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Air density at heights between 130 and 160 km, from analysis of the orbit of 1968-59b
F'het.SpocScl.196Q.Vol.17.p~.985 to997.Pammor~ Prcu. PcintedhNoctbankeh~I
AIR DENSITY AT HEIGHTS BETWEEN 130 AND 160 km, FROM ANALYSIS OF THE ORBIT OF 196%59B* D. G. RINGHELE and DOREEN M. C. WALRRR Royal Aircraft Establishment, Famborough, Hams., England (Receiued 21 November1968)
Abstrae-The satellite 1%8-59Bwas a heavy sphere, of mass 272 kg and dia. 0.61 m, launched by the United States Air Fame on 11 July 1%8 into a polar orbit with an initial perigee height of 150 km. Despim the low perigee, the sate&z remained in orbit for 38 days because of its exceptionally large mass/area ratio, and offers the opportunity of finding values of air density at heights lower than has been possible in previous studies of satelbte orbits. Analysis of the orbit gives 28 values of air density, which show that the density increased from 1.49 x lO-# kg/m* at a height of 155 km to 79 x lO_’ kg/m8 at 130 km height. These vahresare in surprisinglygood agreementwith the COSPAR Intematkmd Reference Atmosphere l%S, being about 9 per cent lower than CZRA. When the values of density are converted to a &xl hetght near lSOkm, the day-to-day variations are found to be remarkably smooth between 12 July and 13 August, the deviations from the mean beii less than 4 per cent; but there was a signiiicant increase in density at the time of the increased solar activity centred at 15 August. 1. INlRODUCTION
Knowledge of upper-atmosphere density is scantiest at heights between 120 and 170 km. Numerous measurements have been made at heights between 80 and 110 km, by falling spheres ejected from rockets, and by other techniques; but above 120 km many of the techniques become less accurate, and fewer rocket payloads are launched to the greater heights. At heights from 170 km up to 1200 km, analysis of satellite orbits has provided a fairly complete picture of the main variations in atmospheric properties. But satellites with perigee heights much below 170 km usually remain in orbit for only a week or two and do not yield much useful data. Consequently there has for many years been a need for a small, dense, spherical satellite, of known sire and mass, which would remain in orbit for a month or more even when perigee height was as low as 150 km. This need was at last fulfilled in July 1968 with the launching of the ‘Cannonball’ satellite, designed by the U.S. Air Force Cambridge Research Laboratories.(l) Cannonball was a sphere of dia. 24 in. (0.610 m) with a brass shell 14 in. (38 mm) thick and a mass of 600 lb (272 kg). It carried a sensitive triaxial accelerometer for measuring drag forces. The satellite was launched as one of the OV series, in which a pod is ejected from a suborbital flight by an Atlas missile and is accelerated to orbital speed by a small rocket motor. Cannonball was launched on 11 July 1968 into a polar orbit (inclination 89.8”) with an initial perigee height of 150 km and eccentricity 0.032. Cannonball (OVl-16) was given the international designation 1968-59B, and remained in orbit for 38 days. A cylindrical satellite, called Spades (OVl-15), launched at the same time into an orbit with a similar perigee height but higher apogee, was designated 1968-59A. Cannonball’s spherical shape and known mass make it ideal for obtaining absolute values of air density by measuring its rate of orbital decay. In this paper we use the available orbital data, from U.S.A.F. Spacetrack bulletins, to derive values of air density throughout the satellite’s life. l
14
Crown copyright reserved. Reproduced by permission of the Controller, H.M. Stationery O&e. 985
D. G. KING-HJXE
986
and DOREEN M. C. WALKER
In determining upper-atmosphere density from analysis of a satellite orbit we have to find (a) the air density, and (b) the height at which it is being measured, which requires the determination of perigee height. Of these two tasks the accurate evaluation of perigee height is here the more difficult, and is discussed in detail in Section 2. Readers who are mainly interested in the results rather than the detailed application of orbital theory may prefer to proceed to Sections 3 and 4, where the values of air density are presented. 2.1 Orbits available
2. PERIGEE HEIGHT
The orbital elements of 1968-59B available to us consist of 32 sets of ‘five-card elements’ at the head of U.S.A.F. ‘Spacetrack bulletins’, and 5 orbits at weekly intervals determined by the U.S. Naval Research Laboratories. Of the 32 sets of five-card elements, the Grst and third were discarded, and we worked with the remaining 30 sets, which should allow values of density to be obtained with an average interval of l-3 days. The N.R.L. elements were used as a check. 2.2 Quation for perigee height The perigee distance rP of a satellite in a high-drag orbit suffers two important perturbations. First, there is a sinusoidal oscillation due to gravitational perturbations caused by the odd zonal harmonics in the geopotential :(*) for a polar satellite close to the Earth, the variation in rr, is -9.2 sin w km, where cuis the argument of perigee (equal to the perigee latitude when the orbit is polar). The second major variation is a steady decrease in perigee height due to the effbcts of air drag, given appro~mately by (H/2) ln e,le, where H is the density scale height* at a height 3fH2 above perigee, e. is the initial eccentricity and e the current eccentricity.@) In addition, because the orbit is not an exact ellipse, the perigee distance r, differs slightly from the value for an exact ellipse, a(1 - e), where a is the semi major axis. For a polar orbit, r, = a(1 - e) + B + 1*72(R/a) cos 20 km (1) from Equation (13) of Ref. 4, where B is a small constant, dependent on the definition of a,? and R is the Earth’s equatorial radius, 637892 km. We shall for the moment ignore this perturbation, which is much smaller than the other two, and assume that r, is given by r,=K+R-9*2sincu-H where K is a constant to be determined by comparison with observational values, and (rti - rJ&s is the theoretical decrease in rs due to air drag: (r@ - rJtiae is proportional to H and has therefore been written in Equation (2) with H as a divisor. The perigee height, yr, is found by subtracting from rr the Earth’s radius at perigee latitude, namely R - 21.4 sins w km, for a polar orbit. Thus we shall for the moment assume that the theoretical variation of perigee height ys is given by Yv =K-9*2sinw+21~4sinao--H
f
r&-r= T
km >drsg
*
* DeEned by H = -p~(~pl~), wherep is the air density at height y. $ For a polar orbit of small eccentricity B 6 2.6 eRfu km, so that 3 < 0.08 km for 1968-59B, if Kozai element# are used, as in the Spacetrack bulletins. The cos ;?wterm is the same with other orbital theories.
AIR DENSITY AT HEIGHTS BETWEEN 130 AND 160 km
987
Equation (3) should provide smoother and more accurate values of yt, than direct use of the orbital elements, which would give random jumps of at least f 1 km. 2.3 Evaluation of K The determination of the best value of Kfor use in Equation (3) is not entirely straightforward, because part of the sinusoidal oscillation in e is removed in the Spacetrack five-card elements. Thus the Spacetrack values of a(1 - e) do not conform to Equation (2), but have the form
Ml - 41swetmk =K+R-Asinw-fin: where the constant A is considerably less than 9.2 km, and the approximate form previously Equation (4) may be quoted for (r& - rP)wg is assumed to be of adequate accuracy. rewritten as K=
[a(l-e)-R]sp~,,,,+Asino+~ln;.
H
e.
