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.     

Atmospheric density from the low altitude satellite 1970-48A: Comparison of orbital decay measurements,accelerometer measurements and atmospheric models

Atmospheric densities have been deduced from high resolution radar-determined orbital decay data and from data obtained from a uniaxial accelerometer flown onboard the low altitude satellite 1970-48A. Data were obtained during late June and early July, 1970. The orbital decay-deduced densities, having an effective 6 hr temporal resolution, were determined at an altitude of 143 km, essentially one-half scale height above perigee. The accelerometer deduced densities at the same altitude were obtained on both the approaching-perigee and leaving-perigee portions of each of fifty-nine orbits. A detailed comparison of the densities derived from both types of data is presented. In general, agreement is very good. A comparison of both types of data has also been made with the Jacchia 1970 and 1971 atmospheric models as well as the new OGO-6 atmospheric model. The Jacchia models display reasonable agreement with the data, but the OGO-6 model is unsuitable as a representation of atmospheric density at this altitude.     

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.     

29Th-order harmonics in the geopotential from the orbit of ariel 1 at 29: 2 resonance

In analysing the orbit of Ariel 1 to determine upper-atmosphere winds, it was observed that the orbital inclination underwent a noticeable perturbation in November 1969 at the 29:2 resonance with the Earth's gravitational field, when the satellite track over the Earth repeats every 2 days after 29 revolutions. The variations in the inclination and eccentricity of the orbit between July 1969 and February 1970 have now been analysed, using 35 US Navy orbits, and fitted with theoretical curves to obtain lumped values of 29th-order harmonic coefficients in the geopotential.     

Motion near frozen orbits as a means for mitigating satellite relative drift

Generally, any initially-close satellites—chief and deputy—moving on orbits with slightly different orbital elements, will depart each other on locally unbounded relative trajectories. Thus, constraints on the initial conditions must be imposed to mitigate the chief-deputy mutual departure. In this paper, it is analytically proven that choosing the chief’s orbit to be a frozen orbit can mitigate the natural relative drift of the satellites. Using mean orbital element variations, it is proven that if the chief’s orbit is frozen, then the mean differential eccentricity is periodic, leading to a periodic variation of the differential mean argument of latitude. On the other hand, if the chief’s orbit is non-frozen, a secular growth in the differential mean argument of latitude leads to a concomitant along-track separation of the deputy from the chief, thereby considerably increasing the relative distance evolution over time. Long-term orbital simulation results indicate that the effect of choosing a frozen orbit vis-à-vis a non-frozen orbit can reduce the relative distance drift by hundreds of meters per day.     

Resonant forcing of Mercury's libration in longitude

The period of free libration of Mercury's longitude about the position it would have had if it were rotating uniformly at 1.5 times its orbital mean motion is close to resonance with Jupiter's orbital period. The Jupiter perturbations of Mercury's orbit thereby lead to amplitudes of libration at the 11.86 year period that may exceed the amplitude of the 88 day forced libration determined by radar. Mercury's libration in longitude may be thus dominated by only two periods of 88 days and 11.86 years, where other periods from the planetary perturbations of the orbit have much smaller amplitudes.     

Analytic characterization of measurement uncertainty and initial orbit determination on orbital element representations

This paper presents an approach to characterize the uncertainty associated with the state vector obtained from the Herrick-Gibbs orbit determination approach using transformation of variables. The approach is applied to estimate the state vector and its probability density function for objects in low Earth orbit using sparse observations. The state vector and associated uncertainty estimates are computed in Cartesian coordinates and Keplerian elements. The approach is then extended to accommodate the $J_2$ perturbation where the state vector is written in terms of mean orbital elements. The results obtained from the analytical approach presented in this paper are validated using Monte Carlo simulations and compared with the often utilized similarity transformation for Kepler, mean, and nonsingular elements. The measurement uncertainty characterization obtained is used to initialize conventional nonlinear filters as well as operate a Bayesian approach for orbit determination and object tracking.     

