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1.
J. P. S. Carvalho R. Vilhena de Moraes A. F. B. A. Prado 《Celestial Mechanics and Dynamical Astronomy》2010,108(4):371-388
In this paper we present an analytical theory with numerical simulations to study the orbital motion of lunar artificial satellites.
We consider the problem of an artificial satellite perturbed by the non-uniform distribution of mass of the Moon and by a
third-body in elliptical orbit (Earth is considered). Legendre polynomials are expanded in powers of the eccentricity up to
the degree four and are used for the disturbing potential due to the third-body. We show a new approximated equation to compute
the critical semi-major axis for the orbit of the satellite. Lie-Hori perturbation method up to the second-order is applied
to eliminate the terms of short-period of the disturbing potential. Coupling terms are analyzed. Emphasis is given to the
case of frozen orbits and critical inclination. Numerical simulations for hypothetical lunar artificial satellites are performed,
considering that the perturbations are acting together or one at a time. 相似文献
2.
The motion of a lunar satellite 总被引：2，自引：0，他引：2
Claus Oesterwinter 《Celestial Mechanics and Dynamical Astronomy》1970,1(3-4):368-436
Presented in this theory is a semianalytical solution for the problem of the motion of a satellite in orbit around the moon. The principal perturbations on such a body are due to the nonspherical gravity field of the moon, the attraction of the earth, and, to a lesser degree, the attraction of the sun. The major part of the problem is solved by means of the celebrated von Zeipel Method, first successfully applied to the motion of an artificial earth satellite by Brouwer in 1959. After eliminating from the Hamiltonian all terms with the period of the satellite and those with the period of the moon, it is suggested to solve the remaining problem with the aid of numerical integration of the modified equations of motion.This theory was written in 1964 and presented as a dissertation to Yale University in 1965. Since then a great deal has been learned about the gravity field of the moon. It seems that quite a number of recently determined gravity coefficients would qualify as small quantities of order two. Hence, according to the truncation criteria employed, they should be considered in the present theory. However, the author has not endeavored to update the work accordingly. The final results, therefore, are incomplete in the lunar gravitational perturbations. Nevertheless, the theory does give the largest such variations and it does present the methods by which perturbations may be derived for any gravity terms not actually developed. 相似文献
3.
Giorgio E. O. Giacaglia 《Celestial Mechanics and Dynamical Astronomy》1974,9(2):239-267
Lunisolar perturbations of an artificial satellite for general terms of the disturbing function were derived by Kaula (1962). However, his formulas use equatorial elements for the Moon and do not give a definite algorithm for computational procedures. As Kozai (1966, 1973) noted, both inclination and node of the Moon's orbit with respect to the equator of the Earth are not simple functions of time, while the same elements with respect to the ecliptic are well approximated by a constant and a linear function of time, respectively. In the present work, we obtain the disturbing function for the Lunar perturbations using ecliptic elements for the Moon and equatorial elements for the satellite. Secular, long-period, and short-period perturbations are then computed, with the expressions kept in closed form in both inclination and eccentricity of the satellite. Alternative expressions for short-period perturbations of high satellites are also given, assuming small values of the eccentricity. The Moon's position is specified by the inclination, node, argument of perigee, true (or mean) longitude, and its radius vector from the center of the Earth. We can then apply the results to numerical integration by using coordinates of the Moon from ephemeris tapes or to analytical representation by using results from lunar theory, with the Moon's motion represented by a precessing and rotating elliptical orbit. 相似文献
4.
5.
David R. Cok 《Celestial Mechanics and Dynamical Astronomy》1977,16(4):459-479
The lunar disturbing function for a close-Earth satellite is expressed as a sum of products of harmonics of the satellite's position and harmonics of the Moon's position, and the latter are expanded about a rotating and precessing elliptic orbit inclined to the ecliptic. The deviations of the Moon from this approximate orbit are computed from Brown's lunar theory andthe perturbations in satellite orbital elements due to these inequalities are derived. Numerical calculations indicate that several perturbations in the position of the satellite's node and perigee have magnitudes on the order of one meter.The author is supported in part by a National Science Foundation Graduate Fellowship. 相似文献
6.
