Air density at heights near 150 km in 1970, from the orbit of Cosmos 316 (1969-108A)

Cosmos 316 (1969-108A) was launched on 23 December 1969 into an orbit with an initial perigee height of 154 km at an inclination of 49.5° to the equator. Being very massive, Cosmos 316 had a longer lifetime than any previous satellite with such a low initial perigee: it remained in orbit until 28 August 1970. Because of its interest for upper-atmosphere research, the satellite was intensively observed, and accurate orbits are being determined at RAE from all available observations. Using perigee heights from the RAE orbits so far computed, and decay rates from Spacetrack bulletins, 102 values of air density have been obtained, giving a detailed picture of the variations in density at heights near 150 km between 24 December 1969 and 28 August 1970. The three strongest geomagnetic storms, on 8 March, 21 April and 17 August 1970, are marked by sudden increases in density of at least 23, 15 and 24 per cent respectively. With values of density extending over eight months, it is possible for the first time to examine a complete cycle of the semi-annual variation at a height near 150 km: the values of density, when corrected to a fixed height, exhibit minima in mid January and early August; at the intervening maximum, in April, the density is 30 per cent higher than at the minima.     

The helium drag effect on the orbit of Explorer 19

The orbit of Explorer 19 (1963-53A) has been determined at 60 epochs between February 1976 and October 1976 from over 3000 observations. Using values of the orbital decay rate corrected for the effects of solar radiation pressure, 58 values of air density at a height of 900 km have been evaluated. After correcting for solar and geomagnetic activity and seasonal-latitudinal and diurnal variations in the exospheric temperature, the residual variation exhibited modulations associated with the ‘winter helium bulge’.An examination of three different models of the helium variation has indicated a procedure, which combines distinct features of the CIRA (1972) and Jacchia (1977) model atmospheres, for determining the atmospheric drag effect on Explorer 19. It is proposed that this technique may be equally applicable to any satellite in near-polar orbit at an equivalent height.     

Variations in air density from January 1972 to April 1975 at heights near 200 km

Variations in air density have been determined using the orbit of the satellite Cosmos 462, 1971-106A, which entered orbit on 3 December 1971 with an initial perigee near 230 km and inclination 65.75°, and decayed on 4 April 1975. Accurate orbits determined at 85 epochs give perigee height correct to about 200 m throughout the satellite's lifetime. Using these values of perigee height and orbital decay rates from NORAD elements, 604 values of air density at half a scale height above perigee have been evaluated. These densities have been compared with values from the COSPAR International Reference Atmosphere 1972, taking account of variations due to solar activity and geomagnetic disturbances, and day-to-night variations, to reveal the residual variations in density at a series of standard heights, 245, 240, 232 and 213 km.The main residual variation is semi-annual, with maxima usually in April and October, and minima usually in January and July; but it is irregular in phase and shape. The amplitude of the semi-annual variation is remarkably constant from year to year between 1972 and 1975, and considerably greater than that given by CIRA 1972: the April/July density ratio is 1.68, not 1.32 as in CIRA; the October–November maxima are all lower than the April maxima, whereas CIRA gives the opposite; the July minima are 18% lower than the January minima, as opposed to 10% in CIRA.A standardized semi-annual density variation for the early 1970s is presented, with January minimum of 0.94, April maximum of 1.28, July minimum of 0.77 and October–November maximum of 1.22. In addition, three other recurrent variations are recognizable: in each year the density has a subsidiary minimum in May and maximum in June; there are low values in mid November and high values in late December.     

Upper-atmosphere features revealed by the orbit of 1980-43A

The satellite NOAA-B (1980-43A) was launched in May 1980 into an orbit with perigee height near 260 km and apogee height 1440 km, at an inclination of 92.2°.The lifetime was 11 months. The orbit has been determined at 40 epochs between October 1980 and May 1981 from about 3000 radar and optical observations. The average orbital accuracy, radial and cross-track, was about 100 m, with rather better accuracy in the final 14 days.The variation of orbital inclination has been analysed to determine two good values of atmospheric rotation rate, namely 1.10 ± 0.10 rev day^?1 at 300 km (average local time) and 1.15 ± 0.06 rev day^?1 at 225 km (evening).The effect of atmospheric rotation on the precession of the orbital plane of an actual satellite has never previously been detected; it is clearly apparent for 1980-43A in its last days and conforms to the expected theoretical change.The variation of perigee height has been analysed to determine ten values of atmospheric density scale height, for heights of 280–370 km. These values, accurate to about 3%, exceed by 15% the values indicated by the COSPAR International Reference Atmosphere. Solar activity was higher in the years 1980–1981 than at any time since early 1958 and it appears that the CIRA model underestimates the density and density scale height at high levels of solar activity.     

