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1.
The method applied since 1996 for the analysis of the orbital residuals of the LAGEOS satellites in order to measure the Lense-Thirring effect has been the subject of the present work. This method, based on the difference between the orbital elements of consecutive arcs, is explained and analysed also from the analytical point of view. It is proved that this “difference method” works well for the determination of the secular effects, as in the case of the relativistic precession induced by the Earth's angular momentum, but also very useful for the determination and study of the long-term periodic effects. Indeed, the only limitation in the determination of the periodic effects is the possibility of the reduction of their amplitude by a factor which depends from the periodicity of the given perturbation and from the orbital arc length chosen for the satellite during the data analysis. In the case of the Yarkovsky-Schach effect, the main non-gravitational perturbation seen in the LAGEOS satellites orbital residuals, in particular in its perigee rate and eccentricity vector excitation residuals, we show that the “difference method” is quite good also for the determination of the long-period perturbations induced by this subtle non-conservative force. 相似文献
2.
David M. Lucchesi 《Celestial Mechanics and Dynamical Astronomy》2004,88(3):269-291
We propose a new analytical theory to explain the physical cause of the asymmetric reflectivity effect observed for the LAGEOS satellites. To achieve this result we have modelled the reflection of the Sun visible light from the four germanium Cube-Corner-Retroreflectors of these satellites. The position of the Cube-Corner-Retroreflectors play a crucial role in defining the characteristics of the effect and its impact in the satellites orbit. With this new approach we have been able to reproduce the temporal variation of the asymmetric reflectivity effect acceleration for LAGEOS, and to determine the main characteristic of the effect in the case of LAGEOS II. When considering the orbital elements, we have been able to reproduce the time evolution of LAGEOS eccentricity vector excitations and perigee rate. In the case of LAGEOS II, the asymmetric reflectivity effect need to be modelled with an analytical expression different from that previously introduced for LAGEOS.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
3.
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. 相似文献
4.
R. R. Allan 《Planetary and Space Science》1967,15(12):1829-1845
For a satellite in a nominally circular orbit at arbitrary inclination whose mean motion is commensurable with the Earth's rotation, the dependence of gravity on longitude leads to a resonant variation in eccentricity as well as the long-period oscillation in longitude. Provided forces capable of processing perigee are present, it is shown that the change in eccentricity for a satellite captured in librational resonance is not secular but periodic.
There are corresponding resonance effects for a satellite in a nominally equatorial but eccentric orbit. Here the commensurability condition is that the longitudes of the apses shall be nearly repetitive relative to the rotating Earth. There will be a long-period oscillation in longitude which can take the form of either a libration (trapped) or a circulation (free), and there will also be an oscillation of the orbital plane having the same period as the precession of perigee relative to inertial space. 相似文献
5.
Florent Deleflie Gilles Métris Pierre Exertier 《Celestial Mechanics and Dynamical Astronomy》2006,94(1):83-104
This paper studies the long period variations of the eccentricity vector of the orbit of an artificial satellite, under the
influence of the gravity field of a central body. We use modified orbital elements which are non-singular at zero eccentricity.
We expand the long periodic part of the corresponding Lagrange equations as power series of the eccentricity. The coefficients
characterizing the differential system depend on the zonal coefficients of the geopotential, and on initial semi-major axis,
inclination, and eccentricity. The differential equations for the components of the eccentricity vector are then integrated
analytically, with a definition of the period of the perigee based on the notion of “free eccentricity”, and which is also
valid for circular orbits. The analytical solution is compared to a numerical integration. This study is a generalization
of (Cook, Planet. Space Sci., 14, 1966): first, the coefficients involved in the differential equations depend on all zonal coefficients (and not only on
the very first ones); second, our method applies to nearly circular orbits as well as to not too eccentric orbits. Except
for the critical inclination, our solution is valid for all kinds of long period motions of the perigee, i.e., circulations
or librations around an equilibrium point. 相似文献
6.
The heating of a spinning artificial satellite by natural radiation sources such as the Sun and the Earth results in temperature gradients arising across the satellite's surface. The corresponding anisotropic emission of thermal radiation leads to a recoil force, commonly referred to as “thermal force”. A quantitative theory of this effect is developed, based on more general assumptions than used so far, to model such radiation forces on spherically symmetric LAGEOS-like satellites. In particular, the theory holds for any ratio of the three basic timescales of the problem: the rotation period of the satellite, the orbital period around the Earth, and the relaxation time for the thermal processes. Thus, the simplifying assumption of a comparatively fast rotational motion is avoided, which will fail for LAGEOS within the next decade, owing to magnetic dissipation effects. A number of predictions about the future behaviour of non-gravitational long-term orbital perturbations of LAGEOS become possible with the new theory. In particular the Yarkovsky-Schach thermal force effects are studied arising as a consequence of the solar radiation flux onto the satellite, periodically interrupted by eclipses. Starting on about year 2005, the orbital perturbation effects predicted by the new theory are substantially different from those inferred in the fast-rotation case. This holds not only for the long-term semimajor axis effects, but also for eccentricity and inclination perturbations. 相似文献
7.