The short period luni-solar theory of Kozai is generalized for arbitrary obliquity of the ecliptic and inclination of the moon's orbit to the ecliptic. Analytic first order lunar perturbations to the elements are derived. The theory is illustrated by an application to the communication satellite Intelsat 3F3.Presently at the Department of Environmental Sciences, University of Tel Aviv, Ramat Aviv, Israel. 相似文献
7.
The algorithm for choosing a trajectory of spacecraft flight to the Moon is discussed. The characteristic velocity values needed for correcting the flight trajectory and a braking maneuver are estimated using the Monte Carlo method. The profile of insertion and flight to a near-circular polar orbit with an altitude of ~100 km of an artificial lunar satellite (ALS) is given. The case of two corrections applied during the flight and braking phases is considered. The flight to an ALS orbit is modeled in the geocentric geoequatorial nonrotating coordinate system with the influence of perturbations from the Earth, the Sun, and the Moon factored in. The characteristic correction costs corresponding to corrections performed at different time points are examined. Insertion phase errors, the errors of performing the needed corrections, and the errors of determining the flight trajectory parameters are taken into account. 相似文献
8.
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
9.
G. E. O. Giacaglia 《Celestial Mechanics and Dynamical Astronomy》1977,15(2):191-215
The equations of motion of an artificial satellite are given in nonsingular variables. Any term in the geopotential is considered as well as luni-solar perturbations up to an arbitrary power ofr/r, r being the geocentric distance of the disturbing body. Resonances with tesseral harmonics and with the Moon or Sun are also considered. By neglecting the shadow effect, the disturbing function for solar radiation is also developed in nonsingular variables for the long periodic perturbations. Formulas are developed for implementation of the theory in actual computations. 相似文献
10.
A technique for estimating the state of an artificial satellite in the presence of unmodeled accelerations is presented. The unmodeled acceleration is approximated by a first-order Gauss-Markov sequence which can be separated into a timewise correlated component and a purely random component. Using this approximation, a sequential procedure for estimating the position, velocity, and the unmodeled acceleration is developed. The method is evaluated by reducing range-rate observations obtained by tracking the Apollo 10 and 11 spacecraft during the lunar orbit phase of the mission. Numerical results are presented which show that the observation residual pattern lies within the observation noise standard deviation. The values of the estimated components of the unmodeled acceleration are repeatable from orbit to orbit within a given mission and from mission to mission when the same ground track is covered. Finally, the variation in the radial component of the unmodeled acceleration shows a high correlation with the reported location of the lunar surface mascons. 相似文献
11.
We propose an approach to the study of the evolution of high-apogee twelve-hour orbits of artificial Earth’s satellites. We describe parameters of the motion model used for the artificial Earth’s satellite such that the principal gravitational perturbations of the Moon and Sun, nonsphericity of the Earth, and perturbations from the light pressure force are approximately taken into account. To solve the system of averaged equations describing the evolution of the orbit parameters of an artificial satellite, we use both numeric and analytic methods. To select initial parameters of the twelve-hour orbit, we assume that the path of the satellite along the surface of the Earth is stable. Results obtained by the analytic method and by the numerical integration of the evolving system are compared. For intervals of several years, we obtain estimates of oscillation periods and amplitudes for orbital elements. To verify the results and estimate the precision of the method, we use the numerical integration of rigorous (not averaged) equations of motion of the artificial satellite: they take into account forces acting on the satellite substantially more completely and precisely. The described method can be applied not only to the investigation of orbit evolutions of artificial satellites of the Earth; it can be applied to the investigation of the orbit evolution for other planets of the Solar system provided that the corresponding research problem will arise in the future and the considered special class of resonance orbits of satellites will be used for that purpose. 相似文献
12.
The analysis of the Moon artificial satellite orbits stability and satellite system configuring are important issues of lunar orbital navigational system development. The article analyses the influence of different combinations of perturbations on Moon artificial satellite’s obits evolution. The method of Moon artificial satellite’s orbital evolution analysis is offered; general stability regions of Moon artificial satellite’s orbits are defined and the quality characteristics of the selected orbital groups of the satellite system are evaluated. 相似文献
13.
