967) Abstract-In an earlier paper, values of exospheric density were obtained from the orbit of Echo 2 for the years 1964-65. The results indicated a semi-annual variation in density by a factor of between 2 and 3, considerably larger than predicted by existing atmospheric models. These studies have now been extended to the beginning of 1967, using both Echo 2 and Calsphere 1, to show how the density is responding to increasing solar activity. Variations in density during 1964 have been analysed in more detail. The long-term variation associated with the solar cycle and the short-term variations associated with magnetic and solar disturbances agree with the variations expected on the basis of current models. The semi-annual variation is persisting to higher levels of solar activity, and although its amplitude is diminishing the factor of variation was still l-6 in 1966.

1.INTRODUCTION

In an earlier paper(l) values of exospheric density were obtained from an analysis of the orbit of Echo 2 (19644A) for dates between February 1964 and December 1965. The results indicated that at times of low solar activity the dominant feature of the atmosphere at heights near 1100 km is a semi-annual variation, with the maximum density, in April and October, exceeding the minimum, in July, by a factor of between 2 and 3. This variation is considerably greater than predicted by existing atmospheric models, and cannot be caused entirely by temperature variations in the thermosphere. The large semi-annual variation was confirmed using the secular acceleration of Calsphere 1 (196463C) during 1965, and it was suggested t2) that the cause of this variation might be changes in the helium concentration in the exosphere due to variations in the height of the turbopause, i.e. the level (near 105 km) at which diffusive equilibrium begins to prevail over turbulent mixing. The Smithsonian Astrophysical Observatory has recently issued daily orbital data for Echo 2 for the year 1964. In the present paper these data are analysed to obtain daily values of density, in order to specify more accurately both short-term and semi-annual variations in density at times of very low solar activity. Also the earlier studies are extended to the beginning of 1967, using NASA orbital elements for Echo 2 and “five-card elements” for Calsphere 1, to show how the density of the exosphere is responding to the recent increases in solar activity. 2. CALSPHKRK

1

2.1. Orbital data Calsphere 1 is a polished aluminium sphere having a diameter of 0.36 m and a weight of 0.98 kg. Orbital data are given in the form of “five-card elements” by Spadats/Spacetrack; new values of these elements are issued whenever the predictions based on the previous set develop appreciable errors. The orbital eccentricity is very small, varying between about 0.001 and 0.0025, so that values of air density can be found at the mean height assuming a circular orbit. As a result of the low eccentricity, Calsphere can be 1933

1934

G. E. COOK

and DIANA

W., SCOTT

used to provide an up-to-date record of the response of the exosphere to increasing solar activity without the need for computing the effect of solar radiation pressure on the orbital period. To allow for the irregular motion of the perigee of a near-circular orbit, the corrected anomalistic period is written in the form T, =

1 ti+M’

(1)

v

where cr)is the argument of perigee and M the mean anomaly. is then given by .. FL_ Gi+M (ci, + &)a *

The secular acceleration

(2)

Values of & + i@ and cii + 2 were obtained from the five-card elements using divided differences and the results are shown in Figs. 1 and 2. 2.2. Results The main effect noticeable in Figs. 1 and 2 is the increase in secular acceleration as solar activity increased. The monthly mean of the flux of solar radiation on a wavelength of 10.7 cm increased from around 75 x lo-B W rnqa (c/s)-l during 1965 to 147 x lo--88W m-a (c/s)-l in February 1967; during this time the density increased by a factor of nearly 3. Apart from the general increase in the secular acceleration due to increasing solar activity, there is evidence of a long-term variation with distinct minima in July. During 1965 this long-term variation had the appearance of a semi-annual effect,@) but to investigate the variation for later dates it is necessary to make a correction to allow for the increase in solar activity using some form of model atmosphere. Existing model atmospheres are constructed using values of density obtained at heights below 750 km. Consequently Jacchia’s static diffusion model@) is terminated at 1000 km, while the COSPAR International Reference Atmosphere(4) (CIRA 1965) extends to only 800 km. It should still be possible, however, to construct from these models an empiricd relation which can be used to relate measured densities (or accelerations) to a tied 1eveI of solar activity. Since the time resolution of the Calsphere data is rather coarse, it is only necessary to allow for the long-term variation during the solar cycle. Values of air density p for a height of 1000 km averaged between day and night were obtained from Jacchia’s model as a function of the 10.7 cm radiation flux, S, smoothed over three solar rotations. The density was found to be well represented by the relation p/p,, = exp (04WS

-

&,I},

(3)

where p. is the density corresponding to the standard mean flux S,. Figure 3 shows values of 6 + i$ corrected to S,, = 100 on the basis of equation (3). Since the data show considerable scatter, they were smoothed by drawing a line connecting points midway between each pair of data points. The line in Fig. 3 suggests that the semiannual variation persisted through 1966, the July minimum being much lower than the January minimum. Even though the magnitude of the effect will be underestimated as a result of the wide spacing of the points in Fig. 3 and the smoothing process, the October

VARIATIONS

IN EXOSPHERIC

DENSITY

AT HEIGHTS

NEAR

1935

1100km

11.5002. . .

,J~IOBO

1

. .

13.1078

-

.

,330-/b

. ,3’3070 . ‘3.3058

,1.5062

St -M rev /day

13’1060

,I 3052 . . 11.3010

1

. .

l

,?a-5048

I

. . 13504b .

.

.

13.1042 IN3

MarApr 134040

’ 38800

’

May Jun ’ ’ .l*ocm

Jul Aq ’

’

Scp Ott

’ 39000

’

NW Dot ’

’ ’ 39kOO

I

19Lb

Jon Fob Mar ’

Apr May

’ ’ JPCOO

’

Jun Jul ’ ’ SSlOO

Aug Sop Ott

NW

Dee Jan Feb Mar

’

’

’

’

’ 39400

’ 39100

’

’

‘39600

Date- MJD

FIG. 1. VAIUA~ONOF ui + Ik FORCALSPHERE 1.

maxima appear to exceed the July minima by a factor of about l-5. In 1965 the April maximum exceeded the July minimum by a factor of over 2.3. The average air density experienced by a satellite in a circular orbit of radius a is given byts) P P=

-sz’

where 8 = FScJm, S is the cross-sectional area, CD the drag coefficient, m themass of the satellite and F is a factor which allows for atmospheric rotation. On taking the drag

G. E. COOK

1936

and DIANA

W.

SCOTT

14 i . IL

_ . . . .

.

.

FIG. 3. ACCELERATION OFCAUPHBRE1 ADJUSTED TOA 10.7 cm RADIATION FLUXOF100 x lo-” W m-* (c/s)-‘. TABLE 1. DENSITIES OBTAINED FROMTHE ORBITOF CAISPHERE1, ADJUSTED TO A 10.7cm RADIATION FLUX OF

Approximate date 1965 April July October 1966 January April July October 1967 January

100 x 10-p w

rn-%(c/s)-’

1P PI080

1P

p1180

Q/cm?

(&cm?

