共查询到20条相似文献，搜索用时 140 毫秒
1.
Madeleine Pascal 《Celestial Mechanics and Dynamical Astronomy》1985,36(4):319-347
We consider the motion of a dual spin satellite placed in the gravitational field of n material points, assuming that the satellite has no influence on the motion of these points. The main bodies are located at the libration points of the classical n bodies problem. We investigate the set of relative equilibria of the satellite. As in the elementary case of a gyrostat attracted by a single point, we show that this problem is equivalent to find the extremum of a quadratic function. We obtain all possible equilibria of the satellite by solving two algebraic equations. Sufficient conditions of stability of these relative equilibria are given. 相似文献
2.
Lately, more and more exoplanets are being discovered and the number is expected to increase thanks to the excellent programs dedicated to this task. Thus it is important to study the dynamical behavior of planetary systems. Among all the problems that may be considered, we are interested in four-body planetary systems. In this article, we first examine the possible cases in four-body planetary systems including satellites, in both single and multiple stars. Step decomposition is a methodology explained by A. Abad and J.A. Docobo to deal with n-body problems with hierarchy. The use of this technique permits the reduction of the different cases to five configurations. The analytical integration of one of these cases, a double star with a planet and a satellite orbiting one of the components of the stellar system, is the objective. First the Hamiltonian of the problem is given and then we formulate it in terms of three small parameters which can be reduced to two in this case. After that, using Hori’s biparametric method, the dependence on the angular variables is removed, thereby allowing the integration of the problem. 相似文献
3.
YANG KeJun 《时间频率学报》1996,(1)
在卫星定位与授时中，电离层折射误差的影响是十分重要的．目前采用的主要改正方法是双频法，还有电离层模型法．双频法要求卫星发射两个工作频率，而电离层模型法的偏差又较大，这对于使用单频接收机的用户来讲，电离层折射改正就成为一个严重问题，笔者提出的双极化法正好可以解决单频接收机所遇到的问题．双极化法是基于电离层的双折射特性．一个线极化波在电离层中传播时被分裂成两个圆极化波，即左旋圆极化波和右旋圆极化波传播，左旋与右旋圆极化波在电离层中传播的速度不同，则到达接收点的时间也就不同，通过测量两个圆极化波到达接收点的传播时廷差，即可确定电离层折射误差的改正量． 相似文献
4.
论述的短弧定轨,是指在无先验信息情况下又避开多变元迭代的初轨计算方法,它需要相应的动力学问题有一能反映短弧内达到一定精度的近似分析解．探测器进入月球引力作用范围后接近月球时可以处理成相对月球的受摄二体问题,而在地球附近,则可处理成相对地球的受摄二体问题,但在整个过渡段的力模型只能处理成一个受摄的限制性三体问题．而限制性三体问题无分析解,即使在月球引力作用范围外,对于大推力脉冲式的过渡方式,相对地球的变化椭圆轨道的偏心率很大(超过Laplace极限),在考虑月球引力摄动时亦无法构造摄动分析解．就此问题,考虑在地球非球形引力(只包含J2项)和月球引力共同作用下,构造了探测器飞抵月球过渡轨道段的时间幂级数解,在此基础上给出一种受摄二体问题意义下的初轨计算方法,经数值验证,定轨方法有效,可供地面测控系统参考． 相似文献
5.
The classical problem of the critical inclination in artificial satellite theory has been extended to the case when a satellite may have an arbitrary, significant mass and the rotation momentum vector is tilted with respect to the symmetry axis of the planet. If the planet’s potential is restricted to the second zonal harmonic, according to the assumptions of the main problem of the satellite theory, two various phenomena can be observed: a critical inclination that asymptotically tends to the well known negligible mass limit, and a critical tilt that can be attributed to the effect of transforming the gravity field harmonics to a different reference frame. Stability of this particular solution of the two rigid bodies problem is studied analytically using a simple pendulum approximation. 相似文献
6.
Victor A. Avdyushev 《Celestial Mechanics and Dynamical Astronomy》2003,87(4):383-409
Mainly, the author focuses on Baumgarte's method and its applications in satellite, asteroid, stellar and planetary problems. In the paper arguments are given for the use of energy relations for stabilization in the elliptical two-body problem. Stabilizing properties of Baumgarte's equations and others are discussed. A simple approach is proposed for stabilizing the equations of almost circular motion. By using Baumgarte's technique, the author derives stabilized equations of perturbed restricted three-body problem. It is shown experimentally that stabilization in the problems mentioned above can raise the accuracy of numerical integration by several orders. 相似文献
7.
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
8.
The problem triaxial satellite having a plane of dynamical symmetry in the restricted problem of three bodies has been studied. The first integrals are established and the general solution of the problem can be written in quadratures. The results show that the semi-major axis of the satellite orbit and its rotational angular momentum remain unchanged. The singular solution of this problem has been considered and the elements of satellite orbit can be determined. 相似文献
9.
