Orbit determination and analysis for Cosmos 482 from 1978 to 1981

The orbit of the satellite Cosmos 482 (1972-23A) has been determined at 77 epochs between 8 November 1977 and 18 April 1981 from 5650 optical and radar observations. The computations were made with the RAE orbit determination program PROP 6, and an average accuracy of 150 m radial and cross-track was achieved.Cosmos 482 was a high-drag satellite in an eccentric orbit and, between the first epoch and the last, the orbital period decreased from 157 to 94 min, the eccentricity decreased from 0.32 to 0.04, and the orbital inclination decreased from 52.14° to 51.95° due to the transverse forces caused by atmospheric rotation. The orbit was therefore ideal for determining the atmospheric rotation rate from the decrease in inclination, and seven accurate values of rotation rate have been obtained. The new values strengthen the existing overall picture of upper-atmosphere winds, and are generally in good accord with the previous results.An improved equation has been derived for calculating density scale height H from the decrease in perigee distance, and has been applied to determine seven values of H. The corresponding values of H from the COSPAR International Reference Atmosphere are on average 5% lower than the observational values, for 1980–1981.     

The orbit of 1972-05b in its final phase,with geophysical inferences

The polar orbit of HEOS 2 second-stage rocket, 1972-05B, has been determined on each of the final 16 days before its decay in September 1978, using the RAE orbit refinement program, PROP 6, with about 1360 observations. An accuracy of 30–70 m, both radial and across track, was achieved.Eleven values of density scale height have been determined from the decrease in perigee height, with a 2% error; seven of these values are within 6% of the CIRA 1972 reference-atmosphere values, the rms value being 4% higher than CIRA.The rotation rate of the upper atmosphere, A, was determined from the decrease in orbital inclination as Λ = 1.40 ± 0.05 rev day^?1; i.e. a strong west-to-east zonal wind of 160 ± 20m s^?1, at a mean height of about 240 km. The local time was 01–02 h; solar activity was high; and the latitude of perigee moved steadily from 10°N to 67°S.     

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.     

Upper-atmosphere zonal winds determined from orbital analysis of Cosmos 482, 1972-23A

The orbit of Cosmos 482 has been determined at 55 epochs during the period August 1975–October 1977. Inclined at 52° to the Equator, of eccentricity exceeding 0.3 and perigee height near 210 km, this high drag and high eccentricity orbit is the most eccentric as yet analysed by PROP. The combination of the orbital characteristics, restricted global coverage of observational data, and the many observations of angular measurement at extreme range proved to be troublesome. Cleared of other perturbations, the inclination is analysed to determine the atmospheric rotation rate, λ rev day^?1, of the zonal winds at a height near 235 km. Results reveal a diurnal and seasonal dependence, including a summer value, averaged over local time, of λ = 0.9 and an evening value of λ = 1.4 in the winter months. The resultant wind velocities vary between 48 m s^?1 East to West and 193 m s^?1 West to East, with an average of 48 m s^?1 West to East.     

Determination of zonal wind speeds at heights near 530 km from the orbit of Explorer 24 (1964-76A)

The orbit of Explorer 24 (1964–1976A) has been determined at 18 epochs during the five month period prior to its decay in October 1968, using the RAE orbit refinement computer program PROP6. As a balloon, the satellite was strongly influenced by atmospheric perturbations, despite its high perigee altitude near 490 km. It therefore provided an opportunity of determining atmospheric rotation rates at high altitude. The rotation rate, Λ rev day^?1, was estimated from the observed variation in orbital inclination, after the removal of perturbations including those due to solar radiation pressure.The mean rotation rates, averaged over local time, are Λ = 0.98 for 18 May to 18 August 1968 at 542 km; Λ = 1.06 for 18 May to 13 October 1968 at 533 km.For morning conditions, Λ = 0.9 for 22 June to 20 July 1968 at 540 km; Λ = 0.8 during September 1968 at 513 km.For evening conditions, Λ = 1.1 for 18 May to 15 June 1968, and for 26 July to 7 September 1968, at 540 km and 536 km respectively; Λ = 1.3 for 28 September to 13 October 1968 at 484 km.Further, the maximum W to E zonal wind has been estimated to occur at 20.5 h local time, during the period of the analysis.     