23.1 10.0 15.3 13.8 14.5 9.8 14.7 12.2

19.0 8.2 12.6 11.3 11.9 8.1 12.1 10.0

coefficient(6) as 2.8, we have 6 = 0,291 ma/kg. Using the accelerations in Fig. 3, densities appropriate to a radiation flux of 100 x 1O-22W m-a (c/s)-l have been obtained from equations (1) and (2). Since these densities apply at the mean height of 1080 km, they were adjusted to a height of 1130 km by multiplying by O-820, so that they could be compared with results from Echo 2. The values of density are shown in Table 1. 3. ECHO 2

3.1. Method of analysis The general procedure used to evaluate air density from the orbit of Echo 2 was similar to that described in, Ref. 1. By writing equation (3) of Ref. 1 in terms of the argument of

VARIATIONS

IN EXOSPHERIC

DENSITY

AT HEIGHTS

NEAR

1100 km

1937

latitude instead of the argument of perigee and the eccentric anomaly, however, we were able to derive more accurate values for the rate of change of orbital period, f,, due to solar radiation pressure. Values of i”n obtained using the earlier version of the equation may be in error by up to O-7 x lo-‘, although the error is usually about 0.3 x lO_’ and not therefore sign&ant in the final values of density. 3.2. Orbital acceleration 3.2.1. Smithsonian orbitaldata. Orbital elements for Echo 2 have now been determined(7) by the Smithsonian Astrophysical Observatory from field-reduced Baker-Nunn observations at daily intervals from MJD 38423 to MJD 38760 (29 January to 31 December 1964). In addition to the basic elements, which are determined from observations over 8-day intervals, Ref. 7 gives values for the rate of change of orbital period. These values of FC are shown in Table 2, together with the computed values of & and i: The tabulated values of eccentricity, e, and w given in Ref. (7) for dates between MJD 38640 and MJD 38720 were somewhat inaccurate owing to the small eccentricity and consequent rapid motion of perigee; they were therefore smoothed on the basis of the expected theoretical variations before p’R and air density were evaluated. Between MJD 38677 and 38682 values of PC were inaccurate and density could not be determined. For the 13 days after MJD 38747 the orbital elements were not suiIiciently accurate for & and density to be found. Values of FCand i;l are plotted in Fig. 4 and the rate of change of orbital period due to air drag alone, given by F = FC- FE, in Fig. 5. Six values of FCaround MJD 38680 were very inaccurate due to poor observational coverage of the orbit, and are omitted. It is evident from Figs. 4 and 5 that the radiation pressure effect can be important: the absolute magnitude of ?“Ractually exceeded that of F by about 1 x lo-’ in July 1964. 3.2.2. NASA orbital data. The transmitter aboard Echo 2 became unreliable towards the end of 1965 and recent sets of orbital elements have been determined from camera observations made with the Minitrack Optical Tracking System (MOTS), which is installed at most Minitrack radio tracking stations. There was no obvious deterioration in the quality of the orbital data as the orbit determination became totally dependent on optical observations. A quadratic was fitted to each set of values of o + M obtained from NASA elements between December 1965 and December 1966, and the observed rate of change of orbital period was obtained using equation (2). Values of PC, pn and T are shown in Table 3.

3.3. Evaluation of air density Since the orbital eccentricity e is small, values of air density p,. were evaluated at a height 1H above perigee, H being the best available estimate of the density scale height at perigee, using the equation 3” Q exp (c cos 2~) Pn = - 3nad -

1 + 2eM4 Z,(z)

M4 +c4(2)

(4)

cos 20 + O(e2, $c2, p2) ’

where 0 and 1 are functions of z = se/H, being given by Figs. 1 and 2 of Ref. 1. Z,(z) is the Bessel function of the first kind of imaginary argument and degree n, p is the scale height gradient and the parameter c (= gsin2i) represents the effect of the ellipticity of the atmosphere.

3938

G. E. COOK and DIANA TABLE2. ACCELERATIONS ANDDENSITES

MJD 38423 38424 38425 38426 38427 38428 38429 38430 38431 38432 38433 38434 38435 38436 38437 38438 38439 38440 38441 38442 38443 38444 38445 38446 38447 38448 38449 38450 38451 38452 38453 38454 38455 38456 38457 38458 38459 38460 38461 38462 38463 38464 38465 38466 38467 38468 38469 38470 38471 38472 38473 38474 38475 38476 38477 38478 38479 38480 38481

-107 PO

8.68 9.14 8.95 864 8.42 8.31 8.13 8.85 9.67 10.6 11.1 Il.5 11.9 13.0 13.8 15.1 15.6 15.8 15.8 15.9 16.2 16.6 17.0 16.8 16.6 16.6 16.7 17.4 17.6 17.7 17.1 16.5 15.8 15.4 15.8 14.6 15.2 13.7 12.3 11.9 11.9 11.5 11.0 10.5 10.2 10.1 9.82 9.48 8.57 8.22 7.77 7.08 7.54 7.76 7.20 6.62 6.28 6.17 5.37

10’ i;, 0 0 0 0 8 0 0 :

-Fl -1.9

-2.6 -3.1 -3.5 -3.9 -4.2 -4.5 -4.8 -4.9 -5.1 -5.1 -5.2 -5.2 -5.2 -5.1 -5.0 -49 -4.8 -4.6 -4.4 -4.3 -4.0 -3.8 -3.5 -3.1 -2.9 -2.6 -2.3 -2.0 -1.7 -1.3 -1.0 -0.7 -0.4 -0.06 0.26 0.70 0.99 1.25 1.59 1.99 2.32 2.58 2.90 3.17 3.41 3.60

-10’

W. SCOTT

OBTAINED FROM

f

8.69 9.14 8.95 8.64 8.42 8.31 8.13 8.85 9.67 10.6 11.1 10.4 10.0 10.4 10.7 11.6 11.7 11.6 11.3 11.1 11.3 11.5 11.9 11.6 11.4 11.4 11.6 124 12.7 12.9 12.5 121 11.5 1l-4 12.0 11.1 12.1 10.8 9.7 9.6 9.9 9.8 9.7 9.5 9.5 ;I:6 9.74 9.27 9.21 9.02 8.67 9.53 10.08 9.78 9.52 9.45 9.58 8.97

S.A.O. ORBITAL ELEMENTS

10” PAWcm?

8.52 8.97 8.78 8.47 8.27 8.18 8.01 8.74 9.59 10.5 11.1 10.4 10.0 10.5 10.9 11.8 12.0 11.9 11.7 11.6 11.8 12.1 12.5 12.3 12.1 12.2 12.5 13.4 13.7 14.0 13.6 13.2 12.6 12.5 13.2 12.2 13.3 12.0 10.8 10.7 11.0 10.9 10.8 10.6 10.6 10.8 10.9 10.8 10.3 10.2 10.0 9.58 10.5 11.1 10.7 10.4 10.3 10.4 9.7

yA (km)

1160 1160 1160 1159 1159 1159 1158 1157 1156 1155 1154 1151 1150 1149 1147 1145 1144 1142 1141 1138 1137 1135 1133 1131 1130 1128 1126 1125 1124 1121 1120 1121 1123 1112 1117 1116 1115 1115 1114 1113 ‘1112 1112 1114 1113 1112 1112 1109 1110 1114 1112 1113 1111 1114 1118 1121 1122 1121 1121 1124

lo** pllro (glcm8)

9.55 10.0 9.83 9.45 9.22 9.12 8.90 9.68 10.6 11.6 12.1 11.3 10.8 11.3 11.6 12.5 12.6 12.4 12.2 11.9 12.1 12.3 127 12.3 12.1 12.1 12.3 13.1 13.4 13.6 13.1 12.7 12.2 11.6 12.6 11.6 12.6 11.3 10.1 10.0 10.3 10.1 10.1 9.88 9.87 10.0 10.0 10.0 9.67 953 9.36 8.90 9.88 10.6 10.4 10.1 9.96 10.1 9.50

