Hansen系数及其导数的直接计算方法

回顾总结了7种Hansen系数及其导数的直接计算方法,比较分析了这些方法的计算效率和计算稳定性.研究表明:Hansen系数的递推关系可以用来判别计算结果的稳定性.最后指出, Wnuk方法(双精度计算)和McClain方法(4精度计算)是稳定的,可以用来计算人造卫星轨道摄动.由于大多数人造卫星采用小偏心率轨道,需要计算无奇点摄动,推荐使用McClain方法1 (4精度计算).     

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.     

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.     

Deflation techniques for the determination of periodic solutions of a certain period

The computation of periodic orbits of nonlinear mappings or dynamical systems can be achieved by applying a root-finding method. To determine a periodic solution, an initial guess should be located within a proper area of the mapping or a surface of section of the phase space of the dynamical system. In the case of Newton or Newton-like methods these areas are the basins of convergence corresponding to the considered solution. When several solutions of the same period exist in a particular region, then the deflation technique is suitable for the calculation of all these solutions. This technique is applied here to the Hénon's mapping and the driven conservative Duffing's oscillator.     

基于EfficientNet的星系形态分类研究

星系的结构和形态能够反映星系自身的物理性质,其形态的分类是后续分析研究的一个重要环节.EfficientNet模型使用复合系数对深度网络模型的深度、宽度、输入图像分辨率进行更加结构化的统一缩放,是一种新的深度网络优化扩展方法.将该模型应用于星系数据形态的分类研究中,结果表明基于EfficientNetB5模型的平均准确率、精确率、召回率以及F1分数(精确率与召回率的调和平均数)都在96.6%以上,与残差网络(Residual network, ResNet)中ResNet-26模型的分类结果相比有较大的提升.实验结果证明EfficientNet的深度网络优化扩展方法可行且有效,可应用于星系的形态分类.     

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)     

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.     

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)     

Die Hadamard-Konstruktion Greenscher Funktionen auf gekrümmter Raum-Zeit: Physikalische Zusammenhänge und explizite strenge Resultate

First, in connection with their construction due to HADAMARD, the mathematical and physical meaning of covariant Green's functions in relativistic gravitational fields - according to EINSTEIN: on curved space-time - is discussed. Then, in the case of a general static spherically symmetric space-time the construction equations for a scalar Green's function are cast into symmetry-adapted form providing a convenient starting point for an explicit calculation of the Hadámard building elements. In applying the obtained basic scheme to a special one-parameter family of model metrics one succeeds in advancing to the explicit exact calculation of tail-term coefficients of a massless Green's function which are simultaneously coefficients in the Schwinger-De Witt expansion of the Feynman propagator for the corresponding massive Klein-Gordon equation on curved space-time.     

Some Recurrence Relations Between Hansen Coefficients

A new system of recurrence relations for Hansen coefficients is obtained. This system gives a connection between only those coefficients which are included in the disturbing function of planetary or satellite motion and allows to compute efficiently the Hansen coefficients for perturbations both from internal and external bodies. The recurrence process can be realized both from high to low and from low to high harmonical terms of the disturbing function. The corresponding algorithms of evaluation of Hansen coefficients are presented. The efficiency of the obtained system of recurrence relations is discussed.     

Bayesian galaxy shape measurement for weak lensing surveys – I. Methodology and a fast-fitting algorithm

The principles of measuring the shapes of galaxies by a model-fitting approach are discussed in the context of shape measurement for surveys of weak gravitational lensing. It is argued that such an approach should be optimal, allowing measurement with maximal signal-to-noise ratio, coupled with estimation of measurement errors. The distinction between likelihood-based and Bayesian methods is discussed. Systematic biases in the Bayesian method may be evaluated as part of the fitting process, and overall such an approach should yield unbiased shear estimation without requiring external calibration from simulations. The principal disadvantage of model fitting for large surveys is the computational time required, but here an algorithm is presented that enables large surveys to be analysed in feasible computation times. The method and algorithm is tested on simulated galaxies from the Shear TEsting Programme (STEP).     

Perturbative effects on a Mercurian orbiter due to the solar radiation pressure,solar wind and the coronal mass ejections

To explore the dynamics of a test particle in the near-Mercury’s environment, the orbital motion of an orbiter around Mercury is considered. Different perturbing forces, namely the Mercurian gravity field, the solar radiation pressure, the solar wind and the coronal mass ejections, are taken into account. The order of magnitude of each perturbing term is assessed. The equations of motion in canonical representation are obtained. The Hamiltonian in terms of Hansen coefficients is expressed. A procedure for solution is presented. The short and long periodic terms are removed from the Hamiltonian and the solution is obtained. Long periodic perturbations on the orbital dynamics of an orbiter around Mercury due to the solar events are found as revealed by Eq. (26) in the text. Resonance cases are discussed and the different resonant inclinations are obtained. A procedure for the computation of the position and velocity is presented.     

