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.     

火星非球形引力位田谐项联合摄动分析解

火星非球形引力场模型与地球有明显差别,其非球形引力位中的田谐项系数基本都要比地球的相应值大一个量级,尤其是J_2,2项（赤道椭率项）的大小接近它的动力学扁率项J₂.对于低轨探测器,若要使轨道外推1 d弧段的精度达到500 m(相当于标准单位10^-4量级),在构造环火探测器的轨道分析解时,田谐项与J₂项以及田谐项与田谐项之间的联合摄动不容忽视.根据摄动量级分析和构造的摄动分析解证实,上述联合摄动对轨道沿迹方向的影响可超过10^-4,并给出了数值验证.结果表明,与地球低轨卫星不同,在类似的问题中,构造环火卫星摄动分析解时,必须考虑这些联合摄动项的影响.     

在电子计算机上自动推导Flora群小行星的普遍摄动I．Hansen方法应用

在IBKM 4341电子计算机上应用Hansen方法和运行Broucke R.开发的Poisson级数展开程序系统，自动推导了木星对Flora群小行星的普遍摄动，将将计算得到的摄动系数表与前人应用Bohlin群法所得相应表作了比对。由此得到结论：1．取代Bohlin群法，用在电子计算机上建立的Hansen方法程序能够既快又精确地计算小行星的普遍摄动；2．对于1000″＜n＜1100″（n为小行星的周日平均运动，单位以弧秒／日表示）情形，如果小行星轨道的偏心率e和交角i不太大，Stroemberg表是适用的，最大误差不到20″；3．对于n-1047″情形，因此时n′/n－2／7，接近通约状态（n′为木星的周日平均运动），必须计及（2－7）长周期项，而de la Villemarque所给出的公式不够精确；4．对于975″＜n＜1000″情形，Stromberg表因其精度低而不适用，当e,i较大时尤甚；5．对于n-997″情形，因此时n′／n-3/10，即接近另一种通约状态，必须计及（3－10）长周期项。     

日月轨道计算对TLE深空编目目标预报精度的影响

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     

六颗Flora群小行星普遍摄动的新结果——Ⅰ.应用Hansen方法自动计算

应用在IBM4341计算机上建立的Hansen摄动计算方法的软件，快速自动出了Flora群里五颗其周日平均运动n－997″小行星：（261）Prymno,(587)Hypsipyle,(753)Tifis,(783)Nora,(1598)Paloque和一颗n－975″小行星（855）Newcombia所受木星摄动的三角级数解，与过云用Bolin群法计算所得近似解作比较，因现在计及了（3E－10θ）长周期项和精化了（E－3θ）等主要周期项的系数，使得这些小行星普遍摄动计算的结果有了明显的改进。     

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.     

地球非球形引力位中田谐项摄动的有关问题

在人造卫星绕地球运动中,地球非球形引力摄动是最重要的讨论了容易被忽视的田谐项摄动,尽管它对低轨卫星的影响,只相当于J2项的二阶量,又是短周期效应,但它却包含了大10多倍的地球自转项,必须给以重视.还导出包含全部阶次田谐项的摄动解,并分离出地球自转项,对轨道半长径a还增加了(J2×Jlm)联合摄动的地球自转项,既为理论分析提供依据又可用于分析法定轨和预报.     

基于历史TLE的空间目标轨道预报误差演化规律研究

北美防空司令部(North American Aerospace Defense Command, NORAD)发布的双行根数(Two Line Element, TLE)是广大航天工作者最常用的轨道根数,与其对应的轨道模型是SGP4/SDP4 (Simplified General Perturbation Version 4/Simplified Deep-space Perturbation Version 4)解析模型.由于TLE中并没有包含相应的轨道精度信息,编目轨道的应用范围受到很大的限制.基于Space-Track网站发布的历史TLE数据和配套的SGP4/SDP4动力学模型,采用定轨标预报的方法统计并生成了大量目标轨道的预报误差,通过对预报轨道的时间区间划分给出了每个目标的预报误差随预报时间变化的拟合系数,并进一步对不同类型轨道预报误差的演化规律和特征进行了分类讨论,给出了4种轨道类型目标的轨道预报误差随时间演化的平均解析模型,为拓展双行根数的应用提供有价值的参考.     