VARIATIONS

IN

EXOSPHERIC

DENSITY

AT

HEIGHTS

NEAR

-10’

lOlo

pA @xna)

y, 04

1939

1100 km

Table 2 (cm&.) MJD 384‘82 38483 38484 38485 38486 38481 38488 38489 38490 38491 38492 38493 38494 38495 38496 38491 38498 38499 38500 38501 38502 38503 38504 38505 38506 38507 38508 38509 38510 38511 38512 38513 38514 38515 38516 38517 38518 38519 38520 38521 38522 38523 38524 38525 38526 38527 38528 38529 38530 38531 38532 38533 38534 38535 38536 38537 38538 38539 38540

-10’

fc

5.31 5.25 5.25 5.34 5.53 5.82 5.60 5.04 4.24 ::z 4.47 4.42 3.95 3.68 3.41 340 3.72 4.27 4.41 4.58 4.88 5.05 5.49 5.90 5.91 5.93 6.13 6.49 6.96 8.68 8.85 8.92 8.69 8.60 8.76 8.70 8.81 8.32 8.31 8.22 8.63 8.84 9.28 9.38 9.39 9.57 9.82 9.89 9.91 9.76 9.65 9.93 10.6 10.8 10.9 10.9 10.9 Il.6

10’ TX 3.88 4.05 424 443 4.54 471 481 4.91 494 5.02 5.03 5.03 4.98 492 4.83 472 460 446 429 4% 3.72 3.36 3.03 267 2.27 1.81 1.27 0.61 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.71 -1.6 -2.1 -2.4 -2.7 -28 -2.9

l+

9.19 9.30 9-49 9.77 10.07 10.53 10.41 9.95 9.18 9.26 9.35 9.50 940 8.87 8.51 8.13 i:! 8-56 8.47 8.30 8.24 8.08 8.16 8.17 7.72 7-20 6.74 6.49 6.96 8.68 8.85 8.92 8.69 8.60 S-76 8.70 8.81 8.32 8.31 8.22 8.63 8.84 9.28 9.38 9.39 9.57 9.82 9.89 9.91 9.76 9.65 9.22 9.0 8.7 8.5 8.2 ;:;

10.2 10.5 10.8 11.2 11.0 10.5 z3 9.73 9.83 9.66 9.09 8.67 S-24 8.07 8.20 8.53 8.41 8.20 8.12 7.94 7.98 7.98 7.52 Z 6.30 6.76 8.44 8.63 8.72 8.53 8.47 8.66 8.66 S-81 8.35 8.41 8.37 8.84 9.11 9.62 9.78 9.85 10-l 10.4 10.5 10.6 10.5 10.4 10.0 9.72 9.45 9.23 8.95 8.79 9.50

1124 1125 1125 1127 1127 1130 1132 1135 1136 1137 1139 1141 1143 1145 1146 1149 1150 1153 1154 1157 1157 1159 1159 1161 1162 1163 1163 1164 1164 1165 1165 1165 1164 1163 1162 1162 1160 1160 1158 1156 1155 1153 1151 1150 1147 1146 1144 1143 1141 1140 1138 1137 1136 1134 1133 1131 1129 1128 1126

w

pllaO (g/cm9 9.72 9.37 10.0 10.4 10.6 11.2 11.1 10.7 ;:; 10.1 10.3 10.2 9.63 9.21 8.86 8.71 8.94 9.34 9.31 9.09 9.06 8.86 8.97 i:: 7.93 744 7.17 7.72 9.63 9.84 9.91 9.66 9.56 9.78 9.69 9.86 9.28 9.28 9.20 zi 10.4 10.4 10.5 10.6 10.9 11.0 11.0 10.8 10.7 10.2 9.87 9.56 9.26 8.91 S-72 9.36

G. E. COOK and DIANA

1940

W. SCOTT

Table 2 (cm&.) MJD

-10’ fc

10’ YB

38541 38542 38543 38544 38545 38546 38547 38548 38549 38550 38551 38552 38553 38554 38555 38556 38557 38558 38559 38560 38561 38562 38563 38564 38565 38566 38567 38568 38569 38570 38571 38572 38573 38574 38575 38576 38577 38578 38579 38580 38581 38582 38583 38584 38585 38586 38587 38588 38589 38590 38591 38592 38593 38594 38595 38596 38597 38598 38599

11.9 11.7 11.2 10.6 10.4 10.1 9.97 9.67 9.26 8.75 8.52 8.40 8.28 9.01 9.35 9.35 9.18 8.63 7.72 6.53 5.70 5.05 4.65 4.64 4.55 4.21 3.76 3.41 3.08 2.90 2.21 1.74 1.35 1.06 1.05 1.06 0.63 -0.02 -0+9 -0.12 0.05 0.00 -0.26 -0.50 -0.86 -0.87 -0.80 -0.58 -0.90 -1.01 -0.64 -0.48 0.03 0.22 0.01 -0.07 0.07 0.31 0.81

-3.0 -3.0 -3.0 -2.9 -2.7 -2.6 -2.45 -2.28 -2.10 -1.89 -1.68 -1.46 -1.20 -0.98 -0.72 -0.46 -0.20 0.05 0.35 0.61 0.82 1.07 1.35 l-58 1.82 2.02 2.25 2.47 2.67 2.87 3.06 3.24 3.41 3.58 3.74 3.88 4.02 4.15 4.27 4.38 4.46 4.53 4.60 4.64 4.65 4.65 4.65 4.65 4.60 4.55 4.48 4.37 4.28 4.16 4.00 3.85 3.65 3.43 3.18

-10’ T’ 8.9 8.7 8.2 7.7 7.7 7.5 7.52 7.39 7.16 6.86 6.84 6.94 7.08 8.03 8.63 8.89 8.98 8.68 8.07 7.14 6.52 6.12 ::?2 6.37 6.23 6.01 5.88 5.75 5.77 5.27 4.98 4.76 464 4.79 4.94 4.65 4.13 4.18 4.26 4.51 4.53 4.34 4.14 3.79 3.78 3.85 4.07 3.70 3.54 3.84 3.89 4.31 4.38 4.01 3.78 3.72 3.74 3.99

1O’O P* (g/cm*) yA(km) 9.73 9.52 8.97 8.43 8.43 8.19 8.23 8.08 7.81 7.48 7.45 7.55 7.69 8.70 9.33 9.59 9.68 9.33 8.65 7.63 6.96 6.52 6.36 6.58 6.71 6.55 6.29 6.14 5.98 5.98 Z:G 4.88 4.75 4.88 5.02 4.71 4.18 4.22 4.28 4.52 4.54 4.33 4.12 3.76 3.74 3.82 4.01 3.64 3.48 3.76 3.81 4.21 4.28 3.92 3.69 3.63 3.65 3.90

1127 1126 1125 1125 1124 1124 1124 1123 1122 1124 1123 1122 1122 1122 1123 1123 1123 1124 1122 1124 1128 1128 1125 1126 1128 1131 1130 1128 1130 1132 1133 1133 1135 1135 1136 1138 1137 1138 1140 1141 1142 1142 1144 1146 1146 1147 1149 1150 1152 1153 1154 1154 1157 1158 1157 1163 1162 1161 1161

lO’e pnso(g/cJw 9.62 9.37 8.80 8.27 8.23 8.01 8.04 7.86 7.58 7.31 7.25 7.32 7.46 8.44 9.08 9.34 9.42 9.11 8.39 746 6.91 6.47 6.24 6.48 6.66 6.57 6.29 6.09 5.98 6.03 5.50 5.19 4.98 4.84 5.00 5.18 4.84 4.31 4.38 4.47 4.74 4.75 4.57 4.38 4.00 t :t 4.33 3.96 3.79 4.12 4.18 4.66 4.75 4.34 4.18 4.10 4.11 4.38

