两个新的Hansen系数的递推公式

推导给出了两个新的Hansen系数X_k~(-(n+1),m)的递推关系:■其中,n、m和k是Hansen系数X_k~(-(n+1),m)的3个指标,e为轨道偏心率.递推公式(R5)可以执行普通Hansen系数的向后递推,需要一行初值,公式简单.递推公式(R6)可以执行偏心率函数的向前递推,需要两行初值,比Vakhidov给出的递推公式明显简单.算例说明,这两种递推是有效的.     

计算机控制的高精度频率源设计

通过对通用串行总线(USB)协议和直接数字合成(DDS)技术的研究和分析,设计实现了一种采用DDS技术的高精度频率源,并且能通过计算机应用软件对其进行实时控制.给出了该设计的硬件结构与部分关键程序的结构,同时给出了对该设计性能参数的测量结果,并对其进行了简单分析和探讨.     

碳星的JHK测光及其有效温度

本文给出了银河系24颗碳星的JHK波段的测光结果,文中时论了碳星在(J-H)-(H-K)双色指数图上的分布。给出了各星的热改正和热星等。 文中特别讨论了碳星的有效温度,并利用两种不同的方法分别得出了各星的有效温度。     

宇宙弦和星系两点相关函数

本文对宇宙弦模型中的星系两点相关函数ξ进行了计算,并同Davis和Peebles的观测结果进行了比较,发现宇宙弦模型能较好地解释ξ的观测曲线。一个有意义的结果是我们利用宇宙弦图象自然地给出了其他宇宙模型难以给出的r_c≈3Mpch~(-1)处从1+ξ∝r~(-2)幂律到1+ξ∝r~(-0.85)幂律的转变点。     

人造地球卫星轨道摄动的二阶解

本文讨论人造地球卫星在各种力学因素作用下运动的二阶摄动分析解,给出了方法和相应的解;同时,在此基础上给出半分析半数值方法的基本公式。整个解将适用于任意偏心率(o≤c<1)。     

GPS接收机的中频信号处理算法研究

该文对GPS接收机的中频信号处理算法进行了研究,内容主要涉及信号捕获、载波恢复和伪码跟踪3部分,详细分析了信号捕获过程中所采用的匹配滤波器法、快速傅里叶算法(FFT)、锁频环(FLL)、锁相环(PLL)以及延迟锁定环(DLL)的算法原理,并对环路滤波器作了相应的阐述,给出环路对应的递推公式．     

关于勒让德多项式的算法问题

本文讨论勒让德多项式P_1(x)和缔合勒让德多项式P_(1m)(x)的两种算法,即直接计算和递推算法,并给出相应的计算公式,当1取值较大时,也可以保证达到较高的精度。     

关于海卫Ⅱ运动理论的探讨

本工作试图建立轨道偏心率特别大(e=0.75)的海卫H(Nereid)的运动理论,并用适当方法避免摄动函数的一阶部分中含有长周期项的困难,给出相应的一阶摄动解。     

星系中分子气体物理性质的观测研究

为了研究亮红外星系中分子气体的物理性质,本论文给出了一个小样本近邻亮红外星系初步的观测结果、一个高红移星系IRAS F10214+4724的详细研究以及一个近邻亮红外星系ARP 302的高分辨研究.另外,对Perseus星系团中存在的分子气体给出了高分辨的观测,并研究其气体的运动学状态.对一个小样本的亮红外星系,得到了CO(J=3→2)的成图结果,揭示其气体分布都集中在星系中心或者是并合星系的中心及其星系核的重叠区域.对于其中的一个源NGC 3256,给出了其CO(J=3→2)、     

数字滤波技术应用于VLBI数据采集的方法

在VLBI(VeryLongBaselineInterferometry)数据采集终端中,用数字滤波代替模拟滤波有其显著的优势。本文首先介绍了国外在VLBI数据采集终端中采用数字滤波的进展情况,然后阐述了数字滤波在系统中的实现方案。实现数字滤波的关键是信号处理的速度,降低运算量是实现快速处理的关键,本文给出了实现FIR数字滤波器的3种结构,并在运算量方面进行了分析和比较。在这基础上,还对数字滤波的2种系统实现方案进行了具体分析。高性能的FPGA(FieldProgrammablegateArray)芯片是实现数字滤波器的较好选择,文章最后给出了基于FPGA芯片、用查表(LUT:LookUpTable)的方式实现的数字滤波系统框图。     

Equilibrium solutions of the restricted problem of 2 + 2 axisymmetric rigid bodies

The restricted problem of 2 + 2 homogenous axisymmetric ellipsoids such that their equatorial planes coincide with the orbital plane of the centers of mass is considered. The equilibrium solutions of this problem are shown to exist. Six of these solutions are located about the collinear points of the restricted problem of three axisymmetric ellipsoids. A special case of this problem is studied and sixteen solutions are found in the neighborhood of the triangular Lagrangian points.     

Generalizations of the Jacobian integral

The restricted problem of three bodies is generalized to the restricted problem of 2+n bodies. Instead of one body of small mass and two primaries, the system is modified so that there are several gravitationally interacting bodies with small masses. Their motions are influenced by the primaries but they do not influence the motions of the primaries. Several variations of the classical problem are discussed. The separate Jacobian integrals of the minor bodies are lost but a conservative (time-independent) Hamiltonian of the system is obtained. For the case of two minor bodies, the five Lagrangian points of the classical problem are generalized and fourteen equilibrium solutions are established. The four linearly stable equilibrium solutions which are the generalizations of the triangular Lagrangian points are once again stable but only for considerably smaller values of the mass parameter of the primaries than in the classical problem.     