Hansen系数递推的效率

探讨了偏心率函数的递推方法的效率, 给出了一种成批递推方法, 其计算效率明显优于直接计算方法, 而且递推是正向的. 采用该成批递推方法递推时, 偏心率函数的量级从小到大变化, 可以保证递推的精度.     

M_f和M_m波固体潮Love数k_2的确定——来自空间大地测量的结果

初步探讨用日长和卫星轨道摄动方法研究半月潮Mf 和月潮Mm 的Love数k2 .结果表明 ,日长方法给出k2 =0 .30 32 i0 .0 0 2 8(Mf) ,0 .30 2 6 i0 .0 0 1 2 (Mm) ,卫星轨道摄动方法为k2 =0 .30 83-i0 .0 1 0 0 (Mf) ,0 .30 1 4-i0 .0 0 1 0 (Mm) ,并与理论固体潮计算结果较为相符 .另外 ,上述结果更接近滞弹地球模型计算的结果 ,因此精确地测定长期潮Love数将对固体潮理论和地幔滞弹性提供重要的结束 .     

Direct Calculation Methods of Hansen Coefficients and Their Derivatives

Seven direct calculation methods of Hansen coefficients and their derivatives are reviewed. The computational efficiencies of these methods are compared, and their computational stabilities are analyzed. We show that the recursion relations of Hansen coefficients can be used to determine the stabilities of calculation results. Finally, it is pointed out that Wnuk's method (double precision computation) and McClain's methods (quadruple precision computation) are stable, which can be used to calculate orbit perturbations. Because of small orbital eccentricities of most satellites, the perturbation calculations without singularities are required, and McClain's first method (quadruple precision computation) is recommended.     

Recursive calculation of hansen coefficients

Hansen coefficients are used in expansions of the elliptic motion. Three methods for calculating the coefficients are studied: Tisserand's method, the Von Zeipel-Andoyer (VZA) method with explicit representation of the polynomials required to compute the Hansen coefficients, and the VZA method with the values of the polynomials calculated recursively. The VZA method with explicit polynomials is by far the most rapid, but the tabulation of the polynomials only extends to 12th order in powers of the eccentricity, and unless one has access to the polynomials in machine-readable form their entry is laborious and error-prone. The recursive calculation of the VZA polynomials, needed to compute the Hansen coefficients, while slower, is faster than the calculation of the Hansen coefficients by Tisserand's method, up to 10th order in the eccentricity and is still relatively efficient for higher orders. The main advantages of the recursive calculation are the simplicity of the program and one's being able to extend the expansions to any order of the eccentricity with ease. Because FORTRAN does not implement recursive procedures, this paper used C for all of the calculations. The most important conclusion is recursion's genuine usefulness in scientific computing.     

Computation of elliptic Hansen coefficients and their derivatives

The problem of computation of elliptic Hansen coefficients and their derivatives is considered for constructing a motion theory of an artificial Earth satellite with large eccentricity. An algorithm for analytical and numerical computation of these coefficients and their derivatives is described. The recurrence relations for derivatives of the first and second order and initial values for recurrences are obtained. As an example, numerical values of some elliptic Hansen coefficients are given for the orbit with eccentricityk=0.74.     

平场数据采集间隔对莱曼阿尔法太阳望远镜平场精度的影响分析

莱曼阿尔法太阳望远镜(LST)是先进天基太阳天文台(ASO-S)卫星的载荷之一,它包括白光太阳望远镜(WST),全日面太阳成像仪(SDI)和日冕仪(SCI)等仪器. 1991年Kuhn, Lin和Loranz提出的方法(简称KLL方法)是WST和SDI在轨平场定标的方法之一.为了研究WST和SDI的平场定标精度对KLL方法的相邻位置时间间隔的敏感性,使用太阳动力学观测卫星(SDO)的日震和磁成像仪(HMI)及太阳大气成像仪(AIA)的全日面成像观测数据测试和分析在使用KLL方法时相邻位置时间间隔对所得平场精度的影响.结果显示在LST使用KLL方法进行平场定标时,相邻位置时间间隔越短越好.具体分析表明,WST平场精度对相邻位置采样时间间隔不敏感,而SDI时间间隔需要在240 s范围内.分析结果对卫星姿态调整到稳定所需的时间给出了一定限制.     