VARIATIONS

IN EXOSPHERIC

DENSITY

AT

HEIGHTS

-10’

1019 PI WC-m

NEAR

1100 km

1941

Table 2 (cod.) -10’ 38600 38601 38602 38603 38604 38605 38606 38607 38608 38609 38610 38611 38612 38613 38614 38615 38616 38617 38618 38619 38620 38621 38622 38623 38624 38625 38626 38627 38628 38629 38630 38631 38632 38633 38634 38635 38636 38637 38638 38639 38640 38641 38642 38643 38644 38645 38646 38647 38648 38649 38650 38651 38652 38653 38654 38655 38656 38657

fc

1.12 1.36 1.66 2.78 3.69 4.50 4.89 506 5.19 5.37 564 5.77 5.77 5.69 567 5.83 5.94 5.97 5.89 5.95 6.12 6.49 6.86 6.95 6.72 6.72 6.72 7.18 6.87 6.73 6.70 6.86 7.14 7.45 7.38 7.16 6.97 7.26 7.70 7.68 7.55 7.06 6.69 6.61 5.34 7.32 7.01 5.80 5.67 5.69 5.92 4.82 3.99 4.67 5.01 4.90 5.35 5.01

10’ Y* 2.87 2.49 2.00 1.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.24 0.43 0.58 0.67 0.77 0.88 0.96 1.02 1.06 1.12 1.16 1.19 1.22 1.23 1.25 1.26

i

3.99 3.85 3.66 4.03 3.69 4.50 4.89 5.06 5.19 5.37 564 5.77 5.77 5.69 5.67 583 5.94 5.97 589 5.95 6.12 6.49 6.86 6.95 6.72 6.72 6.72 7.18 6.87 6.73 6.70 6.86 7.14 7.45 7.38 7.16 6.97 7.26 7.70 7.68 7.55 7.06 6.93 7.04 5.92 7.99 7.78 6.68 6.63 6.71 6.98 5.94 5.15 586 6.23 6.13 6.60 6.27

3.90 3.77 3.60 3.96 ::z 4.85 504 5.18 538 5.68 5.83 5.86 5.80 5.80 5.99 6.13 6.18 6.13 6.21 6.41 6.81 722 7.33 7.11 7.12 7.14 7.63 7.31 7.16 7.14 7.31 7.61 7.94 7.85 7.61 7.42 7.36 8.18 8.15 7.99 7.46 7.31 7.41 6.22 8.38 8.14 6.98 6.92 6.99 7.25 6.15 5.33 6.05 6.42 6.30 6.78 6.43

71 (km) 1161 1161 1163 1162 1161 1162 1162 1162 1162 1160 1161 1159 1160 1159 1158 1159 1158 1158 1157 1156 1156 1155 1155 1155 1154 1154 1153 1154 1153 1154 1154 1153 1154 1154 1154 1154 1153 1154 1155 1155 1155 1155 1156 1157 1157 1158 1158 1159 1159 1160 1162 1161 1160 1159 1159 1158 1163 1164

w”

pm0

Qfcm”,

4.39 4.24 4.08 4.47 4.09 502 5.47 568 5.85 6.03 6.38 6.50 6.56 6.47 6.45 6.69 6.82 6.88 6.79 6.85 7.07 7.49 7.94 8.06 7.78 7.80 7.79 8.35 7.97 7.85 7.82 7.98 8.33 8.69 8.60 8.34 8.09 8.06 8.99 8.96 8.78 8.20 8.06 8.21 6.89 9.32 9.05 7.79 7.72 7.82 8.18 6.92 5.96 6.75 7.16 7.00 7.67 7.31

G. E. COOK and DIANA

1942

W. SCOTT

Table 2 (contd.) MJD 38658 38659 38660 38661 38662 38663 38664 38665 38666 38667 38668 38669 38670 38671 38672 38673 38674 38675 38676 38677 38678 38679 38680 38681 38682 38683 38684 38685 38686 38687 38688 38689 38690 38691 38692 38693 38694 38695 38696 38697 38698 38699 38700 38701 38702 38703 38704 38705 38706 38707 38708 38709 38710 38711 38712 38713 38714 38715

-10’ fc 5.01 5.02 5.47 5.69 5.36 4.67 4.78 5.46 5.77 5.89 581 6.03 6.72 7.51 8.20 9.56 9.22 8.76 7.63 3.53 2.28 11.4 11.4 4.89 740 8.31 8.42 9.90 9.89 9.90 9.79 9.79 9.10 10.2 10.4 10.8 11.0 10.8 11.1 10.6 10.0 9.90 9.33 9.56 944 9.36 8.82 9.02 9.21 9.22 8.58 8.85 8.85 8.76 8.56 8.75 9.64 9.67

10’ TB

-10’ 2;

1.27 1.27 1.27 1.27 1.26

6.28 6.29 6.74 6.96 6.62 5.91 6.00 6.65 6.93 7.02 6.90 7.08 7.71 8.45 9.08 10.37 9.95 944 8.23

6.42 6.42 6.88 7.09 6.73 6.00 6.08 6.74 7.01 7.09 6.96 7.13 7.76 8.50 9.13 10.4 10.0 9.52 8.32

1165 1164 1165 1165 1165 1165 1171 1168 1168 1168 1168 1168 1170 1171 1172 1173 1170 1172 1167

7.33 7.30 7.84 8.09 7.68 6.84 7.09 7.77 8.09 8.18 8.02 8.23 9.02 9.91 10.7 12.3 11.6 11.1 9.57

8.31 8.34 9.76 9.70 9.66 9.49 9.45 8.70 9.8

8.71 8.77 10.3 IO.2 10.2 9.98 9.92 9.11 1@2 10.3 10.7 10.8 10.6 10.8 10.3 9.59

1163 1164 1163 1164 1164 1164 1164 1164 1164 1165 1165 1166 1167 1167 1167 1167 1166 1168 1168 1168 1168 1166 1166 1166 1167 1167 1166 1166 1166 1165 1166 1165 1163

9.87 9.96 11.6 11.6 11.6 11.3 11.3 10.4 11.6 11.8 12.2 12.4 12.2 12.4 11.8 11.0 10.8 10.2 10.4 10.2 10.2 9.60 9.98 10.7 108 10-o 10.3 10.4 10.3 10.0 10.3 11.4 11.3

::2”: 1.19 1.16 1.13 1.09 1.05 0.99 0.94 0.88 0.81 0.73 0.68 0%

-8.: -0.14 -0.19 -0.24 -0.30 -0.34 -040 -0.4 -0.5 -0.5 -0.6 -0.6 -0.6 -0.6 -0.7 -0.68 -0.69 -0.71 -0.69 -0.64 -0.56 -0.43 -0.05 0 0 0 0 0 0 0 0 0

1i.z 10.4 10.2 10.5 10.0 ;::2 8.64 8.85 8.75 8.72 8.26 8.59 9.16 9.22 8.58 8.85 8.85 8.76 8.56 8.75 964 9.67

10” pAQ/cm9

ii% i:: 8.85 8.38 8.72 9.30 9.37 8.74 903 9.04 8.97 8.79 9.01 9.96 10.0

y, (km)

We PIISOb,$cm*)

VARIATIONS

IN EXOSPHERIC DENSITY AT HEIGHTS NEAR

1lOOkm

1943

Table 2 (co~td.)