Photometric properties of outer planetary satellites

We present optical broadband photometry for the satellites J6, J7, J8, S7, S9, U3, U4, N1, and polarimetry for J6, obtained between 1970 and 1979. The outer Jovian satellites resemble C-type asteroids; J6 has a rotational lightcurve with period ～9.5 hr. The satellites beyond Jupiter also show C-like colors with the exception of S7 Hyperion. S9 Phoebe has a rotational lightcurve with period near either 11.25 or 21.1 hr. For U4 and N1 there is evidence for a lightcurve synchronous with the orbital revolution. The seven brighter Saturnian satellites show a regular relation between the ultraviolet dropoff and distance to the planet, probably related with differences in the rock component on their surfaces.     

Analysis of 208 U.S. Navy orbits for the satellite 1970-47B at 14th-order resonance

The orbit of 1970-47B passed very slowly through 14th-order resonance, and the changes in orbital inclination and eccentricity have been analysed over a 4-year period, from January 1977 to January 1981, using 208 U.S. Navy orbits. The analysis has yielded values for three pairs of lumped harmonic coefficients of 14th order, which have accuracies equivalent to 0.4, 1.5 and 2.0 cm in geoid height. Three pairs of values of 28th-order lumped harmonic coefficients were also obtained, and the best of these has a standard deviation (S.D.) corresponding to an accuracy of 0.7 cm in geoid height. The lumped harmonic coefficients have been compared with the corresponding values from the latest geopotential models, and agreement is satisfactory.     

Resonant and non-resonant gravity-gradient perturbations of a tumbling tri-axial satellite

Gravity-gradient perturbations of the attitude motion of a tumbling tri-axial satellite are investigated. The satellite center of mass is considered to be in an elliptical orbit about a spherical planet and to be tumbling at a frequency much greater than orbital rate. In determining the unperturbed (free) motion of the satellite, a canonical form for the solution of the torque-free motion of a rigid body is obtained. By casting the gravity-gradient perturbing torque in terms of a perturbing Hamiltonian, the long-term changes in the rotational motion are derived. In particular, far from resonance, there are no long-period changes in the magnitude of the rotational angular momentum and rotational energy, and the rotational angular momentum vector precesses abound the orbital angular momentum vector.At resonance, a low-order commensurability exists between the polhode frequency and tumbling frequency. Near resonance, there may be small long-period fluctuations in the rotational energy and angular momentum magnitude. Moreover, the precession of the rotational angular momentum vector about the orbital angular momentum vector now contains substantial long-period contributions superimposed on the non-resonant precession rate. By averaging certain long-period elliptic functions, the mean value near resonance for the precession of the rotational angular momentum vector is obtained in terms of initial conditions.     

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.     

Speckle observations with PISCO in Merate – V. Astrometric measurements of visual binaries in 2006

We present relative astrometric measurements of visual binaries made during the first semester of 2006, with the Pupil Interferometry Speckle camera and COronagraph at the 102-cm Zeiss telescope of the Brera Astronomical Observatory, in Merate. Our sample contains orbital couples as well as binaries whose motion is still uncertain. We obtained 217 new measurements of 194 objects, with angular separations in the range 0.1–4.2 arcsec, and an average accuracy of 0.01 arcsec. The mean error on the position angles is 05. About half of those angles could be determined without the usual 180° ambiguity by the application of triple-correlation techniques. We also present a revised orbit for ADS 277 for which the previously published orbit resulted in a large residual from our measurements.     

Gravitational Radiation Damping and Evolution of the Orbit of Compact Binary Stars (Solution by the Second Perturbation Method)

The influence of the gravitational radiation damping on the evolution of the orbital elements of compact binary stars is examined by using the method of perturbation. The perturbation equations with the true anomaly as an independent variable are given. This effect results in both the secular and periodic variation of the semi-major axis, the eccentricity, the mean longitude at the epoch and the mean longitude. However, the longitude of periastron exhibits no secular variation, but only periodic variation. The effect of secular variation of the orbit would lead to collapse of the system of binary stars. The deduced formulae are applied to the calculation of secular variation of the orbital elements for three compact binary stars: PSR19 13 + 16, PSR J0737-3039 and M33X-7. The results obtained are discussed.     