Pulsations and planets: The asteroseismology‐extrasolar‐planet connection

The disciplines of asteroseismology and extrasolar planet science overlap methodically in the branch of high‐precision photometric time series observations. Light curves are, amongst others, useful to measure intrinsic stellar variability due to oscillations, as well as to discover and characterize those extrasolar planets that transit in front of their host stars, periodically causing shallow dips in the observed brightness. Both fields ultimately derive fundamental parameters of stellar and planetary objects, allowing to study for example the physics of various classes of pulsating stars, or the variety of planetary systems, in the overall context of stellar and planetary system formation and evolution. Both methods typically also require extensive spectroscopic follow‐up to fully explore the dynamic characteristics of the processes under investigation. In particularly interesting cases, a combination of observed pulsations and signatures of a planet allows to characterize a system's components to a very high degree of completeness by combining complementary information. The planning of the relevant space missions has consequently converged with respect to science cases, where at the outset there was primarily a coincidence in instrumentation and techniques. Whether space‐ or ground‐based, a specific type of stellar pulsations can themselves be used in an innovative way to search for extrasolar planets. Results from this additional method at the interface of stellar pulsation studies and exoplanet hunts in a beyond‐mainstream area are presented (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Modified Gooding Method to Calculate Inclination Functions

In this paper, the expression of V k_lm(I) in the Gooding method is rewritten to be the form convenient for calculation, and a standard recursive lm procedure is used to calculate Ak_lm(I). We have rewritten the Gooding's program under the assumption that l and k have the same odd-even parity, this makes the program be shorten for one half, the computational effciency and readability of the program be raised, the computing time be shortened for 41%, and the computational accuracy and stability are also slightly improved.     

基于Shapelets基函数的引力透镜质量重构方法

引力透镜效应是探测星系团物质分布的有效方法之一.目前,利用引力透镜数据重构星系团质量分布的主流方法可以分为两大类,即参数法和非参数法.在实际研究工作中,受限于质量模型假设和计算分辨率等方面的影响,现有的重构算法仍有诸多亟需解决的问题.基于Shapelets基函数的引力透镜质量重构方法通过基函数来实现引力透镜质量重构,使用Shapelets基函数分解引力透镜势,以引力透镜中多重像的位置和背景星系椭率畸变为限制条件来迭代求解基函数系数从而得到透镜体的质量分布.通过拟合一个模拟的NFW (Navarro,Frenk and White)透镜系统测试了新方法的可行性,结果表明新方法可以在整体上重构出透镜体的质量分布,并拟合出接近真实的源位置,能够为星系团质量测量提供一套灵活且高效的重构算法.     

Are solar cycles predictable?

Various methods (or recipes) have been proposed to predict future solar activity levels – with mixed success. Among these, some precursor methods based upon quantities determined around or a few years before solar minimum have provided rather high correlations with the strength of the following cycles. Recently, data assimilation with an advection-dominated (flux-transport) dynamo model has been proposed as a predictive tool, yielding remarkably high correlation coefficients. After discussing the potential implications of these results and the criticism that has been raised, we study the possible physical origin(s) of the predictive skill provided by precursor and other methods. It is found that the combination of the overlap of solar cycles and their amplitude-dependent rise time (Waldmeier's rule) introduces correlations in the sunspot number (or area) record, which account for the predictive skill of many precursor methods. This explanation requires no direct physical relation between the precursor quantity and the dynamo mechanism (in the sense of the Babcock-Leighton scheme or otherwise). (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fast detection of chaotic behavior in galactic potentials

In the present paper we apply a new method of distinction between ordered and chaotic motion in galactic potentials. The method uses the Fourier Transform of a series of time intervals each one representing the time that elapsed between two successive points on the Poincaré surface of section. Examples of the methods ability to achieve an early and clear detection of an orbit's behavior are provided using two galactic potentials. The new method can also be applied in order to have an early distinction between ordered and sticky orbits. The method is generalized in order to be used in models with more than two dimensions. Finally we have tried to find an one‐number index to give us the nature of the orbit instead of checking by eye the whole spectrum. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)