Thus we obtain K by calculating values of the right-hand side of Equation (5) and choosing A so that any apparent dependence on o is removed. As a test, this procedure was tried first on the satellite Secor 6,1966-51 B, for whichts) we previously found K = 174.4 km from the R.A.E. orbit.@) When the Spacetrack values of a( 1 - e) for Secor 6 were plotted, they showed a scatter of about f3 km and the dependence on o was best eliminated by taking A = 2.0 km: this gave K = 175.8 km, 1.4 km higher than given by the R.A.E. orbit. The Spacetrack values of a( 1 - e) are much less scattered for 1968-59B than for Secor 6, probably because the eccentricity of 1968-59B is much lower (0.032 initially, compared with 0.210). Figure 1 gives the values of [a(1 - e) - R]spacetrackfor 1968-59B, shown as circles, and also the values of K = [a(1 - e) - &racetrack +2-O sin w + zH In ;eo
(6)
with H taken as 28 km, shown as triangles. The triangles exhibit no obvious dependence on o and the standard deviation of the distribution is O-9 km. Their mean value gives K = 145.2 Inn for 1968-59B. The error to be assigned to K should be considerably smaller than for Secor 6, which with much more scattered data gave a value 1.4 km greater than was obtained from the R.A.E. orbit. Thus it seems reasonable to assign K for 1968-59B a bias error of about f 1 km (s.d.). The four N.R.L. orbits (the fifth is too near decay to be useful) give values of a(1 - e) that differ by up to 3.8 km from the corrected Spacetrack values: the N.R.L. values are on average 1.1 km lower. The scatter and the small numbers of values make this comparison inconclusive; but the N.R.L. values and the scatter of O-9 km among the triangles in Fig. 1 are in conformity with the assigned bias error of fl km in K. The value chosen for H, the density scale height, was taken from Fig. 2, which shows the values of H given by the COSPAR International Reference Atmosphere(‘) (CIRA 1965) for the level of solar activity prevailing in July-August 1968 (model 5,10 hr LT). The error in the CIRA 1965 values of H will be assessed later: we shall for the moment assume the values in Fig. 2 are correct. The value of H chosen for use in Equation (6), namely 28 km, applies at a height of 187 km, which is 3H/2 above perigee for a perigee height of 145 km. In fact the average value of perigee height was 145 km during the first 33 days of the satellite’s 38-day life, so the choice of H = 28 km in (6) is satisfactory.
D. G. KING-HBLE and DGREEN M. C. WALKER
988
w*160*
1
148
120”
Iso*
909
I
60. I
146
138 o&d-R OT K, km ‘36
128
124
122
13J1d
IBJul
WJul
2&lul
2Auq
7Auq
IPAuq
174
4oo50
40055
4co60 _ .
40065 40070 __ ..s. . . ..
40075 .
4ow
40085
4t
mo
Fka.1. V~o~a(l-e)-_~K~~oR1968-59B. 0 indicate values of [a(1 - e) - RJ~pa~~rac~. A indicate valuea of K -I-2-Osin a, -I- 14 In co/e. where K = [a(1 - e) - R]~~~~~trst*
2.4 Cakdation of perigee height ‘I’dzing K = 1452 km in Equation (31, we have
.
Ye = 145.2 - 9.2 sin CO+ 21.4 sins CO-
The decrease in rr due to drag, given by the last term on the righthand side of (7), was calculated as follows. Initially, when e > 3H/a, values of (rare- rJ/H were read from Fig. 5 of Ref. 8, which gives the decrease in rp in terms of e/e,, The appropriate height at which to evaluate His 3Hj2 above perigee, and initially we choose H = I& say = 28 km, corresponding to a perigee height of 145 km (since Fig. 2 gives W = 28 km at a height of 187 km). The broken curve in Fig, 3 shows the values of yip obtained using H = 28 km up to MID 40084: during this time y,, has an average value of 145 km, and 28 km is therefore
AIR DENSITY AT HEIGHTS BETWEEN 130 AND 16Okm
120
130
FIG. 2. VALuaSOF DENSlTY
I50
140
160
SCALE HEIGHT u GIVBN BY c&4
160
170
160
1965 (MODEL $10
hr
145
140 Fuigw MOM, km
I35
125
‘3
I
I
Jul
I3,Jul
40045 40050
18,Jul 40055
I
I
I
m~Tp~mlmmp
1-j
I
2SJul
2$ Jul
2+g
7Pug
I2,Aq
l7@1
22Aug
4oo60
40065
40070
40075
40060
40065
4ooso
Dafe-Modified Julian doy FlG.
3.
1%849B GIVEN BY EQUATIONS Values of y, from Equation (7) ----cuNethroughvaluesofy, Variation of y,’ from Equation (11).
VALUES OF PERIGREHEIGHT FOR 0
(7) AND (11).
D. G. KING-HELIX and DOREEN M. C. WALKER
990
the best average value of Hto use. A more detailed calculation ofYp, made by splitting the time interval into four parts and using different values of H on each, shows that the error in Y, as a result of taking a constant value of H is at most O-6 km (around MJD 40079), and decreases to O-1km at MJD 40084. So the choice of a constant value of H (28 km) up to MJD 40084 requires no amendment. By good luck it happens that e -rr 3H/a at MJD 40084. So the changeover to ‘Phase 2 theory’ (applicable for e < 3H/u) can conveniently be made at this time. Thus after day 40084, we have
where H, is the value of H after day 40084, z = ae/;trz, and 19.15 km is the value of (rN r,Jhg when z = 3. Values of [{r,(3) - rs(z))/Hldrsg were read from Fig. 18 of Ref. 9. Between MJD 40084.37 and 40085.96, Ys decreased from 134 to 127 km, and Ha was taken as 22 km, which from Fig. 2 is the value appropriate to a height 3H/2 above 131 km. Between MJD 40085.96 and 40086.76, the mean value of Yp is 125 km; so H was taken as Ha = 18 km and rp was calculated from (rao -
rp)drag= 22*12 + H, rD(zs)_ ‘Jz)] [ 3
hz
km,
where z = ae/H8, and 22.12 km and za are the values of (rM - rJdrag and z respectively at MJD 40085.96. Finally, between MJD 40086.76 and 40087.06, where the mean value of Yp is 120 km, H was taken as H4 = 15 km and Equation (9) was appropriately modsed. The broken curve in Fig. 3, drawn through the values of Y, obtained, should have errors of less than 1 km until within a few hours of decay (which occurred at MJD 40087*48), provided the values of H and the theory used are both accurate enough. The accuracy of H will be discussed later; but the accuracy of the theory is not good enough, because we need to take account of the term 1*72(R/u) cos 2~ km in Equation (l), which has so far been ignored. (The constant B in Equation (1) is too small to be worth including.) So we define a corrected value of perigee height, Yd, given by Y1, = yp + 1.66 cos 2~0 km
(10)
where the mean value of u/R, namely l@IO, has been used. Substituting for y4 from (7), Equation (10) becomes y;
= 146.9 - 9.2 sin o + 18.1 sina o - H
.
(10
Values of yg’ are shown by the solid line in Fig. 3 and will be taken as the correct values of perigee height (f 1 km). 3. EVALUATION OF AIR DENSITY
3.1 Orbital decay rate The thirty values of the mean anomalistic motion n (rev/day) available in the five-card elements were tabulated and differenced to give values of An. Each of these values was divided by the corresponding time interval At (day) to give 29 values of ri = An/At, which are listed in Table 1 and plotted in Fig. 4, at a date half way through the time
AIR DENSITY AT HEICSHTS BETWEEN 130 AND 16Okm
991
interval over which they apply. The variation of fi is remarkably smooth-much smoother than the corresponding graph for Secor 6 for example. t6) So there is no reason to suspect any errors in the values of II, The increase in perigee height between MJD 4006Oand 40070 (Fig. 3) has the effect of halting the increase in ri, as Fig. 4 shows.
‘Ol1 5
1988
I
I
I
I
I
I
I
I
I
I
I
I
I
I I
Ij
II
II
II
J 1
II
II
40075
40080
40085
I
0’ 8Jul
13 Jul
I8 +I
23 Jul
PqJul
2 +ug
40045
40050
40035
40060
40065
40070
Date-Modified
FIG. 4.
Julian
I
I I 40090
day
ORBITAL DECAY RATE li KtR
1968~59B.