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)     

Comparison of chaos detection methods in the circular restricted three‐body problem

In this study, a sample of orbits is considered in the framework of the planar circular restricted three‐body problem. In order to separate ordered from chaotic orbits three numerical methods are compared: the Largest Lyapunov Characteristic Exponent (LLCE) and the Smaller Alignment Index (SALI) provide a fairly good characterization of the chaotic motions, while the computational time required is of the same order; the Correlation Dimension (CD) has the advantage of correctly classifying sticky orbits, but at the expense of a longer computational time. In order to classify a given orbit, any pair of the three methods can be considered, but LLCE and SALI are recommended due to their speed. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new parallel PM code for very large-scale cosmological simulations

We have developed a parallel Particle–Particle, Particle–Mesh (P³M) simulation code for the Cray T3E parallel supercomputer that is well suited to studying the time evolution of systems of particles interacting via gravity and gas forces in cosmological contexts. The parallel code is based upon the public-domain serial Adaptive P³M-SPH (http://coho.astro.uwo.ca/pub/hydra/hydra.html) code of Couchman et al. (1995)[ApJ, 452, 797]. The algorithm resolves gravitational forces into a long-range component computed by discretizing the mass distribution and solving Poisson's equation on a grid using an FFT convolution method, and a short-range component computed by direct force summation for sufficiently close particle pairs. The code consists primarily of a particle–particle computation parallelized by domain decomposition over blocks of neighbour-cells, a more regular mesh calculation distributed in planes along one dimension, and several transformations between the two distributions. The load balancing of the P³M code is static, since this greatly aids the ongoing implementation of parallel adaptive refinements of the particle and mesh systems. Great care was taken throughout to make optimal use of the available memory, so that a version of the current implementation has been used to simulate systems of up to 10⁹ particles with a 1024³ mesh for the long-range force computation. These are the largest Cosmological N-body simulations of which we are aware. We discuss these memory optimizations as well as those motivated by computational performance. Performance results are very encouraging, and, even without refinements, the code has been used effectively for simulations in which the particle distribution becomes highly clustered as well as for other non-uniform systems of astrophysical interest.     

Modified Newton-Raphson methods for preliminary orbit determination

Preliminary orbit determination is a multipoint boundary value problem which may be solved by the generalized Newton-Raphson iteration. When applied formally the method suffers from extensive computer storage requirements, fairly long execution times and in some cases, insufficient accuracy. In this work we seek to remove these practical difficulties via modification of the computational algorithm in such a way that solution storage is eliminated for the most part and computational speed and tolerance to imprecise integration algorithms is improved. The modified methods are applied to nine typical preliminary orbit determination problems to demonstrate fast convergence and short computation times, even with very poor starting values for the iteration. Excellent precision of the resulting solution is also demonstrated as well as the algorithm's ability to handle circular, elliptic, parabolic and hyperbolic orbits.     

An efficient method to calculate Ambarzumian-Chandrasekhar's and hopf's functions

An efficient method is proposed to calculate scalar Ambarzumian-Chandrasekhar's and Hopf's functions. This method is based on the approximation of Sobolev's resolvent function using exponent series, the coefficients of which are readily found from approximate characteristic equation and from a system of linear algebraic equations.The approximate expressions for the above functions are given. For checking purposes the calculations were carried out in single, double, and quadruple precision. For isotropic, Rocard, and Rayleigh scattering we present a sample of results in 14 significant figures.The Hopf function for isotropic and Rayleigh scattering is presented in 18 significant figures and the well-known Hopf constantq() is found in 59 significant figures.     

先进多孔径视宁度廓线仪数值模拟研究

先进多孔径视宁度廓线仪(A-MASP)由两台小望远镜组成,通过望远镜观测太阳表面的米粒结构进行日间湍流廓线测量.两台望远镜之间的相对指向误差可以通过改进的湍流廓线测量公式消除.数值仿真研究表明,使用消除抖动的湍流廓线计算公式后,发现A-MASP对地表附近的湍流不敏感.当两台望远镜距离为0.4 m时,无法测量400 m以下的湍流.在A-MASP中,采样高度的不均匀分布会造成测量结果的失真,可通过等效采样高度的计算方法,对该失真进行修正.通过100层相位屏对大气湍流的仿真,结果表明当望远镜距离不同时,湍流廓线测量的结果各有侧重.当距离较近时(0.4 m),A-MASP对0.4–5 km的湍流廓线测量精度较高.当距离为1.2 m和2.0 m时,对5 km以上的湍流廓线测量较准确.