Analysis of the orbit of 1970-97b (cosmos 378 rocket)

Cosmos 378 rocket, 1970-97B, entered orbit on 17 November 1970, with orbital inclination 74.0°, period 105 min and perigee height 230 km, and decayed on 30 September 1972 after 683 days in orbit. The RAE computer program PROP was used, with more than 1900 observations from 64 stations, to determine the orbit at 39 epochs between February 1971 and September 1972.The main aim of the analysis was to determine the atmospheric rotation rate from the decrease in orbital inclination, which was determined with a mean standard deviation of 0.0010° and a best standard deviation of 0.0003°. After removal of relevant perturbations, analysis of the variation in inclination between July 1971 and April 1972 yields the surprisingly low average atmospheric rotation rate of 0.75 ± 0.05 rev/day, at a mean height of 250 km. The local time at perigee is however strongly biassed towards daytime values (07–16 hr), so the results lend support to the picture of east-to-west winds by day and west-to-east winds by night.Values of scale height are obtained by analysis of the change in perigee height.     

Analysis of the orbit of 1965-11D (COSMOS 54 rocket)

The satellite 1965-11D was the final-stage rocket used to launch Cosmos 54, 55 and 56 into orbit on 21 February 1965. The orbit of 1965-11D was inclined at 56° to the Equator, with an initial perigee height of 280 km; the lifetime was nearly 5 yr, with decay on 23 December 1969. The orbit has been determined at 75 epochs during the life, using the RAE orbit determination program PROP with over 4000 observations, photographic, visual and radar. Observations from the Hewitt camera at Malvern were available for 34 of the 75 orbits and typical accuracies for these orbits are 0.0005° in inclination and 100 m in perigee height.The variations in perigee height have been analyzed to determine reliable values of density scale height, at heights between 240 and 360 km. The analysis also revealed a rapid decrease of 5 km in perigee distance early in 1966, attributed to the escape of residual propellants.The variations in orbital inclination have been analyzed to determine upper-atmosphere zonal winds and 15th-order harmonics in the geopotential. The region of the upper atmosphere traversed by 1965-11D near its perigee is found to have had an average rotation rate of 1.10 ± 0.05 rev/day in 1966–1967, and 1.00 ± 0.03 rev/day between March 1968 and May 1969. In late 1969 there were probably wide variations in zonal winds, with east-to-west winds of order 100 m/s followed by west-to-east winds of order 200 m/s. The changes in inclination at the 15th-order resonance in July 1969 have been analyzed to give the first accurate values of lumped 15th-order harmonics obtained from a high-drag satellite. This success points the way towards similar analyses of the many other high-drag satellites that pass through 15th-order resonance, to evaluate individual geopotential coefficients of order 15 and even degree.     

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.     

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.     

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.     

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.     

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.     

The determination and analysis of the orbit of NIMBUS 1 ROCKET, 1964-52B: Part 1: The orbits

Orbital parameters of the satellite NIMBUS 1 ROCKET (1964-52B) have been determined at 285 epochs using about 14,500 optical and radar observations during the last 2233 days of its life. 1964-52B was in an orbit inclined at about 98.7° to the Equator and it decayed on 13 August 1974. The orbital elements were found using the RAE orbit refinement program PROP 6 giving average orbital accuracies in perigee height and inclination at 110 m and 0.002° respectively.     

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.     

