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1.
辛积分器中沿迹误差的一种补偿方法 总被引：2，自引：0，他引：2
辛积分器严格描述了一摄动Ｈａｍｉｌｔｏｎ系统的流，因而导致天体轨道的沿迹误差随时间呈线性增长趋势。本文利用这一特点，提出了一种对其沿迹误差进行估算的数值方法，从而达到了对数值结果进行沿迹误差补偿的目的，数值结果证实了此方法在较大积分步长和较长积分时间的数值计算中是有效的。 相似文献
2.
数值积分方法是进行天体力学研究的重要工具, 尤其对于行星历表的研究工作而言. 由于在使用数值方法计算天体轨道时, 最终误差通常是难以预知的, 所以在面对精度要求较高或者积分时间较长的工作时具体积分方案的设计---尤其是当使用定步长方法时的步长选择---需要十分谨慎, 因为这将意味着是否能在时间成本可以被接受的范围内使解的精度达到要求. 因此, 在使用数值方法解决实际问题时如何快速寻找效率与精度之间的最佳平衡点是每一个数值积分方法的设计者与使用者都会面临的难题. 为解决这一问题, 在定步长条件下对数值积分方法的舍入误差概率分布函数以及截断误差积累量对步长的依赖关系和随时间的增长关系进行了深入研究. 基于所得结论, 提出了一种仅需较少的数值实验资料即可对选择任意时间步长积分至任意积分时刻时的舍入误差概率分布函数与截断误差积累量进行准确估计的方法, 并使用Adams-Cowell方法对该误差估计方法在圆周期轨道条件下进行了验证. 该误差估计方法在未来有望用于不同数值算法的性能对比研究, 同时也可以对数值积分方法求解实际轨道问题时的决策工作带来重要帮助. 相似文献
3.
A new scale transformation to the integrated velocity vector is designed to monitor the accumulation of numerical errors in
several integrals of motion. The scale factor is derived from the least-squares correction that minimizes the sum of the squares
of the errors of these integrals. In order to preserve an invariant, we employ the velocity scaling method for rigorously
satisfying the constraint. When adjusting many constants, the new scheme like other existing methods is valid to typically
reduce the integration errors below those of an uncorrected integrator. Via integral invariant relations, the new method is
also able to treat slowly-varying quantities, such as the Keplerian energy and the Laplace vector, for a perturbed Keplerian
problem or each of multiple bodies in the solar system dynamics. Consequently it does nearly agree with the rigorous dual
scaling method in the sense of drastically improving the integration accuracy. As one of its advantages, the implementation
of the new method is significantly easier than that of other methods. In particular, the method can be simply applied to a
complicated dynamical system with some constraints. 相似文献
4.
辛算法在动力天文中的应用（Ⅲ） 总被引：3，自引：0，他引：3
文［１］和文［２］从哈密顿系统的整体结构保持一角度阐明了辛算法［３－６］的主要功能，本文将从定量的角度进一步表明辛算法的另一独特优点－可以控制天体运动沿迹误差的快速增长，并对可分离哈密顿系统的显式辛差分格式稍加改进，推广应用到一般动力系统，该系统含有小耗散项或小的不可分离项，计算结果表明，效果极佳，因此，辛算法与传统的数值解法相比，确有很多优点。 相似文献
5.
《Chinese Astronomy and Astrophysics》2023,47(1):177-203
Numerical methods have become a very important type of tool for celestial mechanics, especially in the study of planetary ephemerides. The errors generated during the computation are hard to know beforehand when applying a certain numerical integrator to solve a certain orbit. In that case, it is not easy to design a certain integrator for a certain celestial case when the requirement of accuracy were extremely high or the time-span of the integration were extremely large. Especially when a fixed-step method is applied, the caution and effort it takes would always be tremendous in finding a suitable time-step, because it is about whether the accuracy and time-cost of the final result are acceptable. Thus, finding the best balance between efficiency and accuracy with the least time cost appeared to be a major obstruction in the face of both numerical integrator designers and their users. To solve this problem, we investigate the variation pattern of truncation error and the pattern of rounding error distributions with time-step and time-span of the integration. According to those patterns, we promote an error estimation method that could predict the distribution of rounding errors and the total truncation errors with any time-step at any time-spot with little experimental cost, and test it with the Adams-Cowell method in the calculation of circular periodic orbits. This error estimation method is expected to be applied to the comparison of the performance of different numerical integrators, and also it can be of great help for finding the best solution to certain cases of complex celestial orbits calculations. 相似文献
6.