Variations in air density at heights near 200 km during 1967–1969, from the orbit of 1967-31A

Air density at a height of 180–200 km from July 1967 to September 1969 has been determined from analysis of the high eccentricity orbit of satellite 1967-31A. The data show good correlation between sudden density increase and geomagnetic disturbance. The increases for disturbances of equal strength are approximately 40% greater during night-time than daytime hours. The day-night influence is also observed in the changes in density with changes in the solar flux index, F₁₀. The 27-day density variation is predominant mainly during night-time, although the atmospheric response to F₁₀ variations is quite variable regardless of local time. A semi-annual variation of approx. 40% is observed. Also found is a 25% diurnal variation for heights near 170–180 km, which is in good agreement with the CIRA 1972 atmosphere.     

Air density at heights near 200km from the orbit of 1970-65D

Cosmos 359 rocket, 1970-65D, entered orbit on 22 August 1970, with an initial perigee height of 209 km and inclination 51·2°, and decayed on 6 October 1971. Using the values of perigee height from RAE orbits and decay rates from USAF Spacetrack bulletins, 146 values of air density have been calculated between August 1970 and September 1971, mainly at heights between 180 and 230 km.On ten occasions in 1971 when there were substantial geomagnetic disturbances there were sudden increases in density, the largest being about 32 per cent.When the density was corrected to a fixed height and allowance was made for the day-tonight variation and the effects of solar activity, the dominant feature was a semi-annual variation, with maxima in density centred at 6 November 1970 and 7 April 1971, and minima centred at 5 January and 28 July 1971. The maxima in density are nearly equal and exceed the minima by about 50 per cent.     

Determination and geophysical interpretation of the orbit of China 2 rocket (1971-18B)

The orbit of China 2 rocket, 1971-18B, has been determined at 114 epochs throughout its 5-yr life, using the RAE orbit refinement program PROP 6, with more than 7000 radar and optical observations from 83 stations.The rocket passed slowly enough through the resonances 14:1, 29:2, 15:1 and 31:2 to allow lumped geopotential harmonic coefficients to be calculated for each resonance, by least-squares fittings of theoretical curves to the perturbation-free values of inclination and eccentricity. These lumped coefficients can be combined with values from satellites at other inclinations, to obtain individual harmonic coefficients.The rotation rate of the upper atmosphere, at heights near 300 km, was estimated from the decrease in orbital inclination, and values of 1.15, 1.05, 1.10 and 1.05 rev/day were obtained between April 1971 and January 1976. From the variation in perigee height, 25 values of density scale height were calculated, from April 1971 to decay. Comparison with values from the COSPAR International Reference Atmosphere 1972 shows good agreement between April 1971 and October 1975, but the observational values are 10% lower, on average, than CIRA thereafter.A further 1400 observations, made during the final 15 days before decay, were used to determine 15 daily orbits. Analysis of these orbits reveals a very strong West-to-East wind, of 240 ± 40 ms^?1, at a mean height of 195 km under winter evening conditions, and gives daily values of density scale height in the last 7 days before decay.     

Air density at heights near 300 km,from analysis of the orbit of China 2 rocket (1971-18b)

China 2 rocket, 1971-18B, was launched on 3rd March 1971 into an orbit inclined at 69.9° to the Equator, with an initial perigee height of 265 km. Analysis of its orbit has yielded values of air density at average intervals of 6 days between July 1971 and January 1972. When corrected to a fixed height, the density exhibits a correlation with the geomagnetic index A_p and the solar 10.7-cm radiation. With values of density extending over seven months it is possible to examine a complete cycle of the semi-annual variation at a height near 300 km. The values of density, corrected for the day-to-night variation and for solar and geomagnetic activity, reveal minima in mid-August and late January; at the intervening maximum, in early November, the density is almost 40% higher than at the minima.     

Analysis of the orbital inclination of 1963-27A

The Agena B upper-stage rocket 1963-27A was launched into near-circular orbit, inclined at 82.3° to the Equator, on 29 June 1963. Its orbital elements were available at 52 epochs over the 16 month interval prior to its decay on 26 October 1969. During this period the satellite passed through 31:2 resonance and the variation in orbital inclination near this event was analysed to obtain two lumped geopotential harmonics of order 31. Since the resonance was a weak feature in the data, the resulting values are poorly defined.Either side of the resonance period, the inclination was used to estimate the mean atmospheric rotation rate Λ rev day^?1. The values obtained were Λ = 0.85 ± 0.18 at a height of 440 km for the period June 1968 to February 1969 and Λ = 1.13 ± 0.10 at 338 km for the period June to October 1969.     