Michael E. Hough 《Celestial Mechanics and Dynamical Astronomy》1981,25(2):137-157
The long period dynamics of Sun-synchronous orbits near the critical inclination 116.6° are investigated. It is known that, at the critical inclination, the average perigee location is unchanged by Earth oblateness. For certain values of semimajor axis and eccentricity, orbit plane precession caused by Earth oblateness is synchronous with the mean orbital motion of the apparent Sun (a Sun-synchronism). Sun-synchronous orbits have been used extensively in meteorological and remote sensing satellite missions. Gravitational perturbations arising from an aspherical Earth, the Moon, and the Sun cause long period fluctuations in the mean argument of perigee, eccentricity, inclination, and ascending node. Double resonance occurs because slow oscillations in the perigee and Sun-referenced ascending node are coupled through the solar gravity gradient. It is shown that the total number and infinitesimal stability of equilibrium solutions can change abruptly over the Sun-synchronous range of semimajor axis values (1.54 to 1.70 Earth radii). The effect of direct solar radiation pressure upon certain stable equilibria is investigated. 相似文献
8.
Doreen M.C. Walker 《Planetary and Space Science》1980,28(11):1059-1072
Samos 2, 1961 α 1, launched on 31 January 1961, was the first satellite to enter a sun-synchronous orbit at an inclination of 97.4°. The initial perigee and apogee heights were 474 km and 557 km respectively, the initial period was 94.97 min and the satellite decayed on 21 October 1973 after more than 12 years in orbit.Samos 2 passed through the condition of 31 : 2 resonance in June 1971 and orbital parameters have been determined at 22 epochs from 1674 observations using the RAE orbit refinement program, PROP, between mid-April and Mid-September 1971. The variations of inclination and eccentricity during this time have been analysed and values for six lumped 31st-order harmonic coefficients in the geopotential have been obtained. These have been compared with those derived from the individual coefficients, of order 31 and appropriate degrees, from the most recent Goddard Earth Model, GEM 10C.The decrease in inclination between launch and 1971 has been examined: it is found to be caused mainly by a near-resonant solar gravitational perturbation. 相似文献
9.
Ram Krishan Sharma 《Celestial Mechanics and Dynamical Astronomy》1993,56(4):503-521
Analytical theory for short-term orbit motion of satellite orbits with Earth's zonal harmonicsJ
3 andJ
4 is developed in terms of KS elements. Due to symmetry in KS element equations, only two of the nine equations are integrated analytically. The series expansions include terms of third power in the eccentricity. Numerical studies with two test cases reveal that orbital elements obtained from the analytical expressions match quite well with numerically integrated values during a revolution. Typically for an orbit with perigee height, eccentricity and inclination of 421.9 km, 0.17524 and 30 degrees, respectively, maximum differences of 27 and 25 cm in semimajor axis computation are noted withJ
3 andJ
4 term during a revolution. For application purposes, the analytical solutions can be used for accurate onboard computation of state vector in navigation and guidance packages. 相似文献
10.
Victor J. Slabinski 《Celestial Mechanics and Dynamical Astronomy》1996,66(2):131-179
We report the results of detailed numerical calculations of the thermal thrust on the rapidly-spinning LAGEOS spacecraft. This thrust results from anisotropic emission of thermal radiation from its surface. LAGEOS is a good test case for such calculations because of its relatively simple structure and because precise orbit determinations based on laser ranging give observed thrust effects for comparison.The numerical integration includes the varying heating over spacecraft-surface latitude from earth infrared radiation (for the earth-Yarkovsky force) and the varying solar heating as the spacecraft moves in and out of the earth's shadow (for the solar-Yarkovsky force). The computation allows for the poor thermal coupling between the spacecraft structure and individual surface elements (the fused-silica cube-corner reflectors and their aluminum retainer rings), and the poor conduction between structural hemispheres.A Fourier analysis of the computed force with respect to orbital longitude gives the important frequency components for the computation of long-term orbit perturbations. Empirical formulas fit to the numerical results accurately express the component amplitudes as simple functions of spin axis orbital latitude, the sun aspect angle from the spin axis, and the fraction of the orbit period spent in the earth's shadow. These results. based on first principles, are similar to those from simplified theories of the thermal thrust. but add the following new feature: The decrease in orbit-averaged satellite temperature when the orbit intersects the earth's shadow decreases the earth-Yarkovsky drag by 0.14 pm/s2 from the no-eclipse value.The development of spacecraft-element thermal parameters is the most difficult part of the analysis; the paper tabulates the parameters that should be directly measured before the launch of future geodynamic satellites. 相似文献
11.