3.2 Method of calculatingair density The air density pA at a height +H* above perigee may be found, for a polar orbit with e > 3H*/a, from the following equation, which is derived from Equation (7.26) of Ref. 10 and Equation (16) of Ref. 11: PA =
+
oGo335 cos 2w ... e
(12)
where H* is the estimated value of ETat perigee and may be in error by up to 25 per cent without incurring an error of more than l-2 per cent in PA. The OGO335term represents the effect of atmospheric oblateness. For 1968-59B it turns out that e > 3H*/a until within 3 hr of decay, so that Equation (12) is applicable throughout the life. The values of PA in (12) are obtained in kgfms if H* and a are in km and the drag parameter 6, discussed below, is in ma/kg.
D. 0. KING-H3ZL.Band DOREEN M. C. WALKER
992
The drag parameter 8 in Equation (12) is given by 6 = FSCDlm, where Sis the satellite’s cross-sectional area, O-292 m* for 1968-59B, and m its mass (272 kg). The factor F takes account of the effect of atmospheric rotation, but for a polar orbit, like that of 1968-59B, F = 1. The drag coefficient C!, may be taker@) as 2.2 for a spherical satellite in freemolecule flow, with s.d. of about 5 per cent. If free-molecule flow is to prevail, the mean free path of the air molecules should be at least 10 times the dimensions of the satellite. The satellite has a dia. of O-6 m and the mean free pathos) exceeds 6 m down to a height of 125 km. So we may take B = @292 x 2*2/272 = @00236 ms/kg for heights down to 125 km, with error (from C,) of &5 per cent (s.d.). TABLE1. ~ALIJFLS OFri,y*‘, yA ANDpA FROM1968.59B Time MJD 049.84 40 051.46 40 052.74 40 054.74 40 056.93 40 058-77 40 061.45 40 064.10 40 066.75 40 068.79 40 07@92 40 073.30 40 075.18 40 076.96 40 078.45 40 079.63 40 080-47 40 081.06 40 081.74 40 08239 40 083.10 40 083.97 40 084.77 40 085.32 40 085.71 40 086.17 40 08657 40 08691 (40 087.21 40
1OOi
YA
=J&;fH*
(=v/day9
8.58 9.97 10-36 11.13 11.92 12.42 1269 13.20 13.17 12-80 13.52 1499 16-37 17.99 1944 20.91 23.87 25.21 27.33 31.80 3915 43-08 50.34 65.17 67-61 83.77 Q6.51 1499 1791
149.4 147.8 146.5 145.0 144.1 144.1 1447 146.0 147.6 148-7 149.3 149.2 148.5 147.2 145.7 144-3 143-o 142.1 140*9 139.7 138-o 135.4 132.8 130.4 128.5 126.1 123.9 121.1 116.6
157.4 155.8 154.5 153-o 152-l 152.1 152.7 154-o 155.6 156.7 157.3 157-2 1565 155.2 153.7 152.3 151.0 150.1 148.9 146.7 145.0 141.9 138.8 135-Q 134-o 131.1 128.4 124-6 119.6
l-280 l-482 l-534 l-625 1.697 l-716 l-654 1*600 1.476 1.347 l-321 1.375 1443 l-535 l-623 1.717 l-952 2051 2206 2785 3.291 3.655 4.316 5-703 5.708 7.084 7-916 11.99 14.00)
Equation (12) has been used, with the 29 values of ti available, to obtain 29 values of pd, at heights yA = y/ + +H*. Between MID 40049 and 40082, H* was taken constant at 16 km, the value appropriate to a height of 145 km, and from day 40082 onwards the value of H* at perigee height was used. The values of pA are given in Table 1 and plotted against yA in Fig. 5 : the last of the 29 values of pA in Table 1 is omitted from Fig. 5 because it is below 125 km and because there is no check on the accuracy of the perigee height at this late stage (6 hr before decay). ARJEULTS 4.1 Variation CJJ&PZS~~~ with height In Fig. 5 the 28 values of air density obtained from analysis of the orbit of 196859B, shown as circles, are plotted against height. The broken curve shows the variation of
AIR DENSITY AT HEIGHTS BETWEEN 130 AND 16Okm
993
la2 la
I.5
20
2-5
33)
4.0
5.0
6.0
70
&o 9.OlOO
IO*pA kg/m3
FKL 5.
VARUlSON OF AIR DENSlTk?~1 WITH BEIGHT)‘~ DURING JULY-Auciusr FROMORBITOF l%fMPB.
1968, AS FOIJND
density with height given by the COSPAR International Reference Atmoqhere 1965, for the appropriate level of solar activity (model 5) and for 10 hr LT (though the time of day chosen is unimportant because CIRA I%5 gives a day-to-night variation of less than 5 per cant at these heights). The dotdash we shows the values of density given by Jacchia’s model atmosphere fnu for an exospheric temperature of 1100°K. There have been no previous values of air density determined from satellite orbits at heights below 160 km; so our values agree remarkably well with the CIRA and Jacchia models. The densities obtained from 1968-59Bare about 9 per cent lower than those of CIRA. The consistency of the group of 16 points from 196%59Bat heights between 152 and 158 km is remarkable, and indicates that the relative errors in perigee height are less than 4 km. 4.2 Yaridons with time To examine whether the density varies signiticantiy with time, the 19 values of pA at heights between 148 and 158 km were converted to the mean height of 153 km using CIR4 1965, the density pm, at a height of 153 km being found from the equation p(CIRA ; 153)
plas = pd p(CIXA; FA) ’ where p(CrRa; u) denotes the value of p given by CIRA 2965 (model 5) at height y. %mihuly, the values of PAat heights between 139 and 151 km were converted to the mean height of 145 km. The values of pla3and plfi are plotted against time in Fig. 6, together with the values of S1o,r the solar radiation energy on a wavelength of 1@7cm measured by N.R.C., Ottawa, and A,, the daily geomagnetic planetary amplitude, as given by the Institut fiir Geophysik, C%W.ingen.The values are plotted at the beginning of the day after the date for which they are given, i.e. with a time lag of 6 hr for S,,, and 12 hr for A,.
994
D. G. KINGHELE
S&r
and DOREEN
radiition
4007@
40060
40050
me-~odifi~ FIG.
M. C. WALKER
6. AIRDENSITY
AT BEIGEIT OF
SOLAR RADIATION
153 km
ENERGY &,.,,
40080
Aug 40090
Julion day
AND
145 km, plsl AND ~145,WITH DAILY
AND DAILY
GEOMAGNEl’IC
VALUES OF
INDEX A,.