Analysis of the orbit of 1970-65D,cosmos 359 rocket

Cosmos 359 rocket 1970-65D, was launched on 22 August 1970 into an orbit inclined at 51·2° to the Equator, with an initial perigee height of 209 km: it decayed on 6 October 1971 after a lifetime of 410 days. The orbit has been determined at 42 epochs during the lifetime, using the RAE orbit refinement program, PROP, with over 2600 observations. Observations from the Hewitt cameras at Malvern and Edinburgh were available for 10 of the 42 orbits.Ten values of density scale height, at heights between 185 and 261 km, have been determined from analysis of the variations in perigee height.Upper-atmosphere zonal winds and 15th-order harmonics in the geopotential have been evaluated from the changes in orbital inclination. The average atmospheric rotation rate, for heights near 220 km, is found to be 1·04 rev/day; but there are striking departures from the average, with well-established values of 1·30, 0·75, 1·35 and 0·95 over four successive 75-day intervals. The changes in inclination at the 15th-order resonance in November 1970 give values of lumped 15th-order harmonics, which will provide equations for evaluating coefficients of order 15 and even degree (16,18,…) and also show that useful results on the geopotential can be obtained from satellites with perigee as low as 200 km.     

Features of the upper atmosphere revealed by analysis of the orbit of cosmos 1009 rocket, 1978-50B

COSMOS 1009 rocket was launched on 19 May 1978 into an orbit with initial perigee height 150 km and apogee 1100 km: its lifetime was only 17 days. The orbit has been determined daily during the final 14 days of its life, using the RAE orbit refinement program PROP6,with about 1100 observations supplied by NORAD. An average accuracy of about 60 m, radial and cross-track, was achieved.The orbits were analysed to reveal three features of the upper atmosphere at heights between 125 and 175 km. From the decrease in perigee height, five values of density scale height, accurate to ±4%, were obtained. The first three were within 10% of those from CIRA 1972; the fourth, after a magnetic storm, was higher than expected; the fifth gave evidence of the decrease in drag coefficient at heights below 130 km.Atmospheric oblateness produced a change of 4° in perigee position during the last four days of the life. Analysis showed that the ellipticity of the upper atmosphere was approximately equal to that of the Earth, f, for the first two of the four days, and about $\text{1}\text{2}\text{f}$ in the last two.The orbital inclination decreased during the 14 days by about 50 times its standard deviation, and the observed variation was analysed to determine zonal winds at heights of 150–160 km at latitudes near 47° north. The zonal wind was very weak (0±30 m/s) for 23–28 May at local times near 03h; and 90±30 m/s east-to-west for 29 May to 4 June at local times near 01 h.     

Analysis of the orbit of 1968-90A (Cosmos 248)

The satellite 1968-90A (Cosmos 248), was launched in October 1968 into an orbit inclined at 62.25° to the equator, with an initial perigee height of 475 km, apogee height 543 km, and orbital period 94.8 min. The orbit has been determined at 57 epochs over nearly one and a quarter cycles of the argument of perigee from January 1972 until December 1975 with the aid of the RAE orbit refinement program PROP, using nearly 3000 observations. For most of these orbits the standard deviations in inclination are less than 0.0009° (corresponding to about 100m in cross-track distance). The values of eccentricity give perigee heights accurate to between 30 and 120m.The main purpose of the orbit determination was to provide accurate values of the eccentricity for use in determining the odd zonal harmonics in the Earth's gravitational potential. These values have been analysed to determine the amplitude of the oscillation in eccentricity, which is found to be 0.00433 ± 0.00001.     

Propagation of the geomagnetic density and temperature effect into the exosphere

The propagation of the geomagnetic effect into the exosphere is investigated based on a free-flight particle kinetic model of exospheric densities and temperatures. Exobasic neutral gas conditions and their variations during a geomagnetic storm occurrence are adopted as given by the OGO-6 model. The contributions of particles originating at different exobasic locations to the density and temperature at exospheric regions are taken into account according to the time needed to reach these regions. A short-time geomagnetic variation of exobasic conditions is simulated by a Gaussianshaped A_p -index variation with an FWHM of 20 min. It is then shown that the relative amplitude and the half width of the geomagnetic density variation increase strongly with exospheric heights. The density peak and the main temperature peak are shown to be delayed by more than one and two hours, respectively, at heights above 10,000 km. The temperature variation changes from a singlepeaked to a double-peaked structure at greater exospheric heights. It is shown that the exospheric density response to geomagnetic disturbances is detectable in observations of the geocoronal He-1-584 Å resonance radiation.     

Air density at heights near 200 km from the orbit of 1969-20B

The rocket of Cosmos 268, 1969-20B, entered orbit on 5 March 1969, with an initial perigee height of 230 km and inclination of 48.40°. Accurate orbits were computed at RAE from all available observations. Using the values of perigee height from the RAE orbit and decay rates from Spacetrack bulletins, 103 values of density have been calculated between July 1969 and February 1970. On three occasions when geomagnetic activity was strong there were sudden increases in density. When the density was corrected to a fixed height, the semi-annual variation was apparent. There was a strong minimum in July 1969, a maximum in October–November 1969 and a weak minimum in January 1970.     

