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Exospheric conditions, to a height of 3500 km, derived from satellite accelerations in 1964
Planet. Space Sci. 1966. Vol. 14. pp. 291 to 297.
Pergamon Press Ltd.
Printed in Northern Ireland
EXOSPHERIC CONDITIONS, TO A HEIGHT OF 3500km, DERIVED FROM SATELLITE ACCELERATIONS IN 1964 K. FEA Space Research Group, Physics Department,
University College London
(Received 26 October 1965) Abstract-The relation of density with height to 3500 km is derived from observations on satellites in 1964, close to the time of minimum solar activity, and the scale height is obtained with height from this relation. The exospheric temperature is obtained from entering the tabulated atmospheric models by Jacchia and indications are obtained of the mean molecular weight at various heights. It seems likely that only hydrogen is seen at 3500 km height and that perturbations other than air drag at this height are not large. The composition at 1000 km is approximately two thirds helium and one third hydrogen, by numbers, for an exospheric average temperature of 795°K.
An earlier communication(i) announced a preliminary value for the air density at a height of 3500 km, derived from photographic data obtained in 1964. A later paper@) gives a revised value and discusses the interpretation of the observed acceleration of the Lincoln Laboratory (M.I.T.) balloon satellite 1963 30D. This present paper is a continuation of these studies; by including data from a number of other satellites at lower altitudes it is possible to obtain indications of the exospheric temperature, scale heights and mean molecular weights up to 3500 km. The first results are presented here. Details are given t2) of the photographic observations of the 1963 30D balloon satellite (2.4 m dia.) made with the 24-in. reflector at the University of London Observatory. The orbit of 1963 30D had then an average height of 3500 km, with orbital eccentricity O-04. The eccentricity is steadily increasing due to solar radiation pressure effects, but the satellite remains useful for studying drag effects near the same height of 3500 km through 1965 at least; a further program of photographic observations is currently being made. Advantage has been taken of the long (about 90 days) periods when the orbit is entirely in sunlight, for then the acceleration in the orbital mean motion due to solar radiation pressure is very small. At other times, when the orbit contains shadow, the acceleration due to solar radiation pressure is much larger than contribution from air drag; furthermore, since the cross-sectional area and reflexion coefficient are not known sufficiently well, it is probably not possible to extract the contribution to the acceleration by air drag with useful accuracy. Therefore the air densities derived from the accelerations of this satellite are at present conftned to the situations when the orbit is roughly normal to the direction of the Sun. This configuration gives a “mean” value for the air density, excluding the regions of minimum and maximum temperature and density, though the diurnal variations may not be appreciable at these heights. Some discussion has been given t2) of perturbations other than air drag affecting the accelerations of balloon satellites at these great heights. The preliminary conclusion is that the acceleration seen in the case of 1963 30D during an all-in-sunlight phase most probably is mainly due to air drag, the other perturbations not exceeding 10 % of the total acceleration. However, it is possible that the electro-magnetic forces discussed by Drell et ~1.‘~)may later be shown to be significant. * A test should become possible when spheres of * The importance of the electro-magnetic drag forces in the case of the Echo satellites, suggested by Drell et ~1.‘~’is probably over-estimated. No inconsistencies in the derived air densities and scale heights have been found so far, and arc not found in the present study. 291
292
K. FEA
different diameters are in orbit at these heights (e.g. the “Pageos” balloons, which will be similar to the large Echo-type satellites and are scheduled for near polar orbits with small eccentricity and mean heights of about 4000 km). For the purpose of the present study it is assumed that the acceleration observed for 1963 30D in 1964 (July to September) is due only to air drag, and that the air density at 3500 km quoted by Feat2) is probably not in error by more than 20%. If later studies show other perturbations to be significant than the conclusions must be revisedthough it will be seen that the present picture is consistent with the absence of these perturbations. During 1964, and up to the time of writing, there were no suitable objects in orbit for determining air densities between 1500 and 3500 km. The greatest altitude that could be surveyed, below the mean height of 1963 30D of 3500 km, was 1150 km-the mean height of the near-circular, near-polar orbit of 1964 04A (Echo 2; dia. 41 m). Observations were attempted in late 1964 on Echo 2 but poor weather made it necessary to rely entirely on data from other sources. Fortunately an all-in-sunlight period for Echo 2 occurred from July 31 through September 3, 1964,* and it was possible to obtain from the Smithsonian Astrophysical Observatory orbit elements at l-day intervals for this period, based on field reduced data from the Baker-Nunn cameras. The orbit elements specially provided by the Smithsonian Astrophysical Observatory have proved invaluable in the analysis of the photographic observations made with the 24-in. telescope. The acceleration found for Echo 2 was corrected for the acceleration in the argument of perigee according to the method given by Fea. t2) The area/mass ratio? for Echo 2 was taken as 57.6 cm2 g-l, and the drag coefficient, C,, as 2.8 using the data of Cook.