38716 38717 38718 38719 38720 38721 38722 38723 38724 38725 38726 38727 38728 38729 38730 38731 38932 38733 38734 38735 38736 38737 38738 38739 38740 38741 38742 38743 38744 38745 38746 38747

9.38 9.07

8.73 8.60 8.48 8.62 8.68 8.63 8.67 8.67 8.57 8.63 8.61 8.87 8.66 8.34 7.98 7.73 7.81 8.01 8.25 8.19 8.24 8.06 8.80 9.35 9.80 9.93 10.4 10.6 11.0 10.7

0 0 0 0 0 0 0 0 0 0 ii 0 0 8 8 0 0 0 0 8 0

-0.63 -1.04 -1.31 -1.5 -1.7 -1.9 -2.1

9.38 9.07

8.73 8.60 8.48 8.62 8.68 8.63 8.67 8.67 8.57 8.63 8.61 8.87 8.66 8.34 7.98 7.73 7.81 8.01 8.25 8.19 8.24 8.06 8.80 8.72 8.76 8.62 8.9 8.9 9.1 8.6

9.72 9.42 9.10 8.98 8.87 9.03 9.11 9.07 9.13 9.14 9.04 9.11 9.08 9.36 9.13 8.78 8.38 8.12 8.16 8.30 8.51 8.42 8.43 8.19 8.88 8.75 8.74 8.56 8.76 8.71 8.89 8.42

1161 1161 1161 1160 1159 1159 1158 1159 1158 1158 1158 1158 1157 1157 1158 1158 1158 1158 1159 1159 1161 1161 1161 1162 1164 1165 1165 1166 1167 1167 1168 1168

10.9 10.6 10.2 10.1 9.90 10.1 10.1 10.1 10.1 10.2 10.0 10.1 10.1 10.4 10.2 9.76 9.32 9.02 9.10 9.26 9.57 9.46 9.47 9.24 10.1 9.98 9.97 9.80 10.1 10.0 10.3 9.71

Echo 2 is a spherical balloon with a diameter of 41 m and a mass of 256 kg, giving an area-to-mass ratio of 5.16 ma/kg. As in Ref. 1 the drag coefficient was taken as 2.8, while H was taken as 230 km and ~1as O-3. On the assumption that the rotational speed of the atmosphere exceeds the rotational speed of the Earth by a factor of l-2, we have F = O-974, so that 6 = 14-l m”/kg. The parameter c was taken as O-054. 3.4. Results from S.A.O. orbital data Air density has been evaluated from the Smithsonian orbital data at daily intervals and values of pL and yr. are given in Table 2. The height yA varies between 1109 and 1173 km, and the densities were adjusted to a height of 1130 km using the relation

as in Ref. 1. Values of pus0 are given in Table 2 and shown in Fig. 6. This detailed study confirms the existence of the pronounced semi-ammal variation in exospheric density near solar minimum first found in Ref. 1; in 1964 the October maximum

1944

G. E. COOK and DIANA

FIG.~. VALUESOF OBSERVED ACCELERATM~N ?=AND &OR 14

9

0

I

__ ’

*

M420

I.

I

I

I

.

440

460

P&r

1

480

I

ACCELLBWION

DUE TO SOLAR RADIATIONPRESSURE

ECHO~, ~RTA~NEDPROMSMTHSON~ANORI~~TALDATA. I

I

I

-.

.

&b

W. SCOTT

_

I

I

I

I

I

I

-a

*6r

'I I

500

520

Hay

1 540

.

A.

1964 ( Jul

560

580

, bOD

:"s LEO

I

I

l

I

_

.

l

. 640

I

5Ld LLO

I

I

. .

I

I

I

;--

I

cd 680

1 . 700

NW

, 720

OK 140

FIG.~. VALUESOF DRAG ACCELERATION FOR ECHO2, OBTAINED FROM SMITHSONIAN ORBITALDATA.

16,760

VARIATIONS

IN EXOSPHERIC

DENSITY

AT HEIGHTS

NEAR

FIG.~. VALUES OF AIR DENSITY OBTAINED FROM SMITHSONIAN ORBITALDATA,REDUCJSD

The flux of solar radiation

1130km. on a wavelength of 10.7 cm, the daily geomagnetic centric Sun-perigee angle are also shown.

1100 km

1945

TO AHEIGHTOF

index A, and the geo-

exceeds the July minimum by a factor of 3.0, while the April maximum exceeds the July minimum by a factor of 25. The densities in Fig. 6 extend to a slightly earlier date than the values given in Ref. 1. As noted before, the density in February 1964 appeared to be abnormally high, even after allowing for the relatively high level of solar activity; this result cannot be explained at present, except on the basis of an unknown initial effect, e.g. outgassing. In Fig. 6 variations in atmospheric density at a height of 1130 km are compared with the 10.7 cm radiation flux, Sr,,.,, and the geomagnetic planetary amplitude A,. The latter quantity has been displaced forwards by 1 day to bring the peaks into line with the corresponding density peaks. This l-day lag is not sigticant, being due to the averaging effect produced by the evaluation of ?‘Cfrom observations spread over 8 days. It really occurs because magnetic storms tend to commence suddenly and to decay more slowly. The dependence of exospheric temperature on the geomagnetic planetary 3-hr index K, has been fairly accurately defined (g*g)from the analysis of satellite drag data for heights 10

1946

G. E. COOK and DIANA

W. SCOTT

below 750 km, obtained from precisely reduced Baker-Nunn observations. It is of interest to see whether the density variations which correlate with magnetic disturbances have the magnitude expected on the basis of current atmospheric models, i.e. on the assumption that the variations result from heating in the thermosphere. It would be incorrect to compare these density variations in Fig. 6 with Jacchia’s model using the latest relationship between exospheric temperature and the magnetic index. Instead, we go back to earlier results~lo) obtained from the orbit of Explorer 9 with a time resolution of 1 day, which indicated that the variation of exospheric temperature with the A, index is given by dT/dA, = lo*0 for A, < 60. On using this relation, we conclude from Jacchia’s model that for a change in A, of 50 the density should increase by a factor of about 1.14 at a height of 1000 km. This agrees well with the density increases that occurred on MJD 38459, 38487 and 38661, although the density on MJD 38557 was rather greater than expected. The densities are not sufficiently accurate to allow a detailed correlation with the A,, index, but there is general qualitative agreement, most of the peaks in A, corresponding to peaks in the density. 1964 was a year of minimum solar activity and there was very little variation in the 10.7 cm radiation flux. In fact, S exceeded the generally prevailing level by more than 7 x lO-aa on only two occasions. The corresponding density peaks, on MJD 38452 and 38623, can be completely removed using the empirical relation (6) given in the next section. 3.5. ResuIts from NASA orbital data Air density has been evaluated from the NASA orbital elements, normally at 7-day intervals, for dates between MJD 39101 and 39513 (7 December 1965 and 23 December 1966). Values of p,. and yr. are given in Table 3 and plotted in Fig. 7. The height yr. varies between 1058 and 1140 km and the densities were again adjusted to a height of 1130 km to facilitate comparison with the earlier results. Values of pIlao are shown in Fig. 8 together with the 10.7 cm radiation flux. The very high values of pn in November-December 1966 are due to a high level of solar activity coinciding with a low perigee height. After adjustment to 1130 km, the density in December 1966 still exceeded the lowest value in July 1964 by a factor of over 5, while it exceeded the December 1964 value by a factor of about 2.5. Figure 8 indicates that in 1966 the semi-annual effect is becoming lost in the large variations produced by solar activity. Nevertheless, an April maximum and a July minimum can still be clearly discerned. In Fig. 9 the scatter in the data has been reduced by taking the running means of every three successive values. The perigee height of the orbit is shown in Fig. 10, together with the geocentric Sun-perigee angle and the geomagnetic planetary amplitude A,. There appears to be evidence of a day-to-night variation in Fig. 9: each of the last three minima in Sun-perigee angle at MJD 39280, MJD 39375 and MJD 39470 coincides with a peak in density. It is worth noting, however, that two of these peaks correspond to magnetically disturbed conditions, while the third corresponds to the very high solar radiation in November-December. We return to this point after allowing for the variations in solar activity. To adjust the values of density to a fixed level of solar activity it is necessary to use a rather more sophisticated relationship than equation (3), and to make allowance separately for long-term effects over one solar cycle and short-term effects over one solar rotation. Again an empirical relation was constructed for the density at 1000 km using Jacchia’s