From Fig. 6 it appears that the variations in p153between MJD 40049 and 40080 are scarcely large enough to be sign&ant : pGa never departs from l-67 x Ws kg/m5 by more than 4 per cent, and its variation is smoother than any comparable results at greater heights. However, there is quite a large increase in plG at the time of the high solar activity centred at MJD 40083, and since solar activity is known to control air density at heights above 200 km, it is probable that the increase in pl& is a response to solar activity. The magnitude of the increase is difficult to specify exactly, because the peak in density is only maintained
AIR DENSITY
995
AT HEIGHTS BETWJ%N 130 AND 160 km
for half a day, but it appears probable that an increase in S,,., from 140 to 180 x 10-22 W m-2 Hz-l increases p146by about 10 per cent. If so, plsa would be expected to increase by about 5 per cent as S,,., increased from 130 to 150 x 10-22 W m-2 Hz-l between MJD 40059 and 40065 : this is consistent with the values of piss in Fig. 6, but the actual increase (of 4 per cent) is too small to be confidently distinguished from mere scatter. The geocentric Sun-perigee angle p is shown at the top of Fig. 6, the local time in hours and latitude at perigee being marked on the curve: any day-to-night or latitudinal variation in air density is evidently too small to have a recognizable influence on the values of pm. Also there are no variations in density recognizably correlated with the geomagnetic index A,,: this is not surprising, since no important geomagnetic storms occurred between MJD 40050 and 40084. 4.3 Profile of density in July-August 1968 The values of plas which form the peak in Fig. 6 are the three values above the broken curve in Fig. 5 at heights between 141 and 147 km. If we reduce them by 10 per cent, 16 per cent and 7 per cent respectively, to allow for the apparent effect of solar activity, they are all brought slightly below the broken curve in Fig. 5. If this correction is made, the unbroken curve in Fig. 5 represents the profile of density vs. height from our analysis of 1968-59B. The values are listed in Table 2 below, at 5-km intervals. TABLE2. PROFILE OFAIRDENSITY IN JIJLY-AUGUST 1968 FROMANALYSIS OFTHEORBITOF 1968-59B (S,,., ti 150 x 10-** W m-*Hz-l) Height (km) Air density (lo-’ kg/m’)
(125) (12.4)
130 7.9
135 5.3
140 3.8
145 2.7
150 1.98
155 1.49
160 1.15
4.4 Comparisons with previous results The lowest height at which absolute values of density have previously been obtained from satellite orbits(14*16)was near 170 km. These values were during 1963-4, when the Sun was inactive, and it was found (is) that there was quite a large day-to-night variation down to 170 km, with the maximum daytime density exceeding the minimum night-time density by nearly 40 per cent. However, the mean values of density agreed quite well with CIRA 1965 and Jacchia’s model. Perhaps the most satisfactory measurements of air density at heights between 120 and 160 km by rocket techniques are the values deduced from the growth of chemiluminescent clouds.(16*“) Sheppard us) has obtained values at Woomera for April-May 1965, when solar activity was much lower than in 1968: his values, which are subject to errors off 30 per cent, agree with C1RA 1965 and with our values to within 35 per cent at heights between 125 km and 150 km, with the difference increasing slowly above that height. Golomb and others (17)obtained values of density for June 1966 and January 1967, when solar activity was closer to the 1968 level: their values are within 20 per cent of our results and CIRA 1965 up to 145 km, but diverge widely above 150 km. Variations in the density at heights near 150 km during 19667 were studiedus) in an analysis of the orbit of 1966-1016. The substantial variation discovered-a variation by a factor of Isir--was probably a combination of day-to-night and semi-annual variations, which happened to coincide in time. Since plM in Fig. 6 shows no significant variation as p changes from 20” to 90”, the day-to-night variation at this height in July-August 1968 probably did not exceed a factor of 1.2.
D. G. KINCMFiLE and DOREEN M, C. WALKER
9%
5. ACCURACY OF THE RESUL’IS The main error in the absolute values of density is likely to arise from the biis error in perigee height, estimated in Section 2.3 as &-1 km (s.d.), and the bias error in C,, given in Section 3.2 as =t5 per cent (ad.) for y, > 125 km. Since Fig. 5 cotis the CIRA 1965 values of density which were used in obtaining H, the term H{(r& - r$fH>a, in Equation (3) should not be in error by more than about 3 per cent (ad.): the corresponding error in perigee height increases from xero initially to 0.7 km at MJD 400859 and about 1-O km at the final point used (MJD 40086.9, ye = 124 km). Errors in pa due to errors in etit, S’fmand the theory used in Equation (12), are estimated as 2,1,1 and 1 per cent respectively. The value of li most likely to be in error is the last one, 65 hr before decay, R = 06179 rev/day% : its accuracy can be checked by using it, with the appropriate theory (Equation (65) of Ref. 3, with ,u = O-33), to calculate the remaining lifetime; the result is 6.7 hr-only 0.2 hr in error. So even the last value of pB (omitted from Fig. 5) is apparently based on a correct value of fi. When these component errors are combined, with an error e in perigee height giving a proportional error of [exp (e/H*) - 11 in pl, the resultant error in the absolute values of density p4 is about 8 per cent up to day 40081 typ > 145 km), increasing to 14 per cent for the point at MJD 40086-l QA = 132 km) and 20 per cent for the last point plotted (MJD 40086.9, yA = 124 km). The variations in density, unlike the absolute values, are not affected by bias errors in yII or Co and should be more accurate. The scatter in yI, is probably less than O-5 km, as noted in Section 4.1, and the variations in density up to MJD 40085, shown in Fig. 6, should not be in error by more than 3 per cent (s.d.)-a conclusion which is amply confirmed by the smoothness of the values of pnn.
6. CONCTXJSIONS
In this paper we have analysed the orbit of 1968-59B between 12 July and 19 August 1968, and have obtained 28 values of air density at heights from 160 km down to 124 km, to give the first profile of density versus height in this region from satellite orbits (Fig. 5). The absolute values of density, most of which are subject to errors estimated as A8 per cent (s.d.), due mainly to possible bias errors in Co and yr, are given in Table 2: the density increases from 1.49 x KY@kg/ma at a height of 155 km to 7*9 x 10-O kg/ma at 130 km. These values agree remarkably well with those given by the COSPAR InternationalReference Atmosphere 1965, being about 9 per cent lower than in the appropriate CIRA model. The relative accuracy of the values of density is estimated as better than f3 per cent (s.d.), and the variation of density with time for a tied height is shown in Fig. 6. The large increase in solar activity between 12 and 15 August 1968, when solar radiation energy at 10.7 cm wavelength increased from 140 to 180 x lO-= W m-* Hz?, is accompanied by an increase of about 10 per cent in the density at a height of 145 km. Apart from this increase, the fluctuations in density are limited to variations of f4 per cent about the mean, and are much smoother than at heights above 180 km, even though the close spacing in time would tend to accentuate irregularities (the average interval between the values is only about 32 hr). Any latitudinal or day-to-night variations in density were too small to be detected. REFJzREN5 1. K. S. W.
CHAMPION, Upperatmosphere density.In AFCRL in ~pmt?.
Rep. (1967).
Air Force Cumbrk&eRes. Lab.
2. D. G. TCwA-kq G. E. COOKand D. W. Scan, Planer.Space SC&17,629 (1969).
AIR DENSITY AT HEIGHTS BERN 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
130 AND 16Okm
997
G. I?,. Coax and D. G. KIN&&L,E, Proc. R. Sot. A27S, 357 (1963). Y. KOZAI,Ash: J. 64,367 (1959). D. G. Kma-Hm~ and J. &?cmmN, Plwtet. Space Sci. 16,675 (1968). R. H. GILDING and R. MILNER,R.A.E. Tech. Rep. No. 67283 (1967). CIRA 1965 (COSPAR Internutionul Reference Atmosphere 1%5), North-Holland, Amstexdam (1965). D. G. Km&Hms, G. E. CXKX and D. M. C. WALUR, R.A.E. Tech. Nute No. GW 533 (1959). D. 0. KINI+Has, G. E. Cho~ and D. M. C. WALKER,R.A.E. Tech. Note No. GW 565 (1960). D. G. K~QXELE, Theoryof Sutellite Orbits in un Atmosphere. Buttenvorths, London (1964). D. 0. Km&&z, AnnfsG&phys. 22,40 (1966). G. E. coon, Pkmet. @ace Sci. 13,929 (1965). L. G. JACCHU,Satin. contt. Aetrophye. 8,215 (1%5). R. L. JACOBS,AZAA Paper No. 65-507 (1965). D. G. K~Q-HEIZ and E. QUINX,Planet. Space Sci. 14,1023 (1966). L. M. SHEPPARD, Rust. W.R.E. Tech. Note No. HSA 131 (1968). D. GOLQMB,F. P. DBLGRBCO,0. HAMNO, R. H. JOHNSON and M. A. MACLEOD, Space Resetweh VUl:p. 705. North-Holland, Amsterdam (1968). 18. D. G. Kmc+Hm+nd J. I-bwsm~, Planet. S’ceSci. l&l883 (1967).