(4) The orbit was assumed circular-a reasonable approximation in view of the small eccentricity of about 0.014 and the large scale height of more than 200 km. The mean height was then 1150 km. It is necessary to add some data below 1150 km to define that part of the log density vs. height curve where the curvature becomes large. Further, data below 800 km can be used to enter the tabulated model atmospheres of Jacchiafs) and to indicate the exospheric temperature. In November 1964 observations were made on the balloon satellite 1963 53A (Explorer 19 ; dia. 3.7 m) with the photo-electric/photographic tracking instrument sited by the Physics Department of University College London at Mirikata, Woomera (South Australia). The photographic observations have been reduced with the aid of preliminary elements by the Smithsonian Astrophysical Observatory. The acceleration obtained for a lo-day period in early November referred again to an all-in-sunlight phase. The acceleration, due primarily to air drag, gave a value for the air density at 690 km, using a relation given by King-Hele.(6) This is not a mean density for this height, since the measure refers to a region near perigee, which was then some two hours east of the maximum of the diurnal bulge. A mean value for the density at 690 km can be obtained by using the tables and relations given by Jacchia.(5) The density given by the 1963 53A observations for November 1964 was 1.24 x 10-r’ g cm-3 at 690 km. The area/mass ratio assumed was 13.9 cm2 g-l and the C, was taken as * This one month period occurs near the middle of the three month period during which 1963 30D was observed. t Assuming a loss of 10 % of the published mass, due to the probable leakage of the gas used for inflation.
OBSERVED EXOSPHERIC
CONDITIONS,
1964
293
2.4. From the tabulated atmospheric models of Jacchia (5) the asymptotic exospheric temperature obtained was 844°K. Using also the relation given for obtaining the minimum nighttime temperature, fTb, from the observed temperature at some other point-his relation (13)-we find To is 668°K; the maximum daytime temperature (1.28 T,,) is 855°K. From the tabulated models, for 690 km, the minimum and maximum densities are then 4.72 x lo-l8 and 1.33 x 10-l’ g cmd3 respectively. Therefore the mean density is 9.00 x lo-l8 g cmWsand the corresponding “mean” temperature 795°K. This last temperature is taken to be the exospheric temperature in the period under discussion. During the months discussed, July through November, 1964, the solar flux at 10.7 cm wavelength was fairly constant and at a very low level. In fact the lowest value since 1954 was recorded at Ottawa on July 26, 1964. The mean value for the 5 months was 70.0 ( x lO-22w/m2 per c/s band width) with a weak 27-day fluctuation varying the flux from 65 to For the 1963 53A observations the mean Ievel was 73.0. The A, 76, approximately. index indicated very quite conditions geoma~etically-the mean value for the 5 months was 7, with increases to about 30 on a few occasions. Using these mean figures and the relations given by Jacchia, w the minimum exospheric temperature, To, may be predicted to be 670%; this is very close to the figure of 668°K used here. For the period of the 1963 53A observations the calculated T,, would be 681°K. Using the temperature of 795°K and the appropriate model of Jacchia a value for the air density at 500 km is added--the value is l-46 x 1O-18g cm-3. The four values of air density are then:
Height
Density
(km)
(g cm-3)
Log,, (density)
3500
l-65 x 1O-2o
- 19.783
1150
5.55 x 10-19
- 18.256
690
9.00 x 10-1s
- 17,046
500
1.46 x lo-=
- 15.835
It is noted that the mean density for 500 km used here is very close to the figure which can be extracted from the data given by King-HeIe.(‘) The curve of log,, (density) versus height is drawn in Fig. 1. To the four points the best curve has been fitted, bearing in mind the assumptions that the curvature must tend to zero above 3500 km and also become small below 500 km. Clearly one should not place too much confidence in the curve; nevertheless repeated fitting gave satisfactory results. From the curve one may obtain the slope and therefore the density scale height, H. Although the curve is determined by the points at 690 and 500 km the curvature is too large below 1000 km to give useful scale heights. The plot of H against height is shown in Fig. 2. Taking the exospheric temperature to be 795°K for all the region under discussion the values of H in Fig. 2 may be used to obtain indications of the mean molecular weight up to 350 km. Since there is unlikely to be any constituent other than hydrogen present in
K.