VARIATIONS

IN EXOSPHERIC

TABLE 3. ACCELERATIONSAND MJD 39101 39108 39115 39122 39129 39136 39143 39150 39176 39185 39192 39199 39206 39213 39220 39234 39241 39248 39255 39262 39269 39276 39283 39290 39297 39304 39311 39322 39329 39336 39343 39350 39357 39364 39371 39385 39392 39399 39406 39412 39426 39433 39440 39447 39452 39464 39471 39478 39485 39492 39499 39506 39513

-10’ 4.3 7.6 7.4 8.3 8.6 8.3 ;:; 8.4 6.8 7.2 10.1 11.4 10.9 11.0 12.0 13.0 14.6 150 15.6 17.6 15.4 12.5 11.2 10.3 9’:; 10.5 10.8 13.5 16.2 15.5 17.4 19.3 17.5 14.9 12.5 11.2 14.7 17.4 18.1 22.6 24.1 28.5 27.6 24.8 26.4 23.5 16.4 1.9.3 24.7 18.1 21.7

DENSITY

AT

HEIGHTS

NEAR

1100 km

DENSITIESOBTAINED FROM NASAORBITALELEME~

f# 2.6 0 0 0 0 0 1.2 1.5 0.6 0.1 -0.1 -0.2 0 0 0 0 -1.0 -2.1 -2.6 -2.7 -2.5 -1.7 -0.7 0.4 ;:; 0.7 0 -0.1 -1.8 -3.2 -3.9 -3.9 -3.0 -2.0 ;:; 1.8 0 0 0 -1.9 -3.8 -4.1 -3.7 -1.3 0.2 1.4 2.6 2.6 0 0 0

6.9 7.6 7.4 8.3 8.6 8.3 10.2 10.3 ;:; 7.1 9.9 11.4 10.9 11.0 12.0 12.0 12.5 12.4 12.9 15.1 13.7 11.8 11.6 11.6 9.9 10.0 10.5 10.7 11.7 13.0 11.6 13.5 16.3 15.5 16.0 14.7 13.0 147 17.4 18-l 20.7 20.3 24.4 23.9 23.5 26.6 24.9 19.0 21.9 24.7 18.1 21.7

6.8 7.6 7.6 8.7 9.1 8.9 10.9 10.9 9.5 7.3 7.4 10.2 11.8 11.4 11.6 12.1 11.7 12.0 12.0 12.6 151 13.9 122 12.2 12.4 10.7 10.8 10.8 10.5 11.2 12.8 11.8 14.2 17.7 17.0 17.5 15.9 13.7 15.0 16.9 17.8 21.0 21.5 26.5 26.3 25.9 29.0 26.6 19.8 22.2 24.5 17.8 21.4

1131 1131 1128 1125 1123 1122 1124 1126 1132 1130 1132 1133 1132 1131 1127 1134 1139 1140 1134 1127 1121 1115 1108 1102 1101 1101 1104 1117 1127 1129 1123 1109 1095 1082 1076 1076 1082 1090 1100 1107 1107 1097 1086 1074 1066 1058 1063 1071 1075 1083 1091 1096 1096

6.8 7.6 7.5 8.5 8.9 8.6 10.6 10.7 ;:; 7.5 10.4 11.9 11.4 11.5 12.3 12.3 12.4 12.2 12.5 14.6 13.2 11.2 11.0 11.1 ;:; 10.3 10.4 11.2 12.4 10.9 12.4 14.6 13.7 14.1 13.1 11.7 13.4 15.4 16.3 18.4 18.1 21.2 20.4 19.4 22.2 21.0 15.9 18.5 21.0 15.6 18.7

1948

G. E. COOK and DIANA W. SCOTT

26 -

24

18

.

.

l

.

.

lb

1

.

14

.

. *a*

.

I2

l

.

.

I,

l

.

. 1)

a*

l

,I

IO .

. .

l

I

al Jan 39100

FIG+.7.

.

I

, Fob

1

, Mar

, Apr

39200

VALUES

OF AIR

I

I

DENSITY

1

, May

, Jun

Date

I

1

1966 ,Jul

1

, Aug

39300

- MJ D

pn AT HEIGHT

yA OBTAINED

,Sep

>ct , NC 3c

FROM

,OQC

1967 lJon

00

NASA

ORBITAL

ELEMENTS.

VARIATIONS

IN EXOSPHERIC

DENSITY

AT HEIGHTS

NEAR

1100 km

150

I40

I30 IO%

10 ,

w ml-2 c&/9) -’ 17.0

too

90

60 . 20

14

12

10

9

1 G 3!

34200

39300 Date -MJO

1 39400

3990

0

FIG.& VALUES OF AIR DENSITY OBTAINED FROM NASA ORBITAL ELEMENTS, REDUCED TO A HBIGHTOF 1130klll, AND THE FLUX OFSOLARRADIATIONONAWAVELENGTHOF 10.7 Cm.

1949

1950

G. E. COOK and DIANA

9 39200

39800

Date

1969

I

I

39100

FIG.~O.VARIA~ONOP

Mm- , 39COO

SPP

Ott

Nov

Dee

, Jan

39100

- M J D

FIG.~.VARIATIONOFAIRDENSITYATA

DCC, JOn , FCb

W. SCOTT

11966 1

I W+‘,

HEIGHTOF 113Okm

MOY, Jun

, Jul

39100 DateM.J D.

PERIGEEHEIGHTANDGJEENTRIC

, A”9

, 5CP,

I

Ott,

I

NW,

39400

SMOOTHING.

AFTER

DCc,

11967 Jon

39500

SUN-PERIGEE ANGLE

ANDTHEDAILYGEOMAGNETICINDEX A,.