AIR DENSITY AT HEIGHTS BETWEEN 130 AND 160 km, FROM ANALYSIS OF THE ORBIT OF 196%59B* D. G. RINGHELE and DOREEN M. C. WALRRR Royal Aircraft Establishment, Famborough, Hams., England (Receiued 21 November1968)
Abstrae-The satellite 1%8-59Bwas a heavy sphere, of mass 272 kg and dia. 0.61 m, launched by the United States Air Fame on 11 July 1%8 into a polar orbit with an initial perigee height of 150 km. Despim the low perigee, the sate&z remained in orbit for 38 days because of its exceptionally large mass/area ratio, and offers the opportunity of finding values of air density at heights lower than has been possible in previous studies of satelbte orbits. Analysis of the orbit gives 28 values of air density, which show that the density increased from 1.49 x lO-# kg/m* at a height of 155 km to 79 x lO_’ kg/m8 at 130 km height. These vahresare in surprisinglygood agreementwith the COSPAR Intematkmd Reference Atmosphere l%S, being about 9 per cent lower than CZRA. When the values of density are converted to a &xl hetght near lSOkm, the day-to-day variations are found to be remarkably smooth between 12 July and 13 August, the deviations from the mean beii less than 4 per cent; but there was a signiiicant increase in density at the time of the increased solar activity centred at 15 August. 1. INlRODUCTION
Knowledge of upper-atmosphere density is scantiest at heights between 120 and 170 km. Numerous measurements have been made at heights between 80 and 110 km, by falling spheres ejected from rockets, and by other techniques; but above 120 km many of the techniques become less accurate, and fewer rocket payloads are launched to the greater heights. At heights from 170 km up to 1200 km, analysis of satellite orbits has provided a fairly complete picture of the main variations in atmospheric properties. But satellites with perigee heights much below 170 km usually remain in orbit for only a week or two and do not yield much useful data. Consequently there has for many years been a need for a small, dense, spherical satellite, of known sire and mass, which would remain in orbit for a month or more even when perigee height was as low as 150 km. This need was at last fulfilled in July 1968 with the launching of the ‘Cannonball’ satellite, designed by the U.S. Air Force Cambridge Research Laboratories.(l) Cannonball was a sphere of dia. 24 in. (0.610 m) with a brass shell 14 in. (38 mm) thick and a mass of 600 lb (272 kg). It carried a sensitive triaxial accelerometer for measuring drag forces. The satellite was launched as one of the OV series, in which a pod is ejected from a suborbital flight by an Atlas missile and is accelerated to orbital speed by a small rocket motor. Cannonball was launched on 11 July 1968 into a polar orbit (inclination 89.8”) with an initial perigee height of 150 km and eccentricity 0.032. Cannonball (OVl-16) was given the international designation 1968-59B, and remained in orbit for 38 days. A cylindrical satellite, called Spades (OVl-15), launched at the same time into an orbit with a similar perigee height but higher apogee, was designated 1968-59A. Cannonball’s spherical shape and known mass make it ideal for obtaining absolute values of air density by measuring its rate of orbital decay. In this paper we use the available orbital data, from U.S.A.F. Spacetrack bulletins, to derive values of air density throughout the satellite’s life. l
14
Crown copyright reserved. Reproduced by permission of the Controller, H.M. Stationery O&e. 985
D. G. KING-HJXE
986
and DOREEN M. C. WALKER
In determining upper-atmosphere density from analysis of a satellite orbit we have to find (a) the air density, and (b) the height at which it is being measured, which requires the determination of perigee height. Of these two tasks the accurate evaluation of perigee height is here the more difficult, and is discussed in detail in Section 2. Readers who are mainly interested in the results rather than the detailed application of orbital theory may prefer to proceed to Sections 3 and 4, where the values of air density are presented. 2.1 Orbits available
2. PERIGEE HEIGHT
The orbital elements of 1968-59B available to us consist of 32 sets of ‘five-card elements’ at the head of U.S.A.F. ‘Spacetrack bulletins’, and 5 orbits at weekly intervals determined by the U.S. Naval Research Laboratories. Of the 32 sets of five-card elements, the Grst and third were discarded, and we worked with the remaining 30 sets, which should allow values of density to be obtained with an average interval of l-3 days. The N.R.L. elements were used as a check. 2.2 Quation for perigee height The perigee distance rP of a satellite in a high-drag orbit suffers two important perturbations. First, there is a sinusoidal oscillation due to gravitational perturbations caused by the odd zonal harmonics in the geopotential :(*) for a polar satellite close to the Earth, the variation in rr, is -9.2 sin w km, where cuis the argument of perigee (equal to the perigee latitude when the orbit is polar). The second major variation is a steady decrease in perigee height due to the effbcts of air drag, given appro~mately by (H/2) ln e,le, where H is the density scale height* at a height 3fH2 above perigee, e. is the initial eccentricity and e the current eccentricity.@) In addition, because the orbit is not an exact ellipse, the perigee distance r, differs slightly from the value for an exact ellipse, a(1 - e), where a is the semi major axis. For a polar orbit, r, = a(1 - e) + B + 1*72(R/a) cos 20 km (1) from Equation (13) of Ref. 4, where B is a small constant, dependent on the definition of a,? and R is the Earth’s equatorial radius, 637892 km. We shall for the moment ignore this perturbation, which is much smaller than the other two, and assume that r, is given by r,=K+R-9*2sincu-H where K is a constant to be determined by comparison with observational values, and (rti - rJ&s is the theoretical decrease in rs due to air drag: (r@ - rJtiae is proportional to H and has therefore been written in Equation (2) with H as a divisor. The perigee height, yr, is found by subtracting from rr the Earth’s radius at perigee latitude, namely R - 21.4 sins w km, for a polar orbit. Thus we shall for the moment assume that the theoretical variation of perigee height ys is given by Yv =K-9*2sinw+21~4sinao--H
f
r&-r= T
km >drsg
*
* DeEned by H = -p~(~pl~), wherep is the air density at height y. $ For a polar orbit of small eccentricity B 6 2.6 eRfu km, so that 3 < 0.08 km for 1968-59B, if Kozai element# are used, as in the Spacetrack bulletins. The cos ;?wterm is the same with other orbital theories.
AIR DENSITY AT HEIGHTS BETWEEN 130 AND 160 km
987
Equation (3) should provide smoother and more accurate values of yt, than direct use of the orbital elements, which would give random jumps of at least f 1 km. 2.3 Evaluation of K The determination of the best value of Kfor use in Equation (3) is not entirely straightforward, because part of the sinusoidal oscillation in e is removed in the Spacetrack five-card elements. Thus the Spacetrack values of a(1 - e) do not conform to Equation (2), but have the form
Ml - 41swetmk =K+R-Asinw-fin: where the constant A is considerably less than 9.2 km, and the approximate form previously Equation (4) may be quoted for (r& - rP)wg is assumed to be of adequate accuracy. rewritten as K=
[a(l-e)-R]sp~,,,,+Asino+~ln;.
H
e.