294
FEA
4C
3.5
3c
2.5
,E 8
M
0
I.
r’
.4”
2
I .s
I-0
0.5
t
log, cknsity L ._
-18
-17
-16
-15
- 19 -20 -21 FIG. 1. CURVE OF LDG~~ (DENSITY) vs. HEIGHT FOR THE DATA GIVEN IN THE PAPER, RELATING TO THE PERIOD JULY THROUGH NOVEMBER, 1964.
the region of 3000 km we may use the relation H = kT/mg
directly ; k is Boltzmann’s constant T is the exospheric temperature
m is the mean molecular mass (in grammes) g is the local value of the acceleration due to gravity If more than one constituent is important then h,, the pressure scale height, is applicable, not directly H. However King-Hele and Rees (*)have given useful approximations enabling h, to be found from data giving H with height. At the lower altitudes these approximations were used to find the mean molecular weight. Two results are of interest. The mean molecular weight at 3500 km is found to be O-99, that is essentially unity. And the mean molecular weight at 1000 km is 2.97. This last may be compared with the data for the upper limit in Jacchia’s models-bearing in mind
OBSERVED EXOSPHERIC
scale
c 0
FIG. 2. VALUFZ3 FOR H,
DENSITY FROM
height
I-O
05 SCALE THE
CONDITIONS,
l-l
(UNITS
GIWXN
2-5
2-o
i-5
HEIffHT
CURVE
295
1964
IN
OF FIG.
lc@o
kill)
VS.
HEICiHT,
DERIVED
1.
his caution regarding the data above 800 km, which are extrapolated from the satellite observations. For the temperature of 795°K the mean molecular weight would be about 3.2, which is in satisfactory accord with the value obtained here. A value of 2.97 would indicate about 65 y0 helium and 35 % hydrogen in terms of numbers of particles. The mean molecule weight of 0.99 at 3500 km indicates pure hydrogen. Furthermore the fact that the departure from unity is so small suggests that the assumptions made in this study are probably reasonable. Large perturbations at 3500 km from sources such as electro-magnetic drag and reflected earth radiation are apparently not present, at least in the case of 1963 30D during an all-in-sunlight phase. However magnetic drag forces might well become appreciable for, for exampfe, spheres ofgreater diameter and in equatorial rather than polar orbits. Also the perturbations from reflected earth radiation are reduced to some extent in the all-in-sunlight phases due to symmetry effects as the orbit precesses relative to the illuminated Earth.
296
K. FEA
If the air density derived for 3500 km height includes an appreciable proportion of ionized R atoms then this fraction may be deducted and Fig. 1 re-plotted using only the neutral particle density for 3500 km height, For example, if 25% of the H atoms ale ionized then the “neutral’” scale height at 3500 km becomes 1400 km (1000 km for 50% ionization) and the mean molecular weight, M, is then 1.17 (or 1.61 for 50% ionization), retaining the atmospheric temperature 795°K This increase in M would suggest a contribution from helium, which seems rather unlikely. Accordingly, more than 25% ionization at 3.500 km gives a mean molecular weight that is difficutt to accept. Further, it would require a perturbation giving a positive acceleration to the satellite to increase again the density observed, to adjust the scale height to a reasonable value, and to reduce M to near unity. Two other comments may be made on the density derived at 3500 km. Johnson@) has given predictions on exospheric composition for various temperatures, up to a height of 2500 km. It is interesting to note that the density found fram the acceleration of 1963 30D is in close agreement with JohnsorCs predictions for solar ~nimum conditions, extrapolating to 3500 km, the difference being less than a factor of two. However the agreement may become less satisfactory as solar activity and exospheric temperatures increase. The values for air density with height derived in this study have also been compared with values obtained by Kockarts (lo) from Nicolet’s latest atmospheric models. The agreement seems to be good. For an exospheric temperature of 800°K (practically the 795°K used here) the densities compare as follows : Height (km)
Density (Fe@ (g cm?