For use in numerical studies of rotational motion, a set of elements is introduced for the torque-free rotational motion of a rigid body around its barycenter. The elements are defined as the initial values of a modification of the Andoyer canonical variables. A computational procedure is obtained for determining these elements from the combination of the spin angular momentum vector and a triad defining the orientation of the rigid body. A numerical experiment shows that the errors of transformation between the elements and variables are sufficiently small. The errors increase linearly with time for some elements and quadratically for some others. 相似文献
7.
关于数值求解天体运动方程的几个问题 总被引：4，自引：0，他引：4
本文讨论三个问题：1.在采用各种非辛（Symplectic）的数值积分器积分天体运动方程时，截断误差将引起人为的能量耗散，这一问题是不能用简单地在相应的力模型中加进一个人为的阻力因子而得以解决的，被歪曲的能量（或数值轨道）必须在积分过程的每一步用能量关系来进行校正，此即能量控制方法．2.当摄动加速度涉及到坐标轴的旋转时，如何在各种积分器中采用能量控制方法．3.对于大偏心率轨道，用数值方法求解相应运动方程时，积分步长必须随运动天体与中心天体之间的距离变化而改变，显然，这对所有积分器都是不方便的，特别是多步积分器．本义给出了一种步长均匀化的处理，可以使上述大偏心率轨道积分问题按定步长计算． 相似文献
8.
Thomas S. Statler 《Icarus》2009,202(2):502-513
Radiation recoil (YORP) torques are shown to be extremely sensitive to small-scale surface topography, using numerical simulations. Starting from a set of “base objects” representative of the near-Earth object population, random realizations of three types of small-scale topography are added: Gaussian surface fluctuations, craters, and boulders. For each, the expected relative errors in the spin and obliquity components of the YORP torque caused by the observationally unresolved small-scale topography are computed. Gaussian power, at angular scales below an observational limit, produces expected errors of order 100% if observations constrain the surface to a spherical harmonic order l?10. For errors under 10%, the surface must be constrained to at least l=20. A single crater with diameter roughly half the object's mean radius, placed at random locations, results in expected errors of several tens of percent. The errors scale with crater diameter D as D2 for D>0.3 and as D3 for D<0.3 mean radii. Objects that are identical except for the location of a single large crater can differ by factors of several in YORP torque, while being photometrically indistinguishable at the level of hundredths of a magnitude. Boulders placed randomly on identical base objects create torque errors roughly 3 times larger than do craters of the same diameter, with errors scaling as the square of the boulder diameter. A single boulder comparable to Yoshinodai on 25143 Itokawa, moved by as little as twice its own diameter, can alter the magnitude of the torque by factors of several, and change the sign of its spin component at all obliquities. Most of the total torque error produced by multiple unresolved craters is contributed by the handful of largest craters; but both large and small boulders contribute comparably to the total boulder-induced error. A YORP torque prediction derived from groundbased data can be expected to be in error by of order 100% due to unresolved topography. Small surface changes caused by slow spin-up or spin-down may have significant stochastic effects on the spin evolution of small bodies. For rotation periods between roughly 2 and 10 h, these unpredictable changes may reverse the sign of the YORP torque. Objects in this spin regime may random-walk up and down in spin rate before the rubble-pile limit is exceeded and fissioning or loss of surface objects occurs. Similar behavior may be expected at rotation rates approaching the limiting values for tensile-strength dominated objects. 相似文献
9.