Thus we obtain K by calculating values of the right-hand side of Equation (5) and choosing A so that any apparent dependence on o is removed. As a test, this procedure was tried first on the satellite Secor 6,1966-51 B, for whichts) we previously found K = 174.4 km from the R.A.E. orbit.@) When the Spacetrack values of a( 1 - e) for Secor 6 were plotted, they showed a scatter of about f3 km and the dependence on o was best eliminated by taking A = 2.0 km: this gave K = 175.8 km, 1.4 km higher than given by the R.A.E. orbit. The Spacetrack values of a( 1 - e) are much less scattered for 1968-59B than for Secor 6, probably because the eccentricity of 1968-59B is much lower (0.032 initially, compared with 0.210). Figure 1 gives the values of [a(1 - e) - R]spacetrackfor 1968-59B, shown as circles, and also the values of K = [a(1 - e) - &racetrack +2-O sin w + zH In ;eo
(6)
with H taken as 28 km, shown as triangles. The triangles exhibit no obvious dependence on o and the standard deviation of the distribution is O-9 km. Their mean value gives K = 145.2 Inn for 1968-59B. The error to be assigned to K should be considerably smaller than for Secor 6, which with much more scattered data gave a value 1.4 km greater than was obtained from the R.A.E. orbit. Thus it seems reasonable to assign K for 1968-59B a bias error of about f 1 km (s.d.). The four N.R.L. orbits (the fifth is too near decay to be useful) give values of a(1 - e) that differ by up to 3.8 km from the corrected Spacetrack values: the N.R.L. values are on average 1.1 km lower. The scatter and the small numbers of values make this comparison inconclusive; but the N.R.L. values and the scatter of O-9 km among the triangles in Fig. 1 are in conformity with the assigned bias error of fl km in K. The value chosen for H, the density scale height, was taken from Fig. 2, which shows the values of H given by the COSPAR International Reference Atmosphere(‘) (CIRA 1965) for the level of solar activity prevailing in July-August 1968 (model 5,10 hr LT). The error in the CIRA 1965 values of H will be assessed later: we shall for the moment assume the values in Fig. 2 are correct. The value of H chosen for use in Equation (6), namely 28 km, applies at a height of 187 km, which is 3H/2 above perigee for a perigee height of 145 km. In fact the average value of perigee height was 145 km during the first 33 days of the satellite’s 38-day life, so the choice of H = 28 km in (6) is satisfactory.
D. G. KING-HBLE and DGREEN M. C. WALKER
988
w*160*
1
148
120”
Iso*
909
I
60. I
146
138 o&d-R OT K, km ‘36
128
124
122
13J1d
IBJul
WJul
2&lul
2Auq
7Auq
IPAuq
174
4oo50
40055
4co60 _ .
40065 40070 __ ..s. . . ..
40075 .
4ow
40085
4t
mo
Fka.1. V~o~a(l-e)-_~K~~oR1968-59B. 0 indicate values of [a(1 - e) - RJ~pa~~rac~. A indicate valuea of K -I-2-Osin a, -I- 14 In co/e. where K = [a(1 - e) - R]~~~~~trst*
2.4 Cakdation of perigee height ‘I’dzing K = 1452 km in Equation (31, we have
.
Ye = 145.2 - 9.2 sin CO+ 21.4 sins CO-
The decrease in rr due to drag, given by the last term on the righthand side of (7), was calculated as follows. Initially, when e > 3H/a, values of (rare- rJ/H were read from Fig. 5 of Ref. 8, which gives the decrease in rp in terms of e/e,, The appropriate height at which to evaluate His 3Hj2 above perigee, and initially we choose H = I& say = 28 km, corresponding to a perigee height of 145 km (since Fig. 2 gives W = 28 km at a height of 187 km). The broken curve in Fig, 3 shows the values of yip obtained using H = 28 km up to MID 40084: during this time y,, has an average value of 145 km, and 28 km is therefore
AIR DENSITY AT HEIGHTS BETWEEN 130 AND 16Okm
120
130
FIG. 2. VALuaSOF DENSlTY
I50
140
160
SCALE HEIGHT u GIVBN BY c&4
160
170
160
1965 (MODEL $10
hr
145
140 Fuigw MOM, km
I35
125
‘3
I
I
Jul
I3,Jul
40045 40050
18,Jul 40055
I
I
I
m~Tp~mlmmp
1-j
I
2SJul
2$ Jul
2+g
7Pug
I2,Aq
l7@1
22Aug
4oo60
40065
40070
40075
40060
40065
4ooso
Dafe-Modified Julian doy FlG.
3.
1%849B GIVEN BY EQUATIONS Values of y, from Equation (7) ----cuNethroughvaluesofy, Variation of y,’ from Equation (11).
VALUES OF PERIGREHEIGHT FOR 0
(7) AND (11).
D. G. KING-HELIX and DOREEN M. C. WALKER
990
the best average value of Hto use. A more detailed calculation ofYp, made by splitting the time interval into four parts and using different values of H on each, shows that the error in Y, as a result of taking a constant value of H is at most O-6 km (around MJD 40079), and decreases to O-1km at MJD 40084. So the choice of a constant value of H (28 km) up to MJD 40084 requires no amendment. By good luck it happens that e -rr 3H/a at MJD 40084. So the changeover to ‘Phase 2 theory’ (applicable for e < 3H/u) can conveniently be made at this time. Thus after day 40084, we have
where H, is the value of H after day 40084, z = ae/;trz, and 19.15 km is the value of (rN r,Jhg when z = 3. Values of [{r,(3) - rs(z))/Hldrsg were read from Fig. 18 of Ref. 9. Between MJD 40084.37 and 40085.96, Ys decreased from 134 to 127 km, and Ha was taken as 22 km, which from Fig. 2 is the value appropriate to a height 3H/2 above 131 km. Between MJD 40085.96 and 40086.76, the mean value of Yp is 125 km; so H was taken as Ha = 18 km and rp was calculated from (rao -
rp)drag= 22*12 + H, rD(zs)_ ‘Jz)] [ 3
hz
km,
where z = ae/H8, and 22.12 km and za are the values of (rM - rJdrag and z respectively at MJD 40085.96. Finally, between MJD 40086.76 and 40087.06, where the mean value of Yp is 120 km, H was taken as H4 = 15 km and Equation (9) was appropriately modsed. The broken curve in Fig. 3, drawn through the values of Y, obtained, should have errors of less than 1 km until within a few hours of decay (which occurred at MJD 40087*48), provided the values of H and the theory used are both accurate enough. The accuracy of H will be discussed later; but the accuracy of the theory is not good enough, because we need to take account of the term 1*72(R/u) cos 2~ km in Equation (l), which has so far been ignored. (The constant B in Equation (1) is too small to be worth including.) So we define a corrected value of perigee height, Yd, given by Y1, = yp + 1.66 cos 2~0 km
(10)
where the mean value of u/R, namely l@IO, has been used. Substituting for y4 from (7), Equation (10) becomes y;
= 146.9 - 9.2 sin o + 18.1 sina o - H
.
(10
Values of yg’ are shown by the solid line in Fig. 3 and will be taken as the correct values of perigee height (f 1 km). 3. EVALUATION OF AIR DENSITY
3.1 Orbital decay rate The thirty values of the mean anomalistic motion n (rev/day) available in the five-card elements were tabulated and differenced to give values of An. Each of these values was divided by the corresponding time interval At (day) to give 29 values of ri = An/At, which are listed in Table 1 and plotted in Fig. 4, at a date half way through the time
AIR DENSITY AT HEICSHTS BETWEEN 130 AND 16Okm
991
interval over which they apply. The variation of fi is remarkably smooth-much smoother than the corresponding graph for Secor 6 for example. t6) So there is no reason to suspect any errors in the values of II, The increase in perigee height between MJD 4006Oand 40070 (Fig. 3) has the effect of halting the increase in ri, as Fig. 4 shows.
‘Ol1 5
1988
I
I
I
I
I
I
I
I
I
I
I
I
I
I I
Ij
II
II
II
J 1
II
II
40075
40080
40085
I
0’ 8Jul
13 Jul
I8 +I
23 Jul
PqJul
2 +ug
40045
40050
40035
40060
40065
40070
Date-Modified
FIG. 4.
Julian
I
I I 40090
day
ORBITAL DECAY RATE li KtR
1968~59B.