690 1150 3500
7.01 X 1o-“s 5-55 x IO--= 1.65 x lO-2o
Density (Rockarts) (g cm-? 6.48 x lo-= 5.11 x 10-lS 1.64 x 1O-2o
These studies are continuing; it is of great interest to determine the variations occurring in the exosphere as the solar cycle progresses. It is hoped that observations may be added in the near furture in the height range 1~~~ km as suitabfe objects are placed in orbit. A~k~QwZe~grnenf~-~~~ work was carried out under the auspices of the British National Committee for Space Research and supported in part by a grant from the Meteorological Office. Thanks are due to Professor C. W. Allen for permission to use the facilities of the University of London Observatory, and to Professor R. L, F. Boyd and Dr. A. P. Willmore for their support. Thanks are also due to Dr. I. I. Shapiro of the Lincoln Laboratory, M.I.T., for most useful discussions and to the Data Division, Smithsonian Astrophysical Observatory, for providing orbit elements.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
K. %A, Nature, Land. 205, 379 (1965). K. FEA, Planet. Space Sci. 13, 1289 (196X% S. D. DRELL, II. M. FOLEYand M, A. RUDERMAN,J, Geophys. Res. 70, 3131 (1965). G. E. CQC)K,Planet. Space Sci. 13,929 (1965). L. G. JACWIA, Static diffusion models of the upper atmosphere with empirical temperature profiles. Smithsonian Zmt. Astrophys. Ubs., Spec. Rep’. No. 170, December (f954). D. G. KNX-&ZE~ Theory o~SateZ~~teOrbits in an Atrn~~~here~Chap. 7. Butierworths, London (1954). D, G. ICING-HELE,.T. &??&x+.Terr. PI%_YX. 27, IQ7 (1965). D. G. ICXNO-&LE and J. MI. KEl?S,Z’roc. Roy. SW. A270,562 (1962). F. S. JOHNSON,Density of an Exosphere, Paper presented at the Aeranomy Symposium afthe International Association for Geomagnetism and Aeronomy, Cambridge, Mass., August (1965). G. KOCKARTS,Private correspondence. October (1965).
OBSERVED
EXOSPHERIC
CONDITIONS,
1964
Pe3ronw-CooTHorueHne Mewp;y ~JIOTHOCT~~O II BbICOTOti A0 3500 KM B~IBOAEITC~~ wa 8 nepao& 6~1113mi&K AfllHHMaJtbHOti OCHoBaHHU Ha6JiIOAeIWl CEYTHMKOB B 19641’. con~esHoiaK~aHOCT~~IlrKajIa~~e0~nyTBep~~ae~ff~0niepeBhfCOTbIB3~B~CHMOCT~ 3K30C#epHaE TeMnO~aTypa AOCTSifaeTCR BXO~AeH~eM B OT ~aHHOr0 COOTHOUIeHWZ. Ta6yjr~posa~~b~eMoAenmaT~oc~ep~r(~~aKK~a)enp~o6peTa~~crryKa3aaaacpe~~ero IIOBHAP~MOM~ wa BbICOTe 3 35OOXM MOJleKy.iIflpEiOrOBeCa Ha pa3JIHYHbIX BbEOTaX. 06Hapy?KliBaIOT TOJIbKOBOAOpO~,TOrAa KaKBO3My~eFlIGi,nOMHMOJI060BO~0COIIpOTIIBZIeHHH BO3nyXa, HeBe.nHKH. COCTaBHa 1OOOKM--np~6~~311TenbHO ABe TpeTM reJIliIR A OAHaT~eTh~OAO~OAa,9ACJeHHO,A.'IR~~eAHe~3K3OC~epHO~TeM~e~aTy~b~B ?%?6-11.
