环火卫星运动的坐标系附加摄动及相应坐标系的选择

与处理地球卫星相关问题类似,在研究和处理环火卫星(尤其是低轨卫星)的轨道问题时,宜采用火心历元平赤道坐标系,即火心天球坐标系,其xy坐标面和x轴方向就是相应的平赤道面和平春分点方向.与地球的岁差章动现象类似,在该坐标系中,火星赤道面在空间的摆动同样会引起坐标系附加摄动.采用类似对地球岁差章动的处理方法,在一定精度前提下,基于IAU2000火星定向模型,处理了火星赤道面摆动中的岁差效应,并在此基础上,研究岁差对环火卫星轨道的影响,给出了相应的火星非球形引力位的变化及其导致的卫星轨道的坐标系附加摄动解,其表达形式简单,引用方便.与高精度数值解的比对表明,该分析解能够满足通常的精度要求.因此,在处理环火卫星(即使是低轨卫星)轨道及其相关问题时,可以采用统一坐标系:火心天球坐标系.而不必像当初处理地球卫星那样,为了避免计算坐标系附加摄动而引进一种混合型赤道坐标系,即采用瞬时真赤道面和历元平春分点方向作为其xy坐标面和x轴方向.在统一坐标系的选择下,实际工作中就不会存在坐标系转换的麻烦.     

考虑阻力系数变化的近地卫星轨道的联合摄动

在文[1]的基础上,本文进一步考虑大气阻力系数变化的影响,并针对一阶解,给出由此产生的近地卫星轨道根数变化的各种摄动项。     

在电离中电感应阻力对带电卫星轨道根数的摄动影响

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     

地球磁场对带电人造卫星轨道根数的摄动影响

研究了地球磁场对带电的非赤道卫星的轨道根数的摄动影响。理论结果表明，地球磁场对带电卫星的轨道半长轴没有摄动影响，既无周期摄动，也无长期摄动，但对轨道偏心率、轨道倾角、升交点赤经、近地点经度和历元平近点角均有周期摄动，且对升交点和近地点经度还有长期摄动效应。通过算例表明，当卫星带有大量电荷时，地球磁场对卫星轨道的摄动影响必须加以考虑。     

地球磁场对带电人造卫星轨道根数的摄动影响

研究了地球磁场对带电的非赤道卫星的轨道根数的摄动影响，理论结果表明，地球磁场对带电卫星的轨道半长轴没有摄动影响，既无周期摄动，也无长期摄动，但对轨道偏心率、轨道倾角、升交点赤经、近地点经度和历元平近点角均有周期摄动，且对升交点和近地点经度还有长期摄动效应，通过算例表明，当卫星带有大量电菏时，地球磁场对卫星轨道的摄动影响必须加以考虑。     

在电离中电感应阻力对带电卫星轨道根数的摄动影响

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，但除对半生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1500km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。     

卫星轨道预报的一种分析方法

人造地球卫星的轨道预报是空间环境监测和实时跟踪测量中一个重要环节，由于监测对象众多，要求精度也不太高，通常采用分析法预报．在已有分析法得到t时刻平均根数的基础上给出一种轨道预报方法，由t时刻的平均根数给出该时刻卫星的位置和速度，在此基础上将地球非球形引力摄动的周期项直接用卫星直角坐标的位置和速度分量表示，这样可以避免在计算轨道根数变化的周期项时出现的奇点问题，从而对根数的选择无特殊要求，可适用于各种轨道，简化预报程序和相应的软件，提高预报效率。     

月球卫星轨道力学综述

月球探测器的运动通常可分为3个阶段，这3个阶段分别对应3种不同类型的轨道：近地停泊轨道、向月飞行的过渡轨道与环月飞行的月球卫星轨道。近地停泊轨道实为一种地球卫星轨道；过渡轨道则涉及不同的过渡方式(大推力或小推力等)；环月飞行的月球卫星轨道则与地球卫星轨道有很多不同之处，它决不是地球卫星轨道的简单克隆。针对这一点，全面阐述月球卫星的轨道力学问题，特别是环月飞行中的一些热点问题，如轨道摄动解的构造、近月点高度的下降及其涉及的卫星轨道寿命、各种特殊卫星(如太阳同步卫星和冻结轨道卫星等)的轨道特征、月球卫星定轨等。     

限制性三体问题中摄动运动方程的坐标系选择

针对限制性三体问题,分别选取以中心天体和摄动体质心为坐标原点的惯性系,及以中心天体为坐标原点的非惯性系,讨论了不同坐标系下天体运动轨道描述的异同。利用运动天体轨道能量E的大小,可以确定受摄运动方程采用椭圆轨道根数还是采用双曲线轨道根数进行描述。为此,推导出一个关于轨道半长径和偏心率满足的临界关系判别式。结果表明,在摄动天体质量较大的情况下,非惯性系中存在大量轨道,这些轨道在原惯性坐标系中是稳定的椭圆轨道,转换到非惯性系中后却无法用椭圆轨道根数进行描述。只能引入双曲线轨道根数来描述轨道,由此将产生非惯性系下摄动运动方程轨道根数类型选择问题。最后,指出选择雅可比坐标系可以避免上述问题,并推导出适用于任意运动区域的具有统一形式的摄动函数展开式。     