K. G. Hadjifotinou M. Gousidou-Koutita 《Celestial Mechanics and Dynamical Astronomy》1998,70(2):99-113
We present a new implementation of the recurrent power series (RPS) method which we have developed for the integration of
the system of N satellites orbiting a point-mass planet. This implementation is proved to be more efficient than previously
developed implementations of the same method. Furthermore, its comparison with two of the most popular numerical integration
methods: the 10th-order Gauss–Jackson backward difference method and the Runge–Kutta–NystrRKN12(10)17M shows that the RPS
method is more than one order of magnitude better in accuracy than the other two. Various test problems with one up to four
satellites are used, with initial conditions obtained from ephemerides of the saturnian satellite system. For each of the
three methods we find the values of the user-specified parameters (such as the method's step-size (h or tolerance (TOL)) that
minimize the global error in the satellites' coordinates while keeping the computer time within reasonable limits. While the
optimal values of the step-sizes for the methods GJ and RKN are all very small (less than T/100, the ones that are suitable
for the RPS method are within the range: T/13<h<T/6 (T being the period of the innermost satellite of the problem). Comparing
the results obtained by the three methods for these step-sizes and for the various test problems we observe the superiority
of the RPS method over GJ in terms of accuracy and over RKN both in accuracy and in speed.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
本文讨论了危险目标再入的有关问题,通过２２８７０和２５１００两个卫星陨落期预报的实践,我们形成了一种计算卫星落点的方法,方法的基本要点是：１算准卫星的面质比;２在１８０公里以下,考虑阻尼系数随高度（大气密度）的变化;３在计算落点时,使用两组根数,调整面质比使两组根数计算的落点基本相同,并验证面质比调整的合理性;４对于ＭＳＩＳ－１９９０模式,我们发现调整后的面质比要比理论的面质比大１．０９倍,也许这 相似文献
11.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):379-393
Recent results on periodic orbits are presented. Planetary systems can be studied by the model of the general 3-body problem and also some satellite systems and asteroid orbits can be studied by the model of the restricted 3-body problem. Triple stellar systems and planetary systems with two Suns are close to periodic systems. Finally, the motion of stars in various types of galaxies can be studied by finding families of periodic orbits in several galactic models. 相似文献
12.
In this paper we study the equilibrium orientation of a gyrostat satellite in the gravity field of a point mass. Direct problem is to find all possible equilibrium orientation when the relative angular momentum vector is given. Inverse problem is to find this relative angular momentum in order to obtain equilibrium in a given orientation. Semi-inverse problem is solved here when some parameters (but not all) giving orientation of the satellite are chosen arbitrarily, giving for what choices real solutions occur. 相似文献
13.
Martín Lara Jesús F. Palacián Ryan P. Russell 《Celestial Mechanics and Dynamical Astronomy》2010,108(1):1-22
Preliminary mission design for planetary satellite orbiters requires a deep knowledge of the long term dynamics that is typically
obtained through averaging techniques. The problem is usually formulated in the Hamiltonian setting as a sum of the principal
part, which is given through the Kepler problem, plus a small perturbation that depends on the specific features of the mission.
It is usually derived from a scaling procedure of the restricted three body problem, since the two main bodies are the Sun
and the planet whereas the satellite is considered as a massless particle. Sometimes, instead of the restricted three body
problem, the spatial Hill problem is used. In some cases the validity of the averaging is limited to prohibitively small regions,
thus, depriving the analysis of significance. We find this paradigm at Enceladus, where the validity of a first order averaging
based on the Hill problem lies inside the body. However, this fact does not invalidate the technique as perturbation methods
are used to reach higher orders in the averaging process. Proceeding this way, we average the Hill problem up to the sixth
order obtaining valuable information on the dynamics close to Enceladus. The averaging is performed through Lie transformations
and two different transformations are applied. Firstly, the mean motion is normalized whereas the goal of the second transformation
is to remove the appearance of the argument of the node. The resulting Hamiltonian defines a system of one degree of freedom
whose dynamics is analyzed. 相似文献
14.
David L. Richardson 《Celestial Mechanics and Dynamical Astronomy》1980,22(3):231-236
A lagrangian formulation for the three-dimensional motion of a satellite in the vicinity of the collinear points of the circular-restricted problem is reconsidered. It is shown that the influence of the primaries can be expressed in the form of two third-body disturbing functions. By use of this approach, the equations for the Lagrangian and for the motion itself are readily developed into highly compact expressions. All orders of the non-linear developments are shown to be easily obtainable using well-known recursive relationships. The resulting forms for these equations are well suited for use in the initial phase of canonical or non-canonical investigations. 相似文献
15.