297
Pergamon Press Ltd.
Printed in Northern Ireland
EXOSPHERIC CONDITIONS, TO A HEIGHT OF 3500km, DERIVED FROM SATELLITE ACCELERATIONS IN 1964 K. FEA Space Research Group, Physics Department,
University College London
(Received 26 October 1965) Abstract-The relation of density with height to 3500 km is derived from observations on satellites in 1964, close to the time of minimum solar activity, and the scale height is obtained with height from this relation. The exospheric temperature is obtained from entering the tabulated atmospheric models by Jacchia and indications are obtained of the mean molecular weight at various heights. It seems likely that only hydrogen is seen at 3500 km height and that perturbations other than air drag at this height are not large. The composition at 1000 km is approximately two thirds helium and one third hydrogen, by numbers, for an exospheric average temperature of 795°K.
An earlier communication(i) announced a preliminary value for the air density at a height of 3500 km, derived from photographic data obtained in 1964. A later paper@) gives a revised value and discusses the interpretation of the observed acceleration of the Lincoln Laboratory (M.I.T.) balloon satellite 1963 30D. This present paper is a continuation of these studies; by including data from a number of other satellites at lower altitudes it is possible to obtain indications of the exospheric temperature, scale heights and mean molecular weights up to 3500 km. The first results are presented here. Details are given t2) of the photographic observations of the 1963 30D balloon satellite (2.4 m dia.) made with the 24-in. reflector at the University of London Observatory. The orbit of 1963 30D had then an average height of 3500 km, with orbital eccentricity O-04. The eccentricity is steadily increasing due to solar radiation pressure effects, but the satellite remains useful for studying drag effects near the same height of 3500 km through 1965 at least; a further program of photographic observations is currently being made. Advantage has been taken of the long (about 90 days) periods when the orbit is entirely in sunlight, for then the acceleration in the orbital mean motion due to solar radiation pressure is very small. At other times, when the orbit contains shadow, the acceleration due to solar radiation pressure is much larger than contribution from air drag; furthermore, since the cross-sectional area and reflexion coefficient are not known sufficiently well, it is probably not possible to extract the contribution to the acceleration by air drag with useful accuracy. Therefore the air densities derived from the accelerations of this satellite are at present conftned to the situations when the orbit is roughly normal to the direction of the Sun. This configuration gives a “mean” value for the air density, excluding the regions of minimum and maximum temperature and density, though the diurnal variations may not be appreciable at these heights. Some discussion has been given t2) of perturbations other than air drag affecting the accelerations of balloon satellites at these great heights. The preliminary conclusion is that the acceleration seen in the case of 1963 30D during an all-in-sunlight phase most probably is mainly due to air drag, the other perturbations not exceeding 10 % of the total acceleration. However, it is possible that the electro-magnetic forces discussed by Drell et ~1.‘~)may later be shown to be significant. * A test should become possible when spheres of * The importance of the electro-magnetic drag forces in the case of the Echo satellites, suggested by Drell et ~1.‘~’is probably over-estimated. No inconsistencies in the derived air densities and scale heights have been found so far, and arc not found in the present study. 291
292
K. FEA
different diameters are in orbit at these heights (e.g. the “Pageos” balloons, which will be similar to the large Echo-type satellites and are scheduled for near polar orbits with small eccentricity and mean heights of about 4000 km). For the purpose of the present study it is assumed that the acceleration observed for 1963 30D in 1964 (July to September) is due only to air drag, and that the air density at 3500 km quoted by Feat2) is probably not in error by more than 20%. If later studies show other perturbations to be significant than the conclusions must be revisedthough it will be seen that the present picture is consistent with the absence of these perturbations. During 1964, and up to the time of writing, there were no suitable objects in orbit for determining air densities between 1500 and 3500 km. The greatest altitude that could be surveyed, below the mean height of 1963 30D of 3500 km, was 1150 km-the mean height of the near-circular, near-polar orbit of 1964 04A (Echo 2; dia. 41 m). Observations were attempted in late 1964 on Echo 2 but poor weather made it necessary to rely entirely on data from other sources. Fortunately an all-in-sunlight period for Echo 2 occurred from July 31 through September 3, 1964,* and it was possible to obtain from the Smithsonian Astrophysical Observatory orbit elements at l-day intervals for this period, based on field reduced data from the Baker-Nunn cameras. The orbit elements specially provided by the Smithsonian Astrophysical Observatory have proved invaluable in the analysis of the photographic observations made with the 24-in. telescope. The acceleration found for Echo 2 was corrected for the acceleration in the argument of perigee according to the method given by Fea. t2) The area/mass ratio? for Echo 2 was taken as 57.6 cm2 g-l, and the drag coefficient, C,, as 2.8 using the data of Cook.