3.2 Method of calculatingair density The air density pA at a height +H* above perigee may be found, for a polar orbit with e > 3H*/a, from the following equation, which is derived from Equation (7.26) of Ref. 10 and Equation (16) of Ref. 11: PA =
+
oGo335 cos 2w ... e
(12)
where H* is the estimated value of ETat perigee and may be in error by up to 25 per cent without incurring an error of more than l-2 per cent in PA. The OGO335term represents the effect of atmospheric oblateness. For 1968-59B it turns out that e > 3H*/a until within 3 hr of decay, so that Equation (12) is applicable throughout the life. The values of PA in (12) are obtained in kgfms if H* and a are in km and the drag parameter 6, discussed below, is in ma/kg.
D. 0. KING-H3ZL.Band DOREEN M. C. WALKER
992
The drag parameter 8 in Equation (12) is given by 6 = FSCDlm, where Sis the satellite’s cross-sectional area, O-292 m* for 1968-59B, and m its mass (272 kg). The factor F takes account of the effect of atmospheric rotation, but for a polar orbit, like that of 1968-59B, F = 1. The drag coefficient C!, may be taker@) as 2.2 for a spherical satellite in freemolecule flow, with s.d. of about 5 per cent. If free-molecule flow is to prevail, the mean free path of the air molecules should be at least 10 times the dimensions of the satellite. The satellite has a dia. of O-6 m and the mean free pathos) exceeds 6 m down to a height of 125 km. So we may take B = @292 x 2*2/272 = @00236 ms/kg for heights down to 125 km, with error (from C,) of &5 per cent (s.d.). TABLE1. ~ALIJFLS OFri,y*‘, yA ANDpA FROM1968.59B Time MJD 049.84 40 051.46 40 052.74 40 054.74 40 056.93 40 058-77 40 061.45 40 064.10 40 066.75 40 068.79 40 07@92 40 073.30 40 075.18 40 076.96 40 078.45 40 079.63 40 080-47 40 081.06 40 081.74 40 08239 40 083.10 40 083.97 40 084.77 40 085.32 40 085.71 40 086.17 40 08657 40 08691 (40 087.21 40
1OOi
YA
=J&;fH*
(=v/day9
8.58 9.97 10-36 11.13 11.92 12.42 1269 13.20 13.17 12-80 13.52 1499 16-37 17.99 1944 20.91 23.87 25.21 27.33 31.80 3915 43-08 50.34 65.17 67-61 83.77 Q6.51 1499 1791
149.4 147.8 146.5 145.0 144.1 144.1 1447 146.0 147.6 148-7 149.3 149.2 148.5 147.2 145.7 144-3 143-o 142.1 140*9 139.7 138-o 135.4 132.8 130.4 128.5 126.1 123.9 121.1 116.6
157.4 155.8 154.5 153-o 152-l 152.1 152.7 154-o 155.6 156.7 157.3 157-2 1565 155.2 153.7 152.3 151.0 150.1 148.9 146.7 145.0 141.9 138.8 135-Q 134-o 131.1 128.4 124-6 119.6
l-280 l-482 l-534 l-625 1.697 l-716 l-654 1*600 1.476 1.347 l-321 1.375 1443 l-535 l-623 1.717 l-952 2051 2206 2785 3.291 3.655 4.316 5-703 5.708 7.084 7-916 11.99 14.00)
Equation (12) has been used, with the 29 values of ti available, to obtain 29 values of pd, at heights yA = y/ + +H*. Between MID 40049 and 40082, H* was taken constant at 16 km, the value appropriate to a height of 145 km, and from day 40082 onwards the value of H* at perigee height was used. The values of pA are given in Table 1 and plotted against yA in Fig. 5 : the last of the 29 values of pA in Table 1 is omitted from Fig. 5 because it is below 125 km and because there is no check on the accuracy of the perigee height at this late stage (6 hr before decay). ARJEULTS 4.1 Variation CJJ&PZS~~~ with height In Fig. 5 the 28 values of air density obtained from analysis of the orbit of 196859B, shown as circles, are plotted against height. The broken curve shows the variation of
AIR DENSITY AT HEIGHTS BETWEEN 130 AND 16Okm
993
la2 la
I.5
20
2-5
33)
4.0
5.0
6.0
70
&o 9.OlOO
IO*pA kg/m3
FKL 5.
VARUlSON OF AIR DENSlTk?~1 WITH BEIGHT)‘~ DURING JULY-Auciusr FROMORBITOF l%fMPB.
1968, AS FOIJND
density with height given by the COSPAR International Reference Atmoqhere 1965, for the appropriate level of solar activity (model 5) and for 10 hr LT (though the time of day chosen is unimportant because CIRA I%5 gives a day-to-night variation of less than 5 per cant at these heights). The dotdash we shows the values of density given by Jacchia’s model atmosphere fnu for an exospheric temperature of 1100°K. There have been no previous values of air density determined from satellite orbits at heights below 160 km; so our values agree remarkably well with the CIRA and Jacchia models. The densities obtained from 1968-59Bare about 9 per cent lower than those of CIRA. The consistency of the group of 16 points from 196%59Bat heights between 152 and 158 km is remarkable, and indicates that the relative errors in perigee height are less than 4 km. 4.2 Yaridons with time To examine whether the density varies signiticantiy with time, the 19 values of pA at heights between 148 and 158 km were converted to the mean height of 153 km using CIR4 1965, the density pm, at a height of 153 km being found from the equation p(CIRA ; 153)
plas = pd p(CIXA; FA) ’ where p(CrRa; u) denotes the value of p given by CIRA 2965 (model 5) at height y. %mihuly, the values of PAat heights between 139 and 151 km were converted to the mean height of 145 km. The values of pla3and plfi are plotted against time in Fig. 6, together with the values of S1o,r the solar radiation energy on a wavelength of 1@7cm measured by N.R.C., Ottawa, and A,, the daily geomagnetic planetary amplitude, as given by the Institut fiir Geophysik, C%W.ingen.The values are plotted at the beginning of the day after the date for which they are given, i.e. with a time lag of 6 hr for S,,, and 12 hr for A,.
994
D. G. KINGHELE
S&r
and DOREEN
radiition
4007@
40060
40050
me-~odifi~ FIG.
M. C. WALKER
6. AIRDENSITY
AT BEIGEIT OF
SOLAR RADIATION
153 km
ENERGY &,.,,
40080
Aug 40090
Julion day
AND
145 km, plsl AND ~145,WITH DAILY
AND DAILY
GEOMAGNEl’IC
VALUES OF
INDEX A,.