一种解析定轨方法

本文给出了人造地球卫星轨道计算的一种解析方法,定轨方案中摄动计算考虑了地球引力场非球形摄动的J2,J3,J4的长期项,长周期项,J2短周期项,大气阻力,太阳光压及日月引力摄动的长期项。初始根数改正量估计采用微分轨道改进算法。在定轨迭代收敛后,残差的均方根误差在5″左右,资料使用率超过80%。     

Coordinate Additional Perturbations to Mars Orbiters and Choice of Corresponding Coordinate System

Similar to the study of the related problems of Earth satellites, in the research of the motion of Mars orbiter especially for low-orbit satellites, it is more appropriate to choose an epoch Mars-centered and Mars-equator reference system, which indeed is called the Mars-centered celestial coordinate system. In this system, the xy-plane and the direction of the x-axis correspond to the mean equator and mean equinox. Similar to the precession and nutation of the Earth, the wiggling of instantaneous Mars equator causes the coordinate additional perturbations in this Mars coordinate system. The paper quotes a method which is similar to the one used in dealing with the coordinate additional perturbations of Earth. According to this method, based on the IAU2000 Mars orientation model and under the precondition of a certain accuracy, we are able to figure out the precession part of the change of Mars gravitation. This lays the foundation for further study of its influence on the Mars orbiter's orbit of precession and the solution of the corresponding coordinate additional perturbations. The obtained analytical solution is easy to use. Compared with the numerical solution with higher accuracy, the result shows that the accuracy of this analytical solution could satisfy the general requirements in use. Therefore, our result verifies that a unified coordinate system, the Mars-centered celestial system in which J2000.0 is chosen as its current initial epoch, could be applied to deal with the relative problems of Mars orbiters, especially for low-orbit satellites. It is different from the method we previously used in dealing with the corresponding problems of Earth satellites, where we adopted the instantaneous equator and epoch (J1950.0) mean equinox as xy-plane and the direction of x -axis. In contrast, the coordinate transformation brings heavy workload and certain inconvenience in relative former works in which the prior system is used. If adopting the unified coordinate system, the transformation could be simply avoided and the computation load could be decreased significantly.     

天球和地球历书原点

国际天球参考系的使用、观测精度的提高和方法的改善要求采用与地球轨道运动无关的运动赤道上的起算点，Guinot提出的非旋转原点可作为这样一种选择。非旋转原点依赖于天球参考极。IAU决定从2003年起采用天球中间极作为天球参考极。非旋转原点在天球参考系的使用，可给出在天球中间极赤道上的天球历书原点，非旋转原点在地球参考系的使用，可给出在天球中间极赤道上的地球历书原点。回顾了非旋转原点的概念、以历书原点为参考的天球参考系和地球参考系的坐标变换，经出了在微角秒精度下天球参考极的坐标和历书原点的位置，讨论了采用历书原点对测定UT1的影响，指出当岁差章动模型、天极补偿、分点改正得到改善时，基于历书原点的UT1定义不需要更改，从而保证了UT1的连续。     

Spacecraft Orbit Determination with The B-spline Approximation Method

It is known that the dynamical orbit determination is the most common way to get the precise orbits of spacecraft. However, it is hard to build up the precise dynamical model of spacecraft sometimes. In order to solve this problem, the technique of the orbit determination with the B-spline approximation method based on the theory of function approximation is presented in this article. In order to verify the effectiveness of this method, simulative orbit determinations in the cases of LEO (Low Earth Orbit), MEO (Medium Earth Orbit), and HEO (Highly Eccentric Orbit) satellites are performed, and it is shown that this method has a reliable accuracy and stable solution. The approach can be performed in both the conventional celestial coordinate system and the conventional terrestrial coordinate system. The spacecraft's position and velocity can be calculated directly with the B-spline approximation method, it needs not to integrate the dynamical equations, nor to calculate the state transfer matrix, thus the burden of calculations in the orbit determination is reduced substantially relative to the dynamical orbit determination method. The technique not only has a certain theoretical significance, but also can serve as a conventional algorithm in the spacecraft orbit determination.     

基于SLR精密轨道的天文定位精度分析

利用全球卫星激光测距服务系统(ILRS,International Laser Ranging Service)标准点资料对Ajisai卫星进行精密定轨,残差均方根(RMS)优于3 cm,得到该星的精密轨道.进而对长春站40 cm空间碎片光电望远镜获得的Ajisai卫星的天文定位资料进行精度分析,外符合精度约3″左右.单独利用天文定位数据进行轨道改进,内符合精度优于3″.改进轨道的x、y、z坐标3分量在观测数据覆盖范围内的精度在100 m之内.同样地对Jason-1卫星作数据分析,结果和Ajisai卫星精度相当.分析各个弧段的精度变化,发现定标星个数减少,会导致天文定位精度下降.据此提出可以把最少定标星比例作为评定数据质量的参考指标之一.     