(4) The orbit was assumed circular-a reasonable approximation in view of the small eccentricity of about 0.014 and the large scale height of more than 200 km. The mean height was then 1150 km. It is necessary to add some data below 1150 km to define that part of the log density vs. height curve where the curvature becomes large. Further, data below 800 km can be used to enter the tabulated model atmospheres of Jacchiafs) and to indicate the exospheric temperature. In November 1964 observations were made on the balloon satellite 1963 53A (Explorer 19 ; dia. 3.7 m) with the photo-electric/photographic tracking instrument sited by the Physics Department of University College London at Mirikata, Woomera (South Australia). The photographic observations have been reduced with the aid of preliminary elements by the Smithsonian Astrophysical Observatory. The acceleration obtained for a lo-day period in early November referred again to an all-in-sunlight phase. The acceleration, due primarily to air drag, gave a value for the air density at 690 km, using a relation given by King-Hele.(6) This is not a mean density for this height, since the measure refers to a region near perigee, which was then some two hours east of the maximum of the diurnal bulge. A mean value for the density at 690 km can be obtained by using the tables and relations given by Jacchia.(5) The density given by the 1963 53A observations for November 1964 was 1.24 x 10-r’ g cm-3 at 690 km. The area/mass ratio assumed was 13.9 cm2 g-l and the C, was taken as * This one month period occurs near the middle of the three month period during which 1963 30D was observed. t Assuming a loss of 10 % of the published mass, due to the probable leakage of the gas used for inflation.
OBSERVED EXOSPHERIC
CONDITIONS,
1964
293
2.4. From the tabulated atmospheric models of Jacchia (5) the asymptotic exospheric temperature obtained was 844°K. Using also the relation given for obtaining the minimum nighttime temperature, fTb, from the observed temperature at some other point-his relation (13)-we find To is 668°K; the maximum daytime temperature (1.28 T,,) is 855°K. From the tabulated models, for 690 km, the minimum and maximum densities are then 4.72 x lo-l8 and 1.33 x 10-l’ g cmd3 respectively. Therefore the mean density is 9.00 x lo-l8 g cmWsand the corresponding “mean” temperature 795°K. This last temperature is taken to be the exospheric temperature in the period under discussion. During the months discussed, July through November, 1964, the solar flux at 10.7 cm wavelength was fairly constant and at a very low level. In fact the lowest value since 1954 was recorded at Ottawa on July 26, 1964. The mean value for the 5 months was 70.0 ( x lO-22w/m2 per c/s band width) with a weak 27-day fluctuation varying the flux from 65 to For the 1963 53A observations the mean Ievel was 73.0. The A, 76, approximately. index indicated very quite conditions geoma~etically-the mean value for the 5 months was 7, with increases to about 30 on a few occasions. Using these mean figures and the relations given by Jacchia, w the minimum exospheric temperature, To, may be predicted to be 670%; this is very close to the figure of 668°K used here. For the period of the 1963 53A observations the calculated T,, would be 681°K. Using the temperature of 795°K and the appropriate model of Jacchia a value for the air density at 500 km is added--the value is l-46 x 1O-18g cm-3. The four values of air density are then:
Height
Density
(km)
(g cm-3)
Log,, (density)
3500
l-65 x 1O-2o
- 19.783
1150
5.55 x 10-19
- 18.256
690
9.00 x 10-1s
- 17,046
500
1.46 x lo-=
- 15.835
It is noted that the mean density for 500 km used here is very close to the figure which can be extracted from the data given by King-HeIe.(‘) The curve of log,, (density) versus height is drawn in Fig. 1. To the four points the best curve has been fitted, bearing in mind the assumptions that the curvature must tend to zero above 3500 km and also become small below 500 km. Clearly one should not place too much confidence in the curve; nevertheless repeated fitting gave satisfactory results. From the curve one may obtain the slope and therefore the density scale height, H. Although the curve is determined by the points at 690 and 500 km the curvature is too large below 1000 km to give useful scale heights. The plot of H against height is shown in Fig. 2. Taking the exospheric temperature to be 795°K for all the region under discussion the values of H in Fig. 2 may be used to obtain indications of the mean molecular weight up to 350 km. Since there is unlikely to be any constituent other than hydrogen present in
K.