D.G. King-Hele 《Planetary and Space Science》1974,22(4):509-524
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. 相似文献
12.
A new nonsingular analytical theory for the motion of near Earth satellite orbits with the air drag effect is developed for long term motion in terms of the KS uniformly regular canonical elements by a series expansion method, by assuming the atmosphere to be symmetrically spherical with constant density scale height. The series expansions include up to third order terms in eccentricity. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. Numerical comparisons of the important orbital parameters semi major axis and eccentricity up to 1000 revolutions, obtained with the present solution, with KS elements analytical solution and Cook, King-Hele and Walker's theory with respect to the numerically integrated values, show the superiority of the present solution over the other two theories over a wide range of eccentricity, perigee height and inclination. 相似文献
13.
A method of realtime autonomous orbit determination for earth satellites using the extended Kalman filtering is proposed. The observed quantities are: the satellite-sun direction vector measured by a sun sensor, the satellite-earth and satellite-moon direction vectors measured by an ultraviolet sensor, and the geocentric distance measured by a radar altimeter. At the same time the satellite attitude to the earth is also determined. Results of our simulation of the autonomous orbit determination show that the precision of the orbit determinations is better than 200 m. The effects of the sampling period, orbital inclination, orbital eccentricity and orbital altitude on the precision of orbit determination are analyzed and compared, and certain principles helpful for improving the precision of orbit determination are suggested. 相似文献
14.
We investigated the motion of the Earth's artificial satellite Interball‐1 by using a method suitable for the computation of large eccentricity orbits. Though the measured and the computed orbital elements differ from each other within the measured error bound, we found a slight tendency for secular decreasing in the semi‐major axis, caused probably by electromagnetic drag. We analysed the dominant role of the Moon in the variations of the orbital eccentricity, leading to zero perigee height and the end of the lifetime of the satellite. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
Using the new generation Earth’s gravity field models EIGEN-2S, GGM01S and EIGEN-GRACE02S generated by the space missions CHAMP and GRACE, we have obtained an accurate measurement of the Lense–Thirring effect with the LAGEOS and LAGEOS II satellites analyzing about 10 years of data with the EIGEN-2S and GGM01S models and about 11 years of data with EIGEN-GRACE02S. This new analysis is in agreement with our previous measurements of the Lense–Thirring effect using the LAGEOS satellites and obtained with the JGM-3 and EGM96 Earth’s models. However, the new determinations are more accurate and, especially, more robust than our previous measurements. In the present analysis we are only using the nodal rates of the two satellites, making no use of the perigee rate, as in our previous analyses. The perigee is affected by a number of non-gravitational perturbations difficult to be modelled and whose impact in the total error budget is not easy to assess. Using the EIGEN-2S model, we obtain a total error budget between 18% and 36% of the Lense–Thirring effect due to all the error sources. Specifically, by using EIGEN-2S, we obtain: μ = 0.85, with a total error between ±0.18 and ±0.36, with GGM01S we get μ = 1.06 with a total error between ±0.19 and ±0.24 and with EIGEN-GRACE02S we obtain μ = 0.99, with a total error between ±0.05 and ±0.1, i.e., between 5% and 10% of the general relativistic predicted value of the Lense–Thirring effect. In addition to the analyses using EIGEN-2S, GGM01S and EIGEN-GRACE02S without the use of the perigee, we have also performed an analysis using the older model EGM96 with our previous method of combining the nodes of the LAGEOS satellites with the perigee of LAGEOS II. However, this analysis was performed over a period of about 10 years, i.e. about 2.5 times longer than any our previous analysis. The result using EGM96 over this longer period of observation agrees with our previous results over much shorter periods and with the EIGEN-2S, GGM01S and EIGEN-GRACE02S measurements of μ. In addition to the accurate determination of frame-dragging and in agreement with our previous analyses of the orbits of the LAGEOS satellites, we have observed, since 1998, an anomalous change in the Earth quadrupole coefficient, J2 which agrees with recent findings of other authors. This anomalous variation of J2 is accurately observed both on the node of LAGEOS and LAGEOS II and it is independent of the model used, i.e., it is observed by using the model EGM96 or by using EIGEN-2S, GGM01S or EIGEN-GRACE02S. However, this anomalous variation of the Earth quadrupole coefficient does not affect at all our determination of the Lense–Thirring effect thanks to the total elimination of the J2-induced errors with our especially devised estimation technique. 相似文献
16.