+,

FORECHO~,

VARIATIONS

IN EXOSPHERIC

DENSITY

AT HEIGHTS

NEAR

1lOOkm

1951

model. The density was found to be well represented by p/p0 = exp (O.O16(S - S,,) + 0*007(S - s)},

(6)

where S is the 10.7 cm flux when the air density is p, p,, is the density corresponding to the standard flux S,, and s is the mean flux over three solar rotations. Using equation (6), the values of air density in Table 3 and the values obtained from NASA orbital data in Ref. 1 have all been adjusted to a standard flux of 100 x 10mz2W m-2 (c/s)-l. The resulting values were smoothed by taking running means of three. The smoothed values, which are shown in Fig. 11, indicate that an appreciable semi-annual variation has persisted from 1964 when the mean flux s was near 70 to January 1967 when the mean flux was 140. The form of the density variation in Fig. 11 is very similar to the form of the variation of the secular acceleration of Calsphere in Fig. 3. The magnitude of the semi-annual effect given by Echo 2 is of course larger owing to the finer time resolution of the data. As solar activity has increased, the magnitude of the semi-annual variation appears to have declined; the October maximum exceeded the July minimum by a factor of about 2.7 in 1964, about 1.9 in 1965 and about 1.6 in 1966. In 1965 the April maximum exceeded the July minimum by a factor of 2.3, which agrees well with the factor indicated by Calsphere. It was mentioned earlier that there is evidence of a day-to-night variation in Fig. 9 and an attempt has been made to remove this effect from the densities for 1966. If the air density varies sinusoidally with the geocentric Sun-perigee angle +,, the mean density p0 at a distance r, from the Earth’s centre is given byor)

F PO = -

3rd

exP ’ 10(z) f

where F is related to the ratio value by

24(z)

+ Pm

{(a-

row8

#,{Z,(z)

+ $e[Z,(z)

+ 31,(z)]}

’

f of the maximum daytime density to the minimum night-time

The only difference between equation (7) and the basic relation used in the derivation of equation (4) is the F-term. Values of prrso for 1966 have been adjusted using equation (7) on the assumption that the maximum daytime value of density exceeds the minimum nighttime value by a factor of 2. These values were then smoothed and the results are shown by crosses in Fig. 11. The maximum change is just over 10 per cent. A number of factors contribute to make it very difficult to estimate the magnitude of the day-to-night variation. First, Echo 2 is not well suited to this purpose since the orbital eccentricity is so small. Second, the motion of perigee relative to the Sun is very limited and perigee never samples true night-time conditions. Third, the oscillation in the Sunperigee angle is in phase with the variation in yL, low values of $, corresponding to low values of yL. This means that the effect of a diurnal variation is linked to the value of density scale height used in equation (5) to adjust the densities pL to a fixed height. Fourth, there are density increases correlated with the magnetic disturbances around MJD 39275 and 39370. These increases, together with one associated with the enhanced magnetic activity around MJD 39205, are visible in the smoother data of Fig. 11 both before and after allowing for a diurnal variation by a factor of 2.

1952

G. E. COOK and DIANA W. SCOTT

a

2 N

VARIATIONS

IN EXOSPHERIC

DENSITY

AT HEIGHTS

NEAR

1100 km

1953

Figure 11 suggests that a diurnal variation by a factor of about 2 is reasonable. If a larger value than 260 km had been used for the scale height in (5), however, the values of density near the minimum perigee heights would have been reduced by less, and the diurnal variation would appear larger. For a 10.7 cm flux of 125 x 1O-22W m-2 (c/s)-l, extrapolation of Jacchia’s model indicates a day-to-night variation by a factor of about 2, while extrapolation of CIRA 1965 indicates a factor of about 5. On the evidence presented here, a factor of 5 is too high and a factor between 2 and 3 is more likely. 4. DISCUSSION

Analysis of the detailed Smithsonian orbital data for Echo 2 has confirmed the existence of an appreciable semi-annual variation in the density of the exosphere during 1964, with the October maximum exceeding the July minimum by a factor of 3.0. During 1964 neither the geomagnetic index nor the 10.7 cm radiation flux showed any appreciable disturbance. However, analysis of the largest density variations which correlate with peaks in the A, index and short-term increases in the 10.7 cm flux has shown that the magnitudes of these variations are consistent with Jacchia’s static diffusion model. It is evident from Figs. 3 and 11 that the empirical relation (6) for the variation of density with the 10.7 cm flux has entirely removed the steady increase in density due to increasing solar activity. We have contirmed, therefore, that both short-term variations associated with magnetic and solar disturbances and long-term variations associated with the solar cycle are correctly predicted in the exosphere by current models. The most interesting feature of Figs. 3 and 11 is the large residual semi-annual variation which is left after adjustment to a fixed level of solar activity. This variation is discussed separately in section 5. The density variations given by Calsphere provide a valuable check on those given by Echo 2, since the orbit of the former is so nearly circular that its orbital period is effectively unperturbed by solar radiation pressure or day-to-night variations in density. Densities obtained from Calsphere and adjusted to a height of 1130 km, which are given in Table 1, show no systematic difference from the densities obtained from Echo in Fig. 11. This suggests that there is no appreciable electric drag acting on Echo 2. Echo 2 is not particularly suitable for investigating diurnal variations in density since the orbital eccentricity is small and also because perigee never samples true night-time conditions. Even so, if an appreciable diurnal variation existed it should still be visible in the orbital acceleration. The corrections made in section 3.5 suggest that in 1966 the maximum daytime density exceeded the minimum night-time value by a factor of between 2 and 3. Figure 6 shows no evidence of a diurnal variation during 1964. 5. SEMI-ANNUAL VARIATION

5.1. Summary of observational results Figure 11 indicates that the air density at a height of 1130 km had maximum values in October 1964, April 1965 and October 1965 and minima in July 1964, January 1965 and August 1965. In 1966, if we use the values corrected for the day-to-night variation, the density had maxima in April and October-November and a minimum in July. In January 1966 the orbital eccentricity was very small and the minimum is not clear because the orbital elements are inaccurate. The ratio of the density at the October maximum to that at the July minimum was 2.7 in 1964, 1.9 in 1965 and 1.6 in 1966. With the finer time resolution

1954

G. E. COOK and DIANA W. SCOTT

obtainable using Smithsonian data, the ratio appears to have been 3-O in 1964. The semiannual variation is, therefore, persisting to higher levels of solar activity, although with diminishing amplitude. 5.2. Interpretation From observational values, of density at heights between 350 and 750 km, it appeared that the semi-annual variation could be incorporated in Jacchia’s static diffusion model assuming it was due to temperature variations in the thermosphere. Jacchia foundt3) that the effect at these heights was well represented by a semi-annual variation in the exospheric temperature whose magnitude is given approximately by AT= 0.94s. For conditions of low solar activity-the model suggests that the magnitude of the semi-annual variation should reach a maximum of about 2 at heights near 500-600 km, and then decrease, so that the variation is almost non-existent at 1000 km. On thebasis of the model, the ratio of the October maximum to the July minimum would have been expected to increase from about 1.25 in 1964, to 1.30 in 1965 and then to 1.44 in 1966. As noted in section 5.1, however, the observed ratios are very different from these predictions. It is evident that the semi-annual variation is much too large to be due only to temperature variations in the thermosphere. In fact, a change of the order of 300°K or more would be required in the exospheric’temperature to produce a change in density by a factor of 3. It was suggested in Ref. (2) that the large semi-annual variation in exospheric density could be attributed to variations in the boundary conditions at the level (near 105 km) where diffusive equilibrium commences, and, in particular, to variations in the helium concentration produced by changes in the height ‘of the turbopause. Further evidence of variations in the conditions at a height of 120 km, which is used as the base of upper atmosphere models, has come from neutral particle measurements made by mass spectrometers carried in Explorer 17(12)and in thermosphere probes.(13) The semi-annual variation of the daytime peak electron density, (14)which is in phase with that of the neutral atmosphere density, might also be explained by composition changes resulting from variations in the turbopause region.(ls) Kockarts and Nicolet(l@ have noted that helium, which is the major constituent in the lower exosphere, is far more sensitive to the height of the turbopause than any other constituent ; a decrease of 5 km in the diffusion equilibrium level corresponds to an increase by a factor of about 2 in the helium concentration in the heterosphere. If this explanation is correct, the turbopause is low in April and October and high in January and July. The reduction in the magnitude of the semi-annual variation between 1964 and 1966 may be due to an increase in the ratio of atomic oxygen to helium as solar activity increases. 6. VARIATIONS IN THE REGION OF THE TURBOPAUSE