G. A. Krasinsky 《Celestial Mechanics and Dynamical Astronomy》2002,84(1):27-55
Differential equations describing the tidal evolution of the earth's rotation and of the lunar orbital motion are presented in a simple close form. The equations differ in form for orbits fixed to the terrestrial equator and for orbits with the nodes precessing along the ecliptic due to solar perturbations. Analytical considerations show that if the contemporary lunar orbit were equatorial the evolution would develop from an unstable geosynchronous orbit of the period about 4.42 h (in the past) to a stable geosynchronous orbit of the period about 44.8 days (in the future). It is also demonstrated that at the contemporary epoch the orbital plane of the fictitious equatorial moon would be unstable in the Liapunov's sense, being asymptotically stable at early stages of the evolution. Evolution of the currently near-ecliptical lunar orbit and of the terrestrial rotation is traced backward in time by numerical integration of the evolutional equations. It is confirmed that about 1.8 billion years ago a critical phase of the evolution took place when the equatorial inclination of the moon reached small values and the moon was in a near vicinity of the earth. Before the critical epoch t
cr
two types of the evolution are possible, which at present cannot be unambiguously distinguished with the help of the purely dynamical considerations. In the scenario that seems to be the most realistic from the physical point of view, the evolution also has started from a geosynchronous equatorial lunar orbit of the period 4.19 h. At t < t
cr
the lunar orbit has been fixed to the precessing terrestrial equator by strong perturbations from the earth's flattening and by tidal effects; at the critical epoch the solar perturbations begin to dominate and transfer the moon to its contemporary near-ecliptical orbit which evolves now to the stable geosynchronous state. Probably this scenario is in favour of the Darwin's hypothesis about originating the moon by its separation from the earth. Too much short time scale of the evolution in this model might be enlarged if the dissipative Q factor had somewhat larger values in the past than in the present epoch. Values of the length of day and the length of month, estimated from paleontological data, are confronted with the results of the developed model. 相似文献
14.
《Chinese Astronomy and Astrophysics》2006,30(3):318-329
The satellite “Tance 1” of the “Double-Star Program” is the first truly scientific experimentation satellite of China. Its orbit is the farthest so far launched in China, with a geocentric apogee reaching 78 thousand kilometers. The tracking of “Tance 1” and of more distant space targets, such as the lunar exploration craft, can be realized with the VLBI technique of radio astronomy. In order to test and verify the role which the VLBI technique plays in the lunar exploration program of China, Shanghai Astronomical Observatory organized the only 3 tracking stations in China (located at Shanghai, Urumqi and Kunming), to carry out test tracking of “Tance 1,” and used the time delay data obtained to determine the orbit of “Tance 1” over a two-day period, so providing a preliminary assessment of the possibility of VLBI orbit determination. The fitting error of the orbit so obtained is about 5.5 m in the time delay and about 2 cm/s in the delay rate (this for checking only), much better than is provided by the preliminary orbit (used merely for ensuring tracking) in which the corresponding figures are around 2 km and 15 cm/s. Further, if the orbit is determined by using both the time delay and time delay rate data (with weights according to their internal accuracies), then the residuals are 5.5 m in the time delay and 2 cm/s in the delay rate. For an appreciation of the true accuracy of the VLBI orbit determination, we used simulation data (of the observed two-day VLBI data) and found the results depended greatly on the error in the dynamic model of the satellite which, however, is difficult to assess, while the formal residuals are of the order of 1 kin in the delay and of cm/s in the delay rate. The simulation computation also indicates that a joint determination using both VLBI and USB data will have an improved accuracy. 相似文献
15.
16.