From Fig. 6 it appears that the variations in p153between MJD 40049 and 40080 are scarcely large enough to be sign&ant : pGa never departs from l-67 x Ws kg/m5 by more than 4 per cent, and its variation is smoother than any comparable results at greater heights. However, there is quite a large increase in plG at the time of the high solar activity centred at MJD 40083, and since solar activity is known to control air density at heights above 200 km, it is probable that the increase in pl& is a response to solar activity. The magnitude of the increase is difficult to specify exactly, because the peak in density is only maintained
AIR DENSITY
995
AT HEIGHTS BETWJ%N 130 AND 160 km
for half a day, but it appears probable that an increase in S,,., from 140 to 180 x 10-22 W m-2 Hz-l increases p146by about 10 per cent. If so, plsa would be expected to increase by about 5 per cent as S,,., increased from 130 to 150 x 10-22 W m-2 Hz-l between MJD 40059 and 40065 : this is consistent with the values of piss in Fig. 6, but the actual increase (of 4 per cent) is too small to be confidently distinguished from mere scatter. The geocentric Sun-perigee angle p is shown at the top of Fig. 6, the local time in hours and latitude at perigee being marked on the curve: any day-to-night or latitudinal variation in air density is evidently too small to have a recognizable influence on the values of pm. Also there are no variations in density recognizably correlated with the geomagnetic index A,,: this is not surprising, since no important geomagnetic storms occurred between MJD 40050 and 40084. 4.3 Profile of density in July-August 1968 The values of plas which form the peak in Fig. 6 are the three values above the broken curve in Fig. 5 at heights between 141 and 147 km. If we reduce them by 10 per cent, 16 per cent and 7 per cent respectively, to allow for the apparent effect of solar activity, they are all brought slightly below the broken curve in Fig. 5. If this correction is made, the unbroken curve in Fig. 5 represents the profile of density vs. height from our analysis of 1968-59B. The values are listed in Table 2 below, at 5-km intervals. TABLE2. PROFILE OFAIRDENSITY IN JIJLY-AUGUST 1968 FROMANALYSIS OFTHEORBITOF 1968-59B (S,,., ti 150 x 10-** W m-*Hz-l) Height (km) Air density (lo-’ kg/m’)
(125) (12.4)
130 7.9
135 5.3
140 3.8
145 2.7
150 1.98
155 1.49
160 1.15
4.4 Comparisons with previous results The lowest height at which absolute values of density have previously been obtained from satellite orbits(14*16)was near 170 km. These values were during 1963-4, when the Sun was inactive, and it was found (is) that there was quite a large day-to-night variation down to 170 km, with the maximum daytime density exceeding the minimum night-time density by nearly 40 per cent. However, the mean values of density agreed quite well with CIRA 1965 and Jacchia’s model. Perhaps the most satisfactory measurements of air density at heights between 120 and 160 km by rocket techniques are the values deduced from the growth of chemiluminescent clouds.(16*“) Sheppard us) has obtained values at Woomera for April-May 1965, when solar activity was much lower than in 1968: his values, which are subject to errors off 30 per cent, agree with C1RA 1965 and with our values to within 35 per cent at heights between 125 km and 150 km, with the difference increasing slowly above that height. Golomb and others (17)obtained values of density for June 1966 and January 1967, when solar activity was closer to the 1968 level: their values are within 20 per cent of our results and CIRA 1965 up to 145 km, but diverge widely above 150 km. Variations in the density at heights near 150 km during 19667 were studiedus) in an analysis of the orbit of 1966-1016. The substantial variation discovered-a variation by a factor of Isir--was probably a combination of day-to-night and semi-annual variations, which happened to coincide in time. Since plM in Fig. 6 shows no significant variation as p changes from 20” to 90”, the day-to-night variation at this height in July-August 1968 probably did not exceed a factor of 1.2.
D. G. KINCMFiLE and DOREEN M, C. WALKER
9%
5. ACCURACY OF THE RESUL’IS The main error in the absolute values of density is likely to arise from the biis error in perigee height, estimated in Section 2.3 as &-1 km (s.d.), and the bias error in C,, given in Section 3.2 as =t5 per cent (ad.) for y, > 125 km. Since Fig. 5 cotis the CIRA 1965 values of density which were used in obtaining H, the term H{(r& - r$fH>a, in Equation (3) should not be in error by more than about 3 per cent (ad.): the corresponding error in perigee height increases from xero initially to 0.7 km at MJD 400859 and about 1-O km at the final point used (MJD 40086.9, ye = 124 km). Errors in pa due to errors in etit, S’fmand the theory used in Equation (12), are estimated as 2,1,1 and 1 per cent respectively. The value of li most likely to be in error is the last one, 65 hr before decay, R = 06179 rev/day% : its accuracy can be checked by using it, with the appropriate theory (Equation (65) of Ref. 3, with ,u = O-33), to calculate the remaining lifetime; the result is 6.7 hr-only 0.2 hr in error. So even the last value of pB (omitted from Fig. 5) is apparently based on a correct value of fi. When these component errors are combined, with an error e in perigee height giving a proportional error of [exp (e/H*) - 11 in pl, the resultant error in the absolute values of density p4 is about 8 per cent up to day 40081 typ > 145 km), increasing to 14 per cent for the point at MJD 40086-l QA = 132 km) and 20 per cent for the last point plotted (MJD 40086.9, yA = 124 km). The variations in density, unlike the absolute values, are not affected by bias errors in yII or Co and should be more accurate. The scatter in yI, is probably less than O-5 km, as noted in Section 4.1, and the variations in density up to MJD 40085, shown in Fig. 6, should not be in error by more than 3 per cent (s.d.)-a conclusion which is amply confirmed by the smoothness of the values of pnn.
6. CONCTXJSIONS
In this paper we have analysed the orbit of 1968-59B between 12 July and 19 August 1968, and have obtained 28 values of air density at heights from 160 km down to 124 km, to give the first profile of density versus height in this region from satellite orbits (Fig. 5). The absolute values of density, most of which are subject to errors estimated as A8 per cent (s.d.), due mainly to possible bias errors in Co and yr, are given in Table 2: the density increases from 1.49 x KY@kg/ma at a height of 155 km to 7*9 x 10-O kg/ma at 130 km. These values agree remarkably well with those given by the COSPAR InternationalReference Atmosphere 1965, being about 9 per cent lower than in the appropriate CIRA model. The relative accuracy of the values of density is estimated as better than f3 per cent (s.d.), and the variation of density with time for a tied height is shown in Fig. 6. The large increase in solar activity between 12 and 15 August 1968, when solar radiation energy at 10.7 cm wavelength increased from 140 to 180 x lO-= W m-* Hz?, is accompanied by an increase of about 10 per cent in the density at a height of 145 km. Apart from this increase, the fluctuations in density are limited to variations of f4 per cent about the mean, and are much smoother than at heights above 180 km, even though the close spacing in time would tend to accentuate irregularities (the average interval between the values is only about 32 hr). Any latitudinal or day-to-night variations in density were too small to be detected. REFJzREN5 1. K. S. W.
CHAMPION, Upperatmosphere density.In AFCRL in ~pmt?.
Rep. (1967).
Air Force Cumbrk&eRes. Lab.
2. D. G. TCwA-kq G. E. COOKand D. W. Scan, Planer.Space SC&17,629 (1969).
AIR DENSITY AT HEIGHTS BERN 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
130 AND 16Okm
997
G. I?,. Coax and D. G. KIN&&L,E, Proc. R. Sot. A27S, 357 (1963). Y. KOZAI,Ash: J. 64,367 (1959). D. G. Kma-Hm~ and J. &?cmmN, Plwtet. Space Sci. 16,675 (1968). R. H. GILDING and R. MILNER,R.A.E. Tech. Rep. No. 67283 (1967). CIRA 1965 (COSPAR Internutionul Reference Atmosphere 1%5), North-Holland, Amstexdam (1965). D. G. Km&Hms, G. E. CXKX and D. M. C. WALUR, R.A.E. Tech. Nute No. GW 533 (1959). D. 0. KINI+Has, G. E. Cho~ and D. M. C. WALKER,R.A.E. Tech. Note No. GW 565 (1960). D. G. K~QXELE, Theoryof Sutellite Orbits in un Atmosphere. Buttenvorths, London (1964). D. 0. Km&&z, AnnfsG&phys. 22,40 (1966). G. E. coon, Pkmet. @ace Sci. 13,929 (1965). L. G. JACCHU,Satin. contt. Aetrophye. 8,215 (1%5). R. L. JACOBS,AZAA Paper No. 65-507 (1965). D. G. K~Q-HEIZ and E. QUINX,Planet. Space Sci. 14,1023 (1966). L. M. SHEPPARD, Rust. W.R.E. Tech. Note No. HSA 131 (1968). D. GOLQMB,F. P. DBLGRBCO,0. HAMNO, R. H. JOHNSON and M. A. MACLEOD, Space Resetweh VUl:p. 705. North-Holland, Amsterdam (1968). 18. D. G. Kmc+Hm+nd J. I-bwsm~, Planet. S’ceSci. l&l883 (1967).