Paul Nacozy 《Celestial Mechanics and Dynamical Astronomy》1976,13(4):495-501
A review and discussion of several investigations concerning the effect of time transformations on numerical integration errors is given. In particular, the discussion treats the relation between time transformations andlocal truncation errors. Additional numerical results are presented which indicate that time transformations reducelocal truncation errors. The results complement those of other studies, especially the recent studies of Danby, Wong, Velez, and Feagin and Mikkilineni. A Sundman time transformation with avarying exponent is introduced and discussed. 相似文献
10.
Wan Yan Wong Adam Moss Douglas Scott 《Monthly notices of the Royal Astronomical Society》2008,386(2):1023-1028
The major theoretical limitation for extracting cosmological parameters from the cosmic microwave background (CMB) sky lies in the precision with which we can calculate the cosmological recombination process. Uncertainty in the details of hydrogen and helium recombination could effectively increase the errors or bias the values of the cosmological parameters derived from the Planck satellite, for example. Here, we modify the cosmological recombination code recfast by introducing one more parameter to reproduce the recent numerical results for the speed-up of the helium recombination. Together with the existing hydrogen fudge factor, we vary these two parameters to account for the remaining dominant uncertainties in cosmological recombination. By using the C osmo MC code with Planck forecast data, we find that we need to determine the parameters to better than 10 per cent for He i and 1 per cent for H, in order to obtain negligible effects on the cosmological parameters. For helium recombination, if the existing studies have calculated the ionization fraction to the 0.1 per cent level by properly including the relevant physical processes, then we already have numerical calculations which are accurate enough for Planck . For hydrogen, setting the fudge factor to speed up low-redshift recombination by 14 per cent appears to be sufficient for Planck . However, more work still needs to be done to carry out comprehensive numerical calculations of all the relevant effects for hydrogen, as well as to check for effects which couple hydrogen and helium recombination through the radiation field. 相似文献
11.
《天文和天体物理学研究(英文版)》2016,(4)
The anisotropies of the B-mode polarization in the cosmic microwave background radiation play a crucial role in the study of the very early Universe. However, in real observations, a mixture of the Emode and B-mode can be caused by partial sky surveys, which must be separated before being applied to a cosmological explanation. The separation method developed by Smith(2006) has been widely adopted,where the edge of the top-hat mask should be smoothed to avoid numerical errors. In this paper, we compare three different smoothing methods and investigate leakage residuals of the E-B mixture. We find that, if less information loss is needed and a smaller region is smoothed in the analysis, the sin- and cos-smoothing methods are better. However, if we need a cleanly constructed B-mode map, the larger region around the mask edge should be smoothed. In this case, the Gaussian-smoothing method becomes much better. In addition, we find that the leakage caused by numerical errors in the Gaussian-smoothing method is mostly concentrated in two bands, which is quite easy to reduce for further E-B separations. 相似文献
12.
Numerical simulation of energetic electron microsignature drifts at Saturn: Methods and applications
Many recent studies show that energetic electron microsignatures are a powerful tool for characterizing key aspects of Saturn’s magnetospheric configuration and dynamics. In all previous investigations, however, analysis of these features was performed through the use of a series of simplifying assumptions (e.g. dipole field model). Furthermore, typical observable parameters of microsignatures (e.g. energy dependent location) have only been discussed qualitatively and a clear understanding about how microsignatures evolve in the magnetosphere is currently lacking. In this study we present a numerical simulation that we developed in order to describe the apparent motion of microsignatures in Saturn’s magnetosphere, under the influence of arbitrary magnetic and electric field models. Our simulations reproduce successfully some typical microsignature properties (energy–time dispersion, high/low lifetime at low/high electron energies). They also indicate how simplifying assumptions used in analytical methods introduce several systematic errors. We demonstrate that, depending on the application and under certain conditions these errors can be neglected, like for instance for small pitch angles and at regions that the dipole approximation is sufficient (inside the orbit of Dione) or for electron energies below few hundred keV. For higher electron energies, systematic errors amplify significantly and existing analytical methods cannot be used. Our model can reconstruct the energy dependent position of microsignatures observed by the MIMI/LEMMS detector with high accuracy, allowing the inference of non-corotational flows (or electric fields) that can be as low as few tens of m s−1. Since, however the calculation of such flows is indirect