利用VLBI数据确定"探测一号"卫星的轨道 总被引：5，自引：0，他引：5
双星计划的“探测一号”是中国首颗真正严格意义上的科学实验卫星,其运行轨道为中国迄今所发射的卫星中距地球最远,远地点地心距达7．8万公里．采用射电天文的VLBI技术可以对“探测一号”以及更远的深空目标,如探月飞行器实现跟踪．为了验证VLBI技术在我国探月计划中的作用,上海天文台组织了国内目前仅有的上海、乌鲁木齐和昆明3个台站对“探测一号”进行试跟踪,利用对“探测一号”约两天的VLBI观测数据,确定“探测一号”卫星的轨道,对VLBI的定轨能力做初步的探讨．按照测控部门提供的初轨 (其精度仅保证跟踪)推算的轨道与VLBI时延的拟合误差平均约2 km,时延率的拟合误差平均约15 cm／s．而利用VLBI数据定轨后的拟合程度相对于初轨有了很大的改善,结果表明,单独利用VLBI时延定轨,时延的拟合精度约5．5 m,作为外部检核的VLBI时延率的拟合精度在2 cm／s左右．单独利用VLBI时延率定轨,时延率的拟合精度约为1．3 cm／s,作为外部检核的VLBI时延的拟合精度约为29 m．而若将时延和时延率数据联合定轨,采用其内符精度加权,VLBI时延和时延率的残差分别为5．5 m和 2 cm／s．为了合理地评估VLBI定轨的真实精度,利用模拟数据进行误差协方差分析,结果表明VLBI定轨精度受动力学模型误差的影响较大,由于"探测一号”卫星的动力学模型难以精确确定,所以利用两天弧段的VLBI数据确定“探测一号”卫星轨道的位置误差为km量级,而速度误差可达cm／s量级．模拟计算还表明, VLBI和USB数据联合定轨可以大大提高定轨精度． 相似文献
17.
双行根数(Two Line Element, TLE)作为一类广泛使用的空间物体编目数据, 其预报精度和误差特性是TLE编目 在空间碎片研究中所要关注的问题之一. TLE编目需要配合SGP4/SDP4 (Simplified General Perturbations 4/Simplified Deep Space 4)模型进行轨道预报, 对深空物体来说, 主要考虑带谐项$J_2$、$J_3$、$J_4$摄动、 第三体日月摄动和特殊轨道共振问题修正等. 其中, SGP4/SDP4模型第三体摄动计算时, 对日月轨道近似采用了长期进动根数和 简单平运动的方式, 在外推10d时存在约2$^\circ$--3${^\circ 相似文献
18.
The solution to the motion of a satellite in an eccentric orbit and in resonance with the second-degree sectorial harmonic of the potential field is developed. The method of solution used parallels the well known von Zeipel method of general perturbations. The solution consists of expressions for the variations of the Delaunay variables. These expressions are composed of the perturbations developed by Brouwer in 1959 for the motion of an artificial satellite plus first-order perturbations due to the second-degree sectorial harmonic (in terms of the Legendre normal elliptic integrals of the first and second kind).This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration. 相似文献
19.
C. Huang J. C. Ries B. D. Tapley M. M. Watkins 《Celestial Mechanics and Dynamical Astronomy》1990,48(2):167-185
The relativistic formulations for the equations which describe the motion of a near-Earth satellite are compared for two commonly used coordinate reference systems (RS). The discussion describes the transformation between the solar system barycentric RS and both the non-inertial and inertial geocentric RSs. A relativistic correction for the Earth's geopotential expressed in the solar system barycentric RS and the effect of geodesic precession on the satellite orbit in the geocentric RS are derived in detail. The effect of the definition of coordinate time on scale is also examined. A long-arc solution using 3 years of laser range measurements of the motion of the Lageos satellite is used to demonstrate that the effects of relativity formulated in the geocentric RS and in the solar system barycentric RS are equivalent to a high degree of accuracy. 相似文献
20.
The general perturbations in the elliptic and vectorial elements of a satellite as caused by the tidal deformations of the non-spherical Earth are developed into trigonometric series in the standard ecliptical arguments of Hill-Brown lunar theory and in the equatorinal elements ω and Ω of the satellite. The integration of the differential equations for variation of elements of the satellite in this theory is easy because all arguments are linear or nearly linear in time. The trigonometrical expansion permits a judgment about the relative significance of the amplitudes and periods of different tidal ‘waves’ over a long period of time. Graphs are presented of the tidal perturbations in the elliptic elements of the BE-C satellite which illustrate long term periodic behavior. The tidal effects are clearly noticeable in the observations and their comparison with the theory permits improvement of the ‘global’ Love numbers for the Earth. 相似文献