Analysis of the orbit of 1966-51C

The satellite 1966-51C was launched in June 1966 into a polar orbit with perigee height 180 km, apogee height 3600 km, and orbital period 125 min. The orbit contracted rapidly under the influence of air drag, and the satellite decayed in March 1967. The only available observations are from the NASA Minitrack system, and 825 of these have been used with PROP6 orbit refinement program, to determine orbital parameters at 20 epochs. For most of these orbits the standard deviations in inclination and right ascension of the node are less than 0.002° (corresponding to about 200 m cross-track) and the standard deviations in eccentricity are less than 0.00002 (150 m in height).The variation in inclination is analysed to determine upper-atmosphere zonal wind speeds, with excellent resolution in local time. The results, for heights near 210 km and a representative latitude near 30°, indicate west-to-east winds of 100 ± 40 m/s for local time 18–21 h, and east-to-west winds of 80 ± 25 m/s for 02–04 h and 09–12 h local time. The values of the right ascension of the node are also analysed, and provide independent confirmation of the wind speeds obtained from the inclination. Analysis of the decrease in perigree distance indicates values of density scale height within 5% of those predicted by the COSPAR International Reference Atmosphere 1972, for the conditions experienced by 1966-51C.     

Perturbations of a spheroidal satellite due to direct solar radiation pressure

The orbital accelerations of certain balloon satellites exhibit marked oscillations caused by solar radiation impinging on the surface of the satellites, which, once spherical, have assumed a spheroidal shape producing a component of force at right-angles to the Sun-satellite direction. Given the characteristics and orientation of the satellite, the equations of force are determined by the formulae of Lucas. Otherwise the phase-angle and magnitude of the right-angle force are determined by trial and error, or best-fit techniques. Using a variation of the approach developed by Aksnes, a semi-analytical algorithm is presented for evaluating the perturbations of the Keplerian elements by direct solar radiation pressure on a spheroidal satellite. The perturbations are obtained by summing over the sunlit part of each orbit and allow for a linear variation in the phase-angle. The algorithm is used to determine the orbital accelerations of 1963-30D due to direct solar radiation pressure, and these results are compared to the observed values over two separate periods of the satellite's lifetime.     

Analysis of thermospheric density variations neglected in modern atmospheric models using accelerometer data

The accuracy of the atmospheric density and its spatiotemporal variations given by the NRLMSISE-00 atmosphere model at the solar minimum are estimated using density measurements of the CACTUS microaccelerometer at heights of 270–600 km. The model errors are found to be noticeably (by a factor of 2–3) higher than the errors in atmospheric densities obtained from satellite drag data at solar minima. Microaccelerometer density data are used to study short-period (during one orbit) spatiotemporal density variations. The analysis of density variations over one orbit reveals orographic and continental effects. The amplitudes of the continental and orographic effects are estimated at 10–15% at a height of 270 km and 40% at a height of 600 km.     

The variation of air density at 240 and 280 km from April to November 1967

Changes in the orbital periods of two satellites, 1962-βτ6 (Injun 3 rocket) and 1965-11D (Cosmos 54 rocket), have been used to deduce the air density at heights of 240 and 280 km during April–November 1967. At both heights the generally low density observed in July and the higher density in April and October were almost certainly part of a semi-annual variation similar to that observed at other heights in the thermosphere. The ratio of the maximum (October) to minimum (July) density was about 1·8 at 240 km and 2·2 at 280 km. Superimposed upon this variation were short-lived increases in density associated with magnetic storms, the largest being of 65 per cent at 280 km on 25 May, and a periodic variation with an amplitude of up to 25 per cent from the monthly mean density, related to the 10·7 cm solar radiation flux. A diurnal variation of density was also detected with a maximum density at 14 hr and a maximum to minimum ratio of 1·7 at 280 km.     

Variations in air density at heights near 150 km, from the orbit of the satellite 1966-101G

The satellite 1966-101G was launched on 2 November 1966 into an orbit with an initial perigee height of 140 km. A satellite with such a low perigee usually decays within a few days, but 1966-101G was exceptionally dense and remained in orbit until 6 May 1967. Analysis of the changes in its orbital period provides an unique opportunity for studying continuously for six months the variations in air density at a height near 150 km.

This paper records the results of such an analysis, applicable for the (medium) level of solar activity prevailing early in 1967. It is shown that at a height of 155 km the air density is greater by day than by night, with the maximum daytime density exceeding the minimum night-time density by a factor of 1.7: in contrast the COSPAR International Reference Atmosphere 1965 predicts that the density should be slightly greater by night than by day. It is also found that the night-time density increases as solar activity increases, and that the density scale height given by CIRA 1965 at heights near 150 km is too low, perhaps by about 20%.