The significance of the Hansen Ideal space frame

Known and unknown properties of Hansen Ideal coordinates are summarized. It is shown that the ideal space frame is a general and necessary component of basic celestial mechanics and astrodynamics, as well as of any theory of motion. A typical consequence is the intimate correlation of the Hansen frame with the Lagrange constraint within the method of the variation of the parameters. The use of observations in the ideal frame may allow conclusions on the intergalactic fundamental coordinate system (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Principal algorithms for the control of Kourovka Observatory SBG camera

We report the algorithms used in the software of the upgraded SBG camera. Fast-moving satellites are observed in the “rotated” coordinate system where one of the axes points towards the pole of the object’s orbit. The ephemeris for this coordinate system is computed based on the ephemeris for the equatorial coordinate system using special transition matrices. The parameters of the matrices are the coordinates of the orbital pole, which are found by averaging the vector products of the radius vectors of the consecutive positions of the satellite. The position angle of the image is computed as the difference between the hour angles of the orbital and celestial poles in the coordinate system, the pole of which coincides with the optical center of the frame. The speed of object tracking is computed via quadratic interpolation of the ephemeris in the “rotated” coordinate system.     

Determination of an intermediate perturbed orbit from three position vectors

We suggest a new approach to solving the problem of finding the orbit of a celestial body from its three spatial position vectors and the corresponding times. It allows most of the perturbations in the motion of a celestial body to be taken into account. The approach is based on the theory of intermediate orbits that we developed previously. We construct the orbit the motion along which is a combination of two motions: the motion of a fictitious attracting center whose mass varies according to Mestschersky’s first law and the motion relative to the fictitious center. The first motion is generally parabolic, while the second motion is described by the equations of the Gylden-Mestschersky problem. The constructed orbit has such parameters that their limiting values at any reference epoch define a superosculating intermediate orbit with a fourth-order tangency. We have performed a numerical analysis to estimate the accuracy of approximating the perturbed motion of two minor planets, 145 Adeona and 4179 Toutatis, by the orbits computed using two-position procedures (the classical Gauss method and the method that we suggested previously), a three-position procedure based on the Herrick-Gibbs equation, and the new method. Comparison of the results obtained suggests that the latter method has an advantage.     

最新规范的参考系及有关问题

在简要阐明参考系、参考架及其历史重大进程的基础上,对几种重要的、最新规范的参考系/参考架(质心天球参考系和地心天球参考系、国际天球参考系、国际地球参考系、太阳系动力学参考系等)的定义、实现和特点作了评述和分析,并对最新规范中与参考系、参考架有关的某些新概念的定义和新模式的应用(自2003年开始贯彻),如:天球中介极(CIP)、天球历书原点(CEO)、地球历书原点(TEO)、地球自转角的新定义、岁差-章动新模式的应用,作了阐述和讨论。     

The effect of the Earth’s oblateness on the Moon’s physical libration in latitude

The Moon’s physical libration in latitude generated by gravitational forces caused by the Earth’s oblateness has been examined by a vector analytical method. Libration oscillations are described by a close set of five linear inhomogeneous differential equations, the dispersion equation has five roots, one of which is zero. A complete solution is obtained. It is revealed that the Earth’s oblateness: a) has little effect on the instantaneous axis of Moon’s rotation, but causes an oscillatory rotation of the body of the Moon with an amplitude of 0.072″ and pulsation period of 16.88 Julian years; b) causes small nutations of poles of the orbit and of the ecliptic along tight spirals, which occupy a disk with a cut in a center and with radius of 0.072″. Perturbations caused by the spherical Earth generate: a) physical librations in latitude with an amplitude of 34.275″; b) nutational motion for centers of small spiral nutations of orbit (ecliptic) pole over ellipses with semi-major axes of 113.850″ (85.158″) and the first pole rotates round the second one along a circle with radius of 28.691″; c) nutation of the Moon’s celestial pole over an ellipse with a semi-major axis of 45.04″ and with an axes ratio of about 0.004 with a period of T = 27.212 days. The principal ellipse’s axis is directed tangentially with respect to the precession circumference, along which the celestial pole moves nonuniformly nearly in one dimension. In contrast to the accepted concept, the latitude does not change while the Moon’s poles of rotation move. The dynamical reason for the inclination of the Moon’s mean equator with respect to the ecliptic is oblateness of the body of the Moon.     

Studies in the application of recurrence relations to special perturbation methods

The integration by recurrent power series of certain differential equations occurring in celestial mechanics is shown to be very much more efficient and accurate than that produced by classical one step methods. It is shown that for any such system of differential equations the machine time taken to carry out an integration is a minimum for a certain choice of the number of terms taken in the recurrent power series. In the two-body orbits considered this number is about 15. For the same accuracy criterion the power series is faster than the Runge-Kutta method of the fourth order by a factor which varies between 6 and 15 depending on the eccentricity of the orbit.