294
FEA
4C
3.5
3c
2.5
,E 8
M
0
I.
r’
.4”
2
I .s
I-0
0.5
t
log, cknsity L ._
-18
-17
-16
-15
- 19 -20 -21 FIG. 1. CURVE OF LDG~~ (DENSITY) vs. HEIGHT FOR THE DATA GIVEN IN THE PAPER, RELATING TO THE PERIOD JULY THROUGH NOVEMBER, 1964.
the region of 3000 km we may use the relation H = kT/mg
directly ; k is Boltzmann’s constant T is the exospheric temperature
m is the mean molecular mass (in grammes) g is the local value of the acceleration due to gravity If more than one constituent is important then h,, the pressure scale height, is applicable, not directly H. However King-Hele and Rees (*)have given useful approximations enabling h, to be found from data giving H with height. At the lower altitudes these approximations were used to find the mean molecular weight. Two results are of interest. The mean molecular weight at 3500 km is found to be O-99, that is essentially unity. And the mean molecular weight at 1000 km is 2.97. This last may be compared with the data for the upper limit in Jacchia’s models-bearing in mind
OBSERVED EXOSPHERIC
scale
c 0
FIG. 2. VALUFZ3 FOR H,
DENSITY FROM
height
I-O
05 SCALE THE
CONDITIONS,
l-l
(UNITS
GIWXN
2-5
2-o
i-5
HEIffHT
CURVE
295
1964
IN
OF FIG.
lc@o
kill)
VS.
HEICiHT,
DERIVED
1.
his caution regarding the data above 800 km, which are extrapolated from the satellite observations. For the temperature of 795°K the mean molecular weight would be about 3.2, which is in satisfactory accord with the value obtained here. A value of 2.97 would indicate about 65 y0 helium and 35 % hydrogen in terms of numbers of particles. The mean molecule weight of 0.99 at 3500 km indicates pure hydrogen. Furthermore the fact that the departure from unity is so small suggests that the assumptions made in this study are probably reasonable. Large perturbations at 3500 km from sources such as electro-magnetic drag and reflected earth radiation are apparently not present, at least in the case of 1963 30D during an all-in-sunlight phase. However magnetic drag forces might well become appreciable for, for exampfe, spheres ofgreater diameter and in equatorial rather than polar orbits. Also the perturbations from reflected earth radiation are reduced to some extent in the all-in-sunlight phases due to symmetry effects as the orbit precesses relative to the illuminated Earth.
296
K. FEA
If the air density derived for 3500 km height includes an appreciable proportion of ionized R atoms then this fraction may be deducted and Fig. 1 re-plotted using only the neutral particle density for 3500 km height, For example, if 25% of the H atoms ale ionized then the “neutral’” scale height at 3500 km becomes 1400 km (1000 km for 50% ionization) and the mean molecular weight, M, is then 1.17 (or 1.61 for 50% ionization), retaining the atmospheric temperature 795°K This increase in M would suggest a contribution from helium, which seems rather unlikely. Accordingly, more than 25% ionization at 3.500 km gives a mean molecular weight that is difficutt to accept. Further, it would require a perturbation giving a positive acceleration to the satellite to increase again the density observed, to adjust the scale height to a reasonable value, and to reduce M to near unity. Two other comments may be made on the density derived at 3500 km. Johnson@) has given predictions on exospheric composition for various temperatures, up to a height of 2500 km. It is interesting to note that the density found fram the acceleration of 1963 30D is in close agreement with JohnsorCs predictions for solar ~nimum conditions, extrapolating to 3500 km, the difference being less than a factor of two. However the agreement may become less satisfactory as solar activity and exospheric temperatures increase. The values for air density with height derived in this study have also been compared with values obtained by Kockarts (lo) from Nicolet’s latest atmospheric models. The agreement seems to be good. For an exospheric temperature of 800°K (practically the 795°K used here) the densities compare as follows : Height (km)
Density (Fe@ (g cm?