Long-term evaluation of three-dimensional heliocentric solar sail trajectories with arbitrary fixed sail setting

The solar radiation effects upon the orbital behaviour of an arbitrarily shaped spacecraft (or a solar sail in particular) in a general fixed orientation with respect to the local coordinate frame are investigated. Through introduction of a quasi-angle in the osculating plane, the motion of the orbital plane becomes uncoupled from the in-plane perturbations. Exact solutions in the form of conic sections and logarithmic spirals can readily be formulated for certain specific initial conditions. An effective out-of-plane spiral transfer trajectory is obtained by reversing the force component normal to the orbital plane at specified positions in the orbit. By choosing the appropriate control angles for the sail orientation, any point in space can be reached eventually. In the case of general initial conditions, the long-term orbital behaviour is assessed asymptotically by means of the two-variable expansion procedure. An implicit expression for the eccentricity is derived and explicit results are established by an iteration scheme. The other orbital elements can be expressed in terms of the eccentricity and their asymptotic series for near-circular initial orbits are also obtained. While equations for the higher-order contributions as well as the periodic parts of their solutions can be formulated readily, their secular terms are determined only for a circular initial orbit.     

Research on the HIP 18856 binary system

The results of a study on the binary HIP 18856 and construction of its orbit are presented.New observational data were obtained at the BTA of SAO RAS in 2007-2019.Earlier,Cvetkovic et al.constructed the orbit for this system.However,it is based on six measurements,which cover a small part of the orbit.The positional parameters of the ESA astrometric satellite Hipparcos published speckle interferometric data(Mason et al.,Balega et al.,Horch et al.)and new ones were used in this study.Based on the new orbital parameters,the mass sum was calculated and the physical parameters of the components were found.The obtained orbital and fundamental parameters were compared with the data from the study by Cvetkovic et al..The comparison shows that the new orbital solution is better than the old one,since it fits new observational data accurately.Also based on a qualitative evaluation performed by Worley&Heintz,the new orbit was classified as"reliable",which means data cover more than half of the orbit with sufficient quantities of residuals of measurements.     

《大气一号》气球卫星轨道倾角变化分析

引起《大气一号》两颗气球卫星（ＤＱ－１Ａ和ＤＱ－１Ｂ）轨道倾角变化的摄动因素主要是太阳光压摄动、大气旋转和日月引力摄动。太阳光压摄动引起气球卫星轨道倾角增大，平均每天变化约０．００１７，大气旋转引起轨道倾角减小，平均每天变化不到０．０００１，但随着高度下降，变化量亦增大，陨落前达０．００２。本文根据卫星轨道摄动理论，给出气球卫星轨道倾角变化的一种定量分析方法，得到的分析结果为：（１）由太阳光压摄动     

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.     

Analytical solutions to the four post-Newtonian effects in a near-Earth satellite orbit

On the basis of the results by Huang et al. (1990), this paper further discusses and analyses the four post-Newtonian effects in a near-Earth satellite orbit: the Schwarzschild solution, the post-Newtonian effects of the geodesic precession, the Lense-Thirring precession and the oblateness of the Earth. A full analytical solution to the effects including their direct perturbations and mixed perturbations due to the Newtonian oblateness (J ₂) perturbation and the Schwarzschild solution is obtained using the quasi-mean orbital element method analogous to the Kozai's mean orbital element one. Some perturbation properties of the post-Newtonian effects are revealed. The results obtained not only can provide a sound scientific basis for the precise determination of a man-made satellite orbit but also is suitable for similar mechanics systems, such as the motions of planets, asteroids and natural satellites.