H. Hiller

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

Abstract 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 Orbit of 1970-97B (Cosmos 378 Rocket).

Abstract 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.

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

Abstract 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. The values of orbital inclination obtained, which had standard deviations down to 0.4 second of arc, were adjusted to account for various perturbations and then used to find the mean rotational speed of the Earths atmosphere to give Λ = 1.06 ± 0.04 rev/day at a mean height of 240 km. Values of density scale height of the upper atmosphere for 1969–1970 were calculated from the change in perigee distance, and found to increase from 31 km at 210 km altitude to 53 km at 270 km altitude. The rms scatter in scale height is about 4 km.

Upper-Atmosphere Rotation Rate Determined from the Orbit of China 6 Rocket (1976-87B).

The orbit of CHINA 6 rocket, 1976-87B, has been determined at 51 epochs during its 17-month life, using the RAE orbit refinement computer program, PROP 6, with over 4000 radar and optical observations from 49 stations. The orbital accuracy is about 100 m, radial and cross-track, on average. The rotation rate of the upper atmosphere, Λ rev/day, for the height-band 200–230 km, was calculated from the decrease in orbital inclination (after being cleared of perturbations) to give the following results: 1. (1) for morning conditions, Λ = 0.9 for May–June and August–September 1977, at 215km mean height; Λ = 0.7 for October–November 1977, at 210km; Λ = 0.8 ± 0.05 for January–February 1978, at 200 km; 2. (2) for evening conditions, Λ = 1.2 for July and September–October 1977, at 215 km; 3. (3) for mean (morning plus evening) conditions, Λ = 1.0 ± 0.1 between October 1976 and May 1977, at 230 km; Λ = 0.8 ± 0.1 for December 1977 to January 1978, at 215 km and mean latitude 57°S. Values of density scale height have been obtained from the variation in perigee height, including several values during the final 16 days to decay. Comparison with CIRA 1972 values shows agreement mostly within 10%.

Features of the Upper Atmosphere Revealed by Analysis of the Orbit of Cosmos 1009 Rocket, 1978-50B.

Abstract 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 1 2 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.

The orbit of proton 4 redetermined, with geophysical implications

Abstract The orbit of Proton 4, 1968-103A, has been redetermined, in greater detail and with better accuracy, in order to clarify previously puzzling features in the variation of orbital inclination. Orbital parameters have been determined at 25 epochs between December 1968 and July 1969, using about 1600 optical and radar observations with the RAE orbit refinement program PROP 6. During January 1969 the orbit passed through 31:2 resonance—when the ground track over the Earth repeats every two days after 31 revolutions of the satellite. A simultaneous least-squares fitting of theoretical curves to the values of inclination and eccentricity between 14 December 1968 and 6 March 1969 has yielded values for two pairs of lumped 31st-order geopotential coefficients, appropriate to an inclination of 51.5°. This is the first specific evaluation of 31st-order coefficients. The 15 values of inclination after the resonance, from March to near decay in July 1969, have been used to determine mean, morning and afternoon-evening values for the rotation rate of the atmosphere at a height near 260 km; the values of rotation rate, namely 1.1, 0.9 and 1.3 rev/day respectively, confirm the trends already established from analysis of other satellite orbits.

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

Abstract 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.

Optimum impulsive transfers between elliptic and non-coplanar circular orbits

Abstract A study has been made of optimum transfers between elliptic and non-coplanar circular orbits having a common centre of attraction and whose planes intersect along the major axis of the ellipse. Elliptic transfer paths with up to three apsidal impulses are considered, with the whole plane change taking place at the (coincident) apocentres of these paths. For three-impulse transfers, the optimum mode is always to transfer from the pericentre of the elliptic orbit to the circular orbit, or vice-versa. For the two-impulse “tilted-Hohmann” type of transfer, the optimum mode for the ellipse-in-circle arrangement of initial and final orbits is also to transfer from pericentre to circle; but the optimum mode is from apocentre to circle for both the circle-in-ellipse and overlap arrangements.

Equations for 15th-Order Geopotential Coefficients from the Orbit of Transit 1B.

Abstract The RAE computer program PROP has been used to re-determine in greater detail the orbit of satellite Transit 1B, 1960 γ 2, using a modified method on occasions when the number of observations was previously thought to be too few to determine the orbit. The satellite had an oibital inclination of about 51°, and it was found possible to determine inclination accurately using only a small number of visual observations from latitudes near 51°N. The main object of the study is to investigate the region of 15th-order resonance revealed by a steep decrease in inclination of about 0.04° between March and November 1962. The analysis leads to the following equations for the 15th-order geopotential coefficients: 0.56 C 17,15 − C 19,15 + 0.74 C 21,15 = (36 ± 4) × 10 −9 and 0.56 S 17,15 − S 19,15 + 0.74 S 21,15 = (35 ± 6) × 10 −9 In addition, an improved value has been obtained for the average rotation rate Λ of the upper atmosphere at a mean height of 380 km between 1963 and 1967, namely Λ = 1.35 ± 0.10 rev/day

Optimum impulsive transfers between non-coplanar elliptic orbits having collinear major axes☆

Abstract The total characteristic velocity has been optimised for impulsive transfers between non-coplanar elliptic orbits having a common centre of attraction and collinear major axes in the same sense. Up to three apsidal impulses have been considered with the whole plane change occurring at the (coincident) apocentres of the semi-elliptic (Hohmann-type) transfer paths. For three-impulse transfers, the optimum mode is to transfer between pericentres of the initial and final elliptic orbits. For two-impulse (tilted-Hohmann) transfers, the optimum mode is to transfer from the pericentre of the inner ellipse to the apocentre of the outer ellipse; for overlap configurations of initial and final elliptic orbits, optimum transfers from one ellipse to another with larger pericentric distance are from apocentre to pericentre.