Analysis of the orbit of 1970-114F in its last 20 days

The satellite 1970-114F, the final-stage rocket of the Molniya 1S communications satellite, decayed in the atmosphere on 3 March 1973. During the last 20 days of its life the orbit suffered exceptionally rapid decay, with the apogee height decreasing from 7000 to 1000 km while the perigee height remained near 110 km. About 650 observations, made by visual observers in Britain and by U.S. Navy sensors, have been used with the PROP6 orbit refinement program to determine orbits at 14 epochs. Although the decay rate was more than ten times greater than in any previous orbit determination with PROP, good orbits were obtained, the standard deviation in inclination being less than 0.002° on eight orbits.The combination of high drag and good accuracy allows three techniques in orbital analysis to be successfully applied for the first time. Since zonal winds have little effect on the orbit, the changes in inclination are analysed to determine meridional winds near perigee, at heights of 110–120 km, latitudes of 63–65°S, and 6–12 hr LT. The changes in right ascension of the node are also successfully analysed for the same purpose. The two methods agree in indicating a south-to-north wind of 40 ± 30 m/sec from 11 to 21 February, a geomagnetically quiet period, and a south-to-north wind averaging 150 ± 30 m/sec from 22 February to 3 March, a geomagnetically disturbed period. Thirdly, the changes in the argument of perigee are analysed to determine atmospheric oblateness, which is found to be equal to the Earth's oblateness, to within ±20%. Lastly, the drag coefficient in transition flow is evaluated and found to be 0.85 ± 0.20.     

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.     

Upper-atmosphere rotation rate from analysis of the orbital inclination of explorer 1

Explorer 1, 1958α, ths first U.S. artificial satellite, was launched on 1 February 1958 and remained in orbit for 12 years. In this paper theoretical curves have been fitted to the values of inclination, giving three values of the average atmospheric rotation rate at heights of 350–400 km, and latitudes 0–20°:

     

20.

Analysis of the orbital inclination of Tansei 3 rocket 1977-12B     

P. Moore 《Planetary and Space Science》1984,32(9):1101-1109

The orbit of Tansei 3rocket(1977-12B) has been determined at 47 epochs between 1 October 1977 and 19 March 1979 using over 1700 observations and the RAE orbit refinement program PROP6. The rate of change of the inclination was examined to evaluate values of the atmospheric rotation rate, Λ rev day^?1. Analysis yielded the value Λ = 1.1 ± 0.05 at height 315 ± 30 km, average conditions; or alternatively Λ = 1.1 ± 0.1 at height 347 ± 12 km, slight winter bias and Λ = 1.07 ± 0.1 at height 270 ± 18 km, average conditions, supplying further evidence of a decrease in rotation rates from the 1960s to the 1970s.Analysis of the inclination at 15th-order resonance yielded the lumped harmonic values

$\text{10}{}^9\text{C}{}^{\mathrm{0,1}}{}_{15}\text{= 13.4 ± 6.2, 10}{}^9\text{S}{}^{\mathrm{0,1}}{}_{15}\text{= 0.7 ± 13.3}$

for inclination 65.485°.     

Feb 1958 to mid 1960	1.5 rev/day
Mid 1960 to Dec 1967	1.2 rev/day
Jan 1968 to Mar 1970	1.3 rev/day

Analysis of the orbital inclination of Tansei 3 rocket 1977-12B

The orbit of Tansei 3rocket(1977-12B) has been determined at 47 epochs between 1 October 1977 and 19 March 1979 using over 1700 observations and the RAE orbit refinement program PROP6. The rate of change of the inclination was examined to evaluate values of the atmospheric rotation rate, Λ rev day^?1. Analysis yielded the value Λ = 1.1 ± 0.05 at height 315 ± 30 km, average conditions; or alternatively Λ = 1.1 ± 0.1 at height 347 ± 12 km, slight winter bias and Λ = 1.07 ± 0.1 at height 270 ± 18 km, average conditions, supplying further evidence of a decrease in rotation rates from the 1960s to the 1970s.Analysis of the inclination at 15th-order resonance yielded the lumped harmonic values

$\text{10}{}^9\text{C}{}^{\mathrm{0,1}}{}_{15}\text{= 13.4 ± 6.2, 10}{}^9\text{S}{}^{\mathrm{0,1}}{}_{15}\text{= 0.7 ± 13.3}$

for inclination 65.485°.