Having postulated that the enhanced semi-annual variation in exospheric density is due to changes in the height of the turbopause, it is worth considering this region in slightly more detail, bearing in mind that dynamical phenomena are likely to have their sources of energy at lower levels. The main features of the 80-120-km region have been determined from the observation of chemiluminescent trails, while the more limited 80-100&m region has also been investigated by radio observations of meteor trails. The most prominent feature is the wave-like structure of the wind profile, the wavelength increasing with height. Hines has explained this structure in terms of the vertical propagation of internal atmospheric gravity waves.(r’) Most chemiluminescent trails exhibit a rapid transition from a turbulent part to a smoothly diffusing part. The height of the transition (the turbopause) varies,

VARIATIONS IN EXOSPHERIC DENSITY AT HEIGHTS NEAR 1100 km

1955

a height of 106 f 4 km having been given by Justus. (l*) Similar values are obtained from measurements of the diffusive separation of argon and nitrogen by rocket-borne neutral particle mass spectrometers. (ls) At present chemical release data are too sparsely distributed to enable long-term variations in the height of the turbopause to be investigated directly. There is also some doubt about the interpretation of the spreading of sodium trails.(20) The exact base of the diffusion-controlled region is difficult to specify, since there is a gradual transition from perfect turbulent mixing to molecular diffusion.(zo) Even if the turbulence ceases abruptly, the dissipation of gravity wave energy by viscous damping may contribute to diffusion above the turbopause.(21) Extensive meteor studies of turbulence in the 80-100&m region have been made by Elford and Roper czl) at Adelaide. By analysing wind shear data obtained from December 1960 to December 1961, they showed the existence of a strong “seasonal” variation in the rate of dissipation of turbulent energy, a minimum value of 1.5 x 10” W/kg occurring in winter and summer (May, November-December), and a maximum of 3.5’ x 1O-2 W/kg in autumn and spring (March and September). This variation is in phase with the seasonal variation in the diurnal tide. Even though few radio meteor echoes actually occur at the level of the turbopause, the existence of an appreciable seasonal or, more likely, semi-annual variation in the intensity of the turbulence below 100 km would be expected to have some effect on the mixing at greater heights and to be related to the height of the turbopause. If conditions in 1966 can be compared with those in 1961, when the level of solar activity was slightly higher, it appears that an increase in the observed rate of turbulent dissipation does not mean that the turbulence penetrates to greater heights. The exospheric density variations indicate that the turbopause is low in April and October, about one month after the maximum values of the turbulent dissipation. If we allow a relaxation time of 2-4 weeks for helium, however, the times almost correspond. The rate of dissipation of turbulent energy is known to increase almost exponentially with height,t21) until a sudden decrease takes place at the turbopause. It would appear, therefore, that the energy dissipation results can only be consistent with the exospheric variations if a lowering of the whole region takes place, i.e. both the meteor region and the turbopause exhibit a semi-annual variation in height The need far experimental studies of the turbopause region was emphasized(22) at the COSPAR Seventh International Space Science Symposium, Vienna, 1966. The information on the semi-annual variation in exospheric density and its interpretation presented in Refs. (1) and (2) and in the present paper provides further evidence to support this requirement. It should be noted, however, that study of the helium belt in the lower exosphere provides a valuable indirect method for probing the region of the turbopause. Acknowledgement-Crow Stationery Office.

copyright reserved. Reproduced by permission of the Controller, H.M. REFERENCES

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

G. E. COOKand D. W. Scorr. Planet. Space Sci. 14,1149 (1966). G. E. COOK, Planet. Space Sci. 15,627 (1967). L. G. JACCHIA,Smithsonian Astrophys. Obs. Spec. Rep. 170 (1964). CZRA 1965 COSPAR International Reference Atmosphere 1965. North-Holland, Amsterdam (1965). G. E. COOK,D. G. ICING-HE=and D. M. C. WALKER,Proc. R. Sot. A2&4,88(1961). G. E. COOK,Planet. Space Sci. 13,929 (1965). Smithsonian Astrophys. Obs. Spec. Reps. 208, 209, 225 (1966). L. G. JACCHIA,J. SLOWEYand F. VERNIANI, J. geophys. Res. 72,1423 (1967). M. ROEMER,Phil. Trans. R. Sot. A262, 185 (1967). L. 0. JACCHIA and J. SLOWEY,Smithsonian Astrophys. Obs. Spec. Rep. 84 (1962).

1956

G. E. COOK and DIANA W. SCOTT

11. G. E. COOK and D. G. KINGHELE, Phil. Trans. R. Sot. A259,33 (1965). 12. C. A. RBBER and M. NICOLET, Planet. Space Sci. 13,617 (1965). 13. N. W. SPENCER,D. R. TAEUSCHand G. R. CARI~AN, AnnIs G6ophys. 22,151 (1966). 14. T. YONEZAWA and Y. ARIMA, J. Radio Res. Labs Japan 6,293 (1959). 15. H. RBHBETH,Space Res. VII, 284 North-Holland, Amsterdam (!967). 16. G. KOCKARTS and M. NICOLET, Ads Gdophys. 18,269 (1962). 17. C. 0. Hws, Can. J. Phys. 38,144l (1960). 18. C. G. JVSTUS, J. geophys. Res. 71,3767 (1966). 19. K. MAIJERSBEROER, D. MILLER, D. OFFERMANNand U. VON ZAHN, Space Res. VII, 1150, NorthHolland, Amsterdam (1967). , 20. F. S. JOHNSON,Space Res. VII, 262, North-Holland, Amsterdam (1967). 21. W. G. ELFORD and R G. ROPER, Space Res. VII, 42, North-Holland, Amsterdam (1967). 22. COSPAR

Information

Bulletin No. 36 (1967).

Pesrom+B pazxbmeltlr cTaTbe anaqexuifl aKcoc@epHot ~~OTHOCTE~B~IJIH nonyreEbI OT OpbnTH 3x0-2 AJIfI 1964?1965r. PeByJIbTaTbI yKaaam Ha nonyro~oBym BapmJJmo ~~OTHOCTHH~KO~~~K~K~~M~~~~~K~,~TO~H~~EIT~JI~EO~~~~~K~~~MKO~~~EI~M~HT, npencKasaHHni-4 CymecTBymaKMK aTMocc)epHmm MonenHMK. 3TK uccJre~oBaHm Tenepb npo~on~amfcb no Havana 19@7r., C npHMeEemieM pi 3x0-2 M KaJIbc@ep-1, 9T06bl IIOKaaaTb, KPK IIJIOTROCTb OTBeUaeT BospacT6Iolqeti COJlHe~HOt aKTHBHOCTU. BapKawa HJIOTHOCTH B TerleHne 1964 r.a~a~~mxipo~a~~ncb 6onee no~po6~0. flOJIrOCpOsHaR BapII~IUI, CBH3aHHaR C COJIHe¶HbIM VHKJIOM, II KOpOTKOCpOVHble BapEa~HIi,CBHaaHHble CMarHElTHblMHHCOJlHe¶HblMEBapHa~HHMM,B comacmi C BapKaqKsMK, omqaemdMr4 Ha OcHoBe TeKywux moneneti. nonyrogoBaH BapKalJHH BCe ewe IIpO~OnIKaeT CylQeCTBOBaTb I4 A0 BbICJ.UEX ypOBHelt COJIIieYHOfi IKTHBHOCTH, II,XOTR ee aMl%'lIiTy~ayMeHbIJIaeTCH, KOa~@¶IJEleHT BapiiaqPiPi6bm eIqe 1,6 B 1966 r.