Analysis of the orbit of 1970-87a (Cosmos 373)

Cosmos 373, 1970-87A, was launched on 20 October 1970 into an orbit inclined at 62.9° to the Equator, with an initial perigee height of 472 km. The orbit has been determined at 25 epochs covering a period of just over 4 yr using the RAE orbit refinement program PROP, with over 1500 observations. Observations from the Hewitt camera at Malvern were available for all 25 orbits.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. The analysis has resulted in extremely accurate values of e with S.D.'s down to 0.000005 and has indicated an amplitude of the oscillation in eccentricity of 0.0085, equivalent to almost 60 km in perigee height—the largest yet recorded for any near-Earth orbit of high accuracy.     

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.     

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 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 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 1970-97b (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 cosmos 268 rocket (1969-20B)

The orbit of Cosmos 268 rocket (1969-20B) has been determined at 28 epochs during its 342-day life, with the aid of the PROP5 orbit refinement program. All available observations were used, including 16 from the Hewitt camera at Malvern, 28 from the 200-mm camera at Meudon, 56 from the kinetheodolite at the Cape Observatory, 700 visual observations from volunteer observers, 500 US Navy observations and 200 British radar observations. The orbits are of very good accuracy for such a high-drag satellite, most of the values of inclination having standard deviations less than 0.002°. The most accurate orbits are those utilizing photographic observations, and the best of these has standard deviations of 0.00001 in eccentricity and 0.0001° in inclination.

The values of inclination obtained, after correction to allow for the effects of other perturbing forces, have been analysed to determine zonal wind speeds in the upper atmosphere at heights a little above perigee (230–250 km) averaged over latitudes up to about 25°. The results show a clear distinction between the wind at night (21 to 03 hr local time), which is west-to-east with an average speed of 140 ± 50 m/sec, and the wind by day (08 to 17 hr), which is east-to-west with an average speed of 110 ± 50 m/sec.     

The orbit of Cosmos 307 rocket and its use in atmospheric research

About 1500 observations from 46 observing stations were used to determine the orbit of Cosmos 307 rocket (1969-94B) at 25 epochs spread throughout its nine-month orbital life. The determination was made using the RAE computer program for the refinement of orbital parameters, PROP.     

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.     

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.     

Lumped geopotential harmonics of order 29, from analysis of the orbit of Cosmos 837 rocket

The orbit of Cosmos 837 rocket (1976-62E) has been determined at 36 epochs between January and September 1978, using the RAE orbit refinement program PROP 6 with about 3000 observations. The inclination was 62.7° and the eccentricity 0.039. The orbital accuracy achieved was between 30m and 150m, both radial and crosstrack. The orbit was near 29:2 resonance in 1978 (exact resonance occurred on 14 May) and the values of orbital inclination obtained have been analysed to derive lumped 29th-order geopotential harmonic coefficients, namely:

$\text{10}{}^9\text{C}{}^{\mathrm{0,2}}{}_{29}\text{= ? 10 ± 15}$

and

$\text{10}{}^9\text{S}{}^{\mathrm{0,2}}{}_{29}\text{= ?76 ± 12}$

. These will be used in future, when enough results at different inclinations have accumulated, to determine individual coefficients of order 29. The values of lumped harmonics obtained from analysis of the values of eccentricity were not well defined, because of the high correlations between them and the errors in removing the very large perturbation (31 km) due to odd zonal harmonics.     

国际天文联合会第248届讨论会(2007年10月15-19日,上海)

2007年10月15-19日在中国科学院上海天文台举办了国际天文联合会第248届讨论会,题目为"巨大的飞跃:从毫角秒级到微角秒级的天体测量".     

A new orbit of Comet 1961 V (Wilson-Hubbard)

A definitive orbit of Comet 1961 V (Wilson-Hubbard), based on 84 observations, is given.     

Air density at heights near 435 km from the orbit of skylab 1 (1973-27A)

On February 8, 1974, Skylab 1 was manoeuvred into a near circular orbit of inclination 50.04° and perigee near 420km. Orbital parameters have been computed at forty-six epochs thereafter using all available observations. Using these orbital elements, supplemented by orbital decay rates derived from NORAD bulletins, 193 values of air density were determined between 23 February, 1974 and 11, August, 1976. Corrected to a fixed height and normalised with respect to exospheric temperature these values reveal the semi-annual variation, exhibiting maxima in March–April and October–November, and minima in January–February and July–August. For 1974–1976 the July minima are more pronounced than the January minima whilst the April and October maxima appear equal. Overall the variation is greater than that indicated by CIRA 1972.     

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.     

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.     

A preliminary analysis of the orbit of the Mars Trojan asteroid (5261) Eureka

Observations and results of orbit determination of the first known Mars Trojan asteroid (5261) Eureka are presented. We have numerically calculated the evolution of the orbital elements, and have analyzed the behavior of the motion during the next 2 Myr. Strong perturbations by planets other than Mars seem to stabilize the eccentricity of the asteroid by stirring the high order resonances present in the elliptic restricted problem. As a result, the orbit appears stable at least on megayear timescales. The difference of the mean longitudes of Mars and Eureka and the semimajor axis of the asteroid form a pair of variables that essentially behave in an adiabatic manner, while the evolution of the other orbital elements is largely determined by the perturbations due to other planets.     

Analysis of the orbit of ariel 1, 1962-15A,near 15th-order resonance

Ariel 1, the first international satellite, was launched on 26 April 1962, into an orbit inclined at 53.85° to the equator, with an initial perigee height near 390 km. On 8 May 1973 the orbit passed through 15th-order resonance and has been determined, with the RAE orbit refinement program PROP, at eight epochs between February and August 1973 using 500 observations.The orbital inclinations during the time of 15th-order resonance, as given by these eight orbits and 31 U.S. Navy orbits, were fitted with a theoretical curve using the THROE computer program, the best fit giving $\text{10}{}^9\text{C}\text{?}{}_{15}\text{= ?370 ± 14}$ and 10⁹S₁₅ = ?114 ± 31.The values of eccentricity were also successfully fitted using THROE, and the results are discussed.     

Analysis of the orbit of 1971-30B at 15th-order resonance

The orbit of the satellite 1971-30B (Tournesol rocket) has been determined from more than 2000 observations at 34 epochs spaced at 8-day intervals between March and November 1978 when the orbit was experiencing 15th-order resonance. The variations in the orbital inclination, which was near 46.4°, and in the eccentricity, which was near 0.01, have been analysed to determine values of six lumped harmonics of order 15. In view of the fact that the orbit passed through resonance quite rapidly, the results are very satisfactory: the standard deviations of the lumped harmonics correspond to accuracies between 1 and 3 cm in geoid height.