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.     

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.     

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 cosmos 387 (1970-111A) near 15th-order resonance

Cosmos 387 (1970-111A) was launched on 16 December 1970 into a near-circular orbit with an average height of 540 km and an inclination of 74.0°. On 5 November 1971 the orbit, in its slow contraction under the influence of air drag, passed through 15th-order resonance, when the ground track repeats after 15 revolutions. The orbit has been determined with the aid of the RAE orbit refinement program PROP at 19 epochs between May 1971 and June 1972, using 1500 optical and radar observations. The average accuracy is about 70 m in perigee height and 0.001° in inclination.The variation of orbital inclination while the satellite was experiencing 15th-order resonance, as given by these 19 orbits and 55 U.S. Navy orbits, has been analysed to obtain equations accurate to 4 per cent for the geopotential coefficients of order 15 and odd degree (15, 17, 19 …). These equations have subsequently been used (with others) in determining individual coefficients of order 15 and odd degree.The variation of eccentricity with argument of perigee showed unexpected complexity, including a tight loop near resonance (Fig. 4). Analysis of the variation in eccentricity has yielded, for the first time, accurate equations for the geopotential coefficients of order 15 and even degree (16, 18 …), thus opening the way to the evaluation of individual coefficients of this type. The variations in the argument of perigee and right ascension of the node have also been analysed.     

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.     

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.     

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.     

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.     

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.     

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.     

Analysis of the orbit of cosmos 395 rocket (1971-13B) near 15th-order resonance

Cosmos 395 rocket (1971-13B) is moving in a near-circular orbit inclined at 74° to the equator. Its average height, near 540 km after launch in February 1971, slowly decreased under the action of air drag and on 24 March 1972 it experienced exact 15th-order resonance, with the successive equator crossings 24° apart in longitude. Its orbit has been determined at 21 epochs between September 1971 and September 1972 using 1100 observations, including 55 from the Malvern Hewitt camera: the mean S.D. in inclination is 0.001° and in eccentricity 0.00001.The variations in inclination i, eccentricity e, right ascension of the node $\text{Ω}$, and argument of perigee ω, near 15th-order resonance are analysed to determine values of lumped 15th-order harmonic coefficients in the geopotential. The inclination yields equations accurate to 4 per cent for coefficients of order 15 and degree 15,17,19..., which are in excellent agreement with those from Cosmos 387 (1970-111A) in an orbit of similar inclination but different resonant longitude. Analysis of the variations in e gives two pairs of equations for the coefficients of order 15 and degree 16, 18..., which are used to obtain tentative values of the (16,15) coefficients. For the first time the resonant variation of other elements ($\text{Ω}\text{and}\text{ω}$) has also been analysed with partial success.     

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.     

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.     

Air density at a height of 128 km,form visual observations of 1972-25g

655 visual observations of 1972-25G, Molniya 1V Rocket, were made when its perigee height was below 130 km, and have been used to determine its orbit at 17 epochs between 5 November 1973 and 24 February 1974 and obtain almost daily values of its rate of decay. These give 52 values of atmospheric density with a relative accuracy of 1 % at a height of 128 km in latitudes 55–65°S. Day-to-day variations correlated with geomagnetic activity of up to 10% are found, plus an irregular semi-annual variation of amplitude 10%. The decrease in inclination has been measured accurately enough to enable the mean atmospheric rotation rate to be determined over the same time-span.     

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.     

Upper-atmosphere rotation rate,from analysis of the orbit of 1970-43B

The orbit of Cosmos 347 rocket (1970-43B) has been determined in the form of 23 sets of orbital elements at intervals during its 8-month life, with the aid of the RAE orbit improvement program PROP, using about 850 observations from 47 observing stations. The values of orbital inclination obtained, which had standard deviations between 0.7 and 10 sec of arc, were analysed to give a mean atmospheric rotation rate of 1.40 ± 0.05 rev/day at a mean height near 240 km, for dates between July and December 1970, and local times ranging from 1800 hr to midnight to 0900 hr. This value is higher than those obtained from other satellites at similar heights.     

Analysis of the orbit of Cosmos 72 (1965-53B) near 15th-order resonance

Cosmos 72 (1965-53B) was launched on 16 April 1965 into a near-circular orbit with an average height of 570 km and inclination 56°. Over the years, the orbit has contracted slowly under the influence of air drag, and On 27 June 1972 passed through exact 15th-order resonance, when successive equator crossings are 24° apart in longitude and the ground track repeats after 15 rev. The orbit has been determined at seven epochs between April 1972 and February 1973, using the RAE orbit refinement program PROP, with 544 optical and radar observations: the average orbital accuracy is about 50 m in height and 0.0008° in inclination.For Cosmos 72 the change in inclination at 15th-order resonance, due to perturbations by 15th-order harmonics in the geopotential, is greater than for any satellite previously analysed— nearly 0.07°—and analysis of the change, using the seven PROP orbits and 45 U.S. Navy orbits, yields equations accurate to 4 per cent for the geopotential coefficients of order 15 and odd degree (15, 17, 19 …). A similar analysis of the variation in eccentricity gives less accurate equations for coefficients of order 15 and even degree (16, 18 …). The variations in right ascension of the node and argument of perigee have also been analysed.     

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.     

Variations in air density,satellite drag coefficient and atmospheric rotation rate from analysis of the orbit of 1966-92D

Variations in air density, the satellite drag coefficient, and the atmospheric rotation rate at 60°S lat and 120–130 km height during the period September 1968–June 1969 have been determined from analysis of the high-eccentricity orbit of the 4th Molyniya 1 upper-stage rocket body, 1966-92D. The results show good correlation between density increases and strong geomagnetic activity, although solar flares of equal geomagnetic index value do not consistently produce density changes of equal magnitude. A 30 per cent semi-annual variation was observed, but there was no indication of the 50 per cent lower thermosphere seasonal-latitudinal variation that was predicted from the CIRA 1972 atmosphere. The satellite drag coefficient was observed to begin decreasing with height at an altitude where the molecular mean free path, λ, was twice the satellite's length. The coefficient decreased to a value approaching 1.0 as the satellite's perigee height fell below the altitude where λ was one-half the length. A mean atmospheric rotation rate of 1.1 ± 0.1 Earth rot/day was obtained for the last 20 days of decay. However, variations were observed with west-to-east wind speeds of ?100 m/sec measured for a local time of 13 hr.