Radiation transfer in a diffuse and specular reflecting slab with Rayleigh scattering

A method of analysis is presented for solving the radiative transfer problem in an absorbing, emitting, inhomogeneous, and anisotropically scattering plane-parallel medium with specular and diffuse reflecting boundaries and internal source (problem 1). Exact relations for the radiation heat flux at the boundaries of problem 1 are obtained in terms of the radiation density and albedos of the corresponding source-free medium with specular reflecting boundaries (problem 2). Two coupled integral equations for the radiation density and the second moment of the radiation intensity for problem 2 with Rayleigh phase functions are obtained. The Galerkin method is used to solve these equations. Albedos of problem 2 are compared with theF _n method. Numerical results for radiation heat fluxes at the boundaries of problem 1 are tabulated for different forms of the internal source.     

A new approach to impulsive rendezvous near circular orbit

A new approach is presented for the problem of planar optimal impulsive rendezvous of a spacecraft in an inertial frame near a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a related characteristic-value function and this related optimization problem can be solved in closed form. The solution of this problem is shown to approach the solution of the original problem in the limit as the boundary conditions approach those of a circular orbit. Using a form of primer-vector theory the problem is formulated in a way that leads to relatively easy calculation of the optimal velocity increments. A certain vector that can easily be calculated from the boundary conditions determines the number of impulses required for solution of the optimization problem and also is useful in the computation of these velocity increments. Necessary and sufficient conditions for boundary conditions to require exactly three nonsingular non-degenerate impulses for solution of the related optimal rendezvous problem, and a means of calculating these velocity increments are presented. A simple example of a three-impulse rendezvous problem is solved and the resulting trajectory is depicted. Optimal non-degenerate nonsingular two-impulse rendezvous for the related problem is found to consist of four categories of solutions depending on the four ways the primer vector locus intersects the unit circle. Necessary and sufficient conditions for each category of solutions are presented. The region of the boundary values that admit each category of solutions of the related problem are found, and in each case a closed-form solution of the optimal velocity increments is presented. Similar results are presented for the simpler optimal rendezvous that require only one-impulse. For brevity degenerate and singular solutions are not discussed in detail, but should be presented in a following study. Although this approach is thought to provide simpler computations than existing methods, its main contribution may be in establishing a new approach to the more general problem.     

Stability in the Full Two-Body Problem

Stability conditions are established in the problem of two gravitationally interacting rigid bodies, designated here as the full two-body problem. The stability conditions are derived using basic principles from the N-body problem which can be carried over to the full two-body problem. Sufficient conditions for Hill stability and instability, and for stability against impact are derived. The analysis is applicable to binary small-body systems such as have been found recently for asteroids and Kuiper belt objects.     

Periodic orbits of the elliptic restricted problem for the Sun-Jupiter-Saturn system

A systematic approach to generate periodic orbits in the elliptic restricted problem of three bodies in introduced. The approach is based on (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to periodic orbits in the elliptic restricted problem. Two families of periodic orbits of the elliptic restricted problem are found by this approach. The mass ratio of the primaries of these orbits is equal to that of the Sun-Jupiter system. The sidereal mean motions between the infinitesimal body and the smaller primary are in a 2:5 resonance, so as to approximate the Sun-Jupiter-Saturn system. The linear stability of these periodic orbits are studied as functions of the eccentricities of the primaries and of the infinitesimal body. The results show that both stable and unstable periodic orbits exist in the elliptic restricted problem that are close to the actual Sun-Jupiter-Saturn system. However, the periodic orbit closest to the actual Sun-Jupiter-Saturn system is (linearly) stable.     

Asymptotic expansions in the perturbed two-body problem with application to systems with variable mass

The main theorems of the theory of averaging are formulated for slowly varying standard systems and we show that it is possible to extend the class of perturbation problems where averaging might be used. The application of the averaging method to the perturbed two-body problem is possible but involves many technical difficulties which in the case of the two-body problem with variable mass are avoided by deriving new and more suitable equations for these perturbation problems. Application of the averaging method to these perturbation problems yields asymptotic approximations which are valid on a long time-scale. It is shown by comparison with results obtained earlier that in the case of the two-body problem with slow decrease of mass the averaging method cannot be applied if the initial conditions are nearly parabolic. In studying the two-body problem with quick decrease of mass it is shown that the new formulation of the perturbation problem can be used to obtain matched asymptotic approximations.     

The Kepler problem and geodesic flows in spaces of constant curvature

The main result of this paper is a theorem on the trajectory equivalence of phase flows on isoenergetic surfaces with a positive energy level in the Kepler problem and perturbed kepler problem. The following two facts are crucial for proving it: firstly, an isomorphism of the phase flow on an isoenergetic surface in the Kepler problem and the geodesic flow in a constant curvature space. The isomorphism is studied in detail. In particular, all the integrals of the Kepler problem are obtained proceeding from the group-theory considerations. The second fact is a generalization of the theorem on structural stability of Anosov flows onto non-compact manifolds.     

The perturbing effects on the planetary satellite

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.     

The eleventh motion constant of the two-body problem

The two-body problem is a twelfth-order time-invariant dynamic system, and therefore has eleven mutually-independent time-independent integrals, here referred to as motion constants. Some of these motion constants are related to the ten mutually-independent algebraic integrals of the n-body problem, whereas some are particular to the two-body problem. The problem can be decomposed into mass-center and relative-motion subsystems, each being sixth-order and each having five mutually-independent motion constants. This paper presents solutions for the eleventh motion constant, which relates the behavior of the two subsystems. The complete set of mutually-independent motion constants describes the shape of the state-space trajectories. The use of the eleventh motion constant is demonstrated in computing a solution to a two-point boundary-value problem.