P. Moore 《Celestial Mechanics and Dynamical Astronomy》1978,17(3):281-297
Lambert and Watson (1976) examine the family of symmetric linear multistep methods for the special second-order initial value problem, and connect the property of symmetry with a property of periodicity. The problems of celestial mechanics may be formulated as second-order initial value problems, but these frequently incorporate the first derivative explicity. It is common for such equations to be reduced to a system of first-order equations. Thus motivated, we utilize ideas from the aforementioned paper to determine the family of linear multistep methods for first-order initial value problems that possess an analogous property of periodicity. This family of orbitally stable methods is illustrated by examining the regularized equations of motion of an artificial earth satellite in an oblate atmosphere. 相似文献
16.
We investigate the evolution of high Earth satellite orbits under gravitational perturbations from the Sun and light pressure forces, without the Earth shadow effect. We present the disturbing function of the problem provided that the satellite is a sphere. The mean value of the disturbing function in the absence of resonances between the mean unperturbed motion of the satellite and the mean motion of the Sun has also been obtained. The semimajor axis of the satellite orbit and the mean value of the disturbing function are shown to be integrals of the averaged osculating equations. TheHill version of the problem, whereby the distance to the satellite is much smaller than the Earth–Sun distance, has been studied in detail: we have constructed the phase portraits of the oscillations at various parameters and described three types of quasiperiodic satellite trajectories—librational and rotational trajectories as well as Earth collision trajectories. Numerical simulations of trajectories have allowed the additional effects caused by light pressure to be described: the displacement of the bounded trajectory of the satellite as a whole relative to the trajectory of the classical three-body problem into a region more distant from the Sun. 相似文献
17.
An aspect of the missing mass problem in galaxies, not easy to address, is whether the dynamical mass distribution is spherical or greatly flattened, following the light. Rotation curves of spirals out of the plane of the disc cannot, by definition, be measured. A way around this problem might be to use satellite glaxies orbiting within a few Holmberg radii of their parents. We address here the difficulties implied in using a satellite in this way: to what extent can one solve uniquely for its orbital parameters? A practical set of solutions which can constrain an orbit is derived here using the tidal radius of the satellite to scale the gravitational pull of the parent. Although data of the quality needed exist as yet for very few systems, we show using M31, NGC 128, and NGC 1023 and their respective satellites, how the dynamics of the interactions can be explored. 相似文献
18.
Hans J. Sperling 《Celestial Mechanics and Dynamical Astronomy》1972,6(3):278-293
Let a rigid satellite move in a circular orbit about a spherically symmetric central body, taking into account only the main term of the gravitational torque. We shall investigate and find all solutions of the following problem: Let the satellite be permitted to spin about an axis that is fixed in the orbit frame; the satellite need not be symmetric, the spin not uniform, and the spin axis not a principal axis of inertia. The complete discussion of this type of spin reveals that the cases found by Lagrange and by Pringle - and the well-known spin about a principal axis of inertia orthogonal to the orbit plane — are essentially the only ones possible; the only further (degenerate) case is uniform spin of a two-dimensional, not necessarily symmetric satellite about certain axes that are orthogonal to the plane containing the body and to the orbit of the satellite around the central body. 相似文献
19.
In the light of the problem of amalgamation and processing of multisource observational data in the combined orbit determination of near-earth satellites of the bi-satellite positioning system, the optimal weighting method of the improved variance component estimation of the two-step systematic error correction of homogeneous observational data is proposed. Analyses show that the multi-source amalgamation measurement model of the heterogeneous observational data essentially is a multi-structure, multi-parameter non-linear regression model, and the optimal weighting method of the combination of model structure characteristic analysis and variance component estimation of the heterogeneous observational data is established. The realization algorithms of the optimal weighting and the combined orbit determination parameter estimation of the two sorts of observational data are designed, and the simulation experiments of the combined orbit determination are carried out by taking the distances among the two satellites and the backup satellite and the homogeneous observational data and the distance between the two satellites and the heterogeneous observational data of satellite sensor angle measurements as the examples. The results of theoretical analysis and simulation calculation show that for the combined orbit determination of homogeneous observational data, the accuracy of orbit determination obtained by adopting the variance component estimation method of the two-step systematic error correction can be more superior than that obtained by means of the traditional empirical weighting method. For the combined orbit determination of heterogeneous observational data, through the introduction of the weighting factor by which the model structure is characterized the accuracies of the combined orbit determination of the near-earth satellite and geostationary satellite are both improved to a certain extent in comparison with the mean weighting mode. 相似文献
20.
The libration points of axisymmetric satellite in the gravitation field of two triaxial rigid bodies
S. M. Elshaboury M. O. Shaker A. E. El-Dessoky M. A. Eltantawy 《Earth, Moon, and Planets》1991,52(1):69-81
In this paper we consider the restricted problem of three rigid bodies (an axisymmetric satellite in the gravitation field of two triaxial primaries). The collinear and triangular equilibrium solutions are obtained. The effect of the primaries on the location of the libration points of a spherical satellite has been studied numerically. 相似文献