690 1150 3500
7.01 X 1o-“s 5-55 x IO--= 1.65 x lO-2o
Density (Rockarts) (g cm-? 6.48 x lo-= 5.11 x 10-lS 1.64 x 1O-2o
These studies are continuing; it is of great interest to determine the variations occurring in the exosphere as the solar cycle progresses. It is hoped that observations may be added in the near furture in the height range 1~~~ km as suitabfe objects are placed in orbit. A~k~QwZe~grnenf~-~~~ work was carried out under the auspices of the British National Committee for Space Research and supported in part by a grant from the Meteorological Office. Thanks are due to Professor C. W. Allen for permission to use the facilities of the University of London Observatory, and to Professor R. L, F. Boyd and Dr. A. P. Willmore for their support. Thanks are also due to Dr. I. I. Shapiro of the Lincoln Laboratory, M.I.T., for most useful discussions and to the Data Division, Smithsonian Astrophysical Observatory, for providing orbit elements.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
K. %A, Nature, Land. 205, 379 (1965). K. FEA, Planet. Space Sci. 13, 1289 (196X% S. D. DRELL, II. M. FOLEYand M, A. RUDERMAN,J, Geophys. Res. 70, 3131 (1965). G. E. CQC)K,Planet. Space Sci. 13,929 (1965). L. G. JACWIA, Static diffusion models of the upper atmosphere with empirical temperature profiles. Smithsonian Zmt. Astrophys. Ubs., Spec. Rep’. No. 170, December (f954). D. G. KNX-&ZE~ Theory o~SateZ~~teOrbits in an Atrn~~~here~Chap. 7. Butierworths, London (1954). D, G. ICING-HELE,.T. &??&x+.Terr. PI%_YX. 27, IQ7 (1965). D. G. ICXNO-&LE and J. MI. KEl?S,Z’roc. Roy. SW. A270,562 (1962). F. S. JOHNSON,Density of an Exosphere, Paper presented at the Aeranomy Symposium afthe International Association for Geomagnetism and Aeronomy, Cambridge, Mass., August (1965). G. KOCKARTS,Private correspondence. October (1965).
OBSERVED
EXOSPHERIC
CONDITIONS,
1964
Pe3ronw-CooTHorueHne Mewp;y ~JIOTHOCT~~O II BbICOTOti A0 3500 KM B~IBOAEITC~~ wa 8 nepao& 6~1113mi&K AfllHHMaJtbHOti OCHoBaHHU Ha6JiIOAeIWl CEYTHMKOB B 19641’. con~esHoiaK~aHOCT~~IlrKajIa~~e0~nyTBep~~ae~ff~0niepeBhfCOTbIB3~B~CHMOCT~ 3K30C#epHaE TeMnO~aTypa AOCTSifaeTCR BXO~AeH~eM B OT ~aHHOr0 COOTHOUIeHWZ. Ta6yjr~posa~~b~eMoAenmaT~oc~ep~r(~~aKK~a)enp~o6peTa~~crryKa3aaaacpe~~ero IIOBHAP~MOM~ wa BbICOTe 3 35OOXM MOJleKy.iIflpEiOrOBeCa Ha pa3JIHYHbIX BbEOTaX. 06Hapy?KliBaIOT TOJIbKOBOAOpO~,TOrAa KaKBO3My~eFlIGi,nOMHMOJI060BO~0COIIpOTIIBZIeHHH BO3nyXa, HeBe.nHKH. COCTaBHa 1OOOKM--np~6~~311TenbHO ABe TpeTM reJIliIR A OAHaT~eTh~OAO~OAa,9ACJeHHO,A.'IR~~eAHe~3K3OC~epHO~TeM~e~aTy~b~B ?%?6-11.
297