Xavier James Raj 《Planetary and Space Science》2009,57(11):1312-1320
A new non-singular analytical theory for the motion of near-Earth satellite orbits with the air drag effect is developed in terms of uniformly regular KS canonical elements. Diurnally varying oblate atmosphere is considered with variation in density scale height dependent on altitude. The series expansion method is utilized to generate the analytical solutions and terms up to fourth-order terms in eccentricity and c (a small parameter dependent on the flattening of the atmosphere) are retained. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. The important drag perturbed orbital parameters: semi-major axis and eccentricity are obtained up to 500 revolutions, with the present analytical theory and by numerical integration over a wide range of perigee height, eccentricity and inclination. The differences between the two are found to be very less. A comparison between the theories generated with terms up to third- and fourth-order terms in c and e shows an improvement in the computation of the orbital parameters semi-major axis and eccentricity, up to 9%. The theory can be effectively used for the re-entry of the near-Earth objects, which mainly decay due to atmospheric drag. 相似文献
17.
HUANG Yong HU Xiaogong HUANG Cheng 《中国科学院上海天文台年刊》2005,(1):14-21
从解析形式出发,利用月球重力场模型JGL165P1,分析了月球重力场(带谐项)对绕月低轨卫星的长期影响。为了减少计算误差,保证计算精度,在分析解中使用循环公式来计算倾角函数。结果指出对于一个高度为100km的极月轨道卫星,冻结轨道存在的可能性不大,但是当轨道倾角在i=90°附近或者高度再高一些,则有可能存在冻结轨道;对于100km高的初始圆轨道,卫星在无控的情况下半年内将会坠落到月球表面,如果高度增加到200km,则不进行轨道控制也不会坠落到月面上。利用仿真软件GEODYN解算出来的结果证实了上述结论。 相似文献
18.
David Vokrouhlický 《Celestial Mechanics and Dynamical Astronomy》1989,46(1):85-104
The orbital effects of the Lorentz force on the motion of an electrically charged artificial satellite moving in the Earth's
magnetic field are determined. The geomagnetic field is considered as a multipole potential field and the satellite electrical
charge is supposed to be constant. The relativistic perturbations of the main geomagnetic field are discussed briefly. The
results are concentrated on the determination of the secular changes, and numerical values are computed for the case of the
LAGEOS satellite. The results are discussed in the context of a possible detection of the Lense-Thirring effect analyzing
the orbital perturbations of the LAGEOS and LAGEOS X satellites. 相似文献
19.
研究了在高空电离层中运动的带电荷的卫星受电感应阻力后对轨道根数产生的摄动影响。研究结果表明 ,电感应阻力对带电卫星的轨道半长轴、轨道偏心率、近地点赤经、历元平赤经均有周期摄动影响 ,但除对半长轴有长期摄动效应外对其它轨道根数均无长期摄动。轨道倾角和升交点赤经不受摄动影响。文中以飞行在高度 1 50 0km的电离层中的导体卫星作为算例。计算结果显示 :带电导体卫星在高空电离层中带有一定电量时电感应阻力对轨道半长轴的缩短产生显著效应 相似文献
20.
Yanchao He Ming Xu Xianghua Jia Roberto Armellin 《Celestial Mechanics and Dynamical Astronomy》2017,128(2-3):275-294
The focus of this paper is the design and station keeping of repeat-groundtrack orbits for Sun-synchronous satellites. A method to compute the semimajor axis of the orbit is presented together with a station-keeping strategy to compensate for the perturbation due to the atmospheric drag. The results show that the nodal period converges gradually with the increase of the order used in the zonal perturbations up to \(J_{15}\). A differential correction algorithm is performed to obtain the nominal semimajor axis of the reference orbit from the inputs of the desired nodal period, eccentricity, inclination and argument of perigee. To keep the satellite in the proximity of the repeat-groundtrack condition, a practical orbit maintenance strategy is proposed in the presence of errors in the orbital measurements and control, as well as in the estimation of the semimajor axis decay rate. The performance of the maintenance strategy is assessed via the Monte Carlo simulation and the validation in a high fidelity model. Numerical simulations substantiate the validity of proposed mean-elements-based orbit maintenance strategy for repeat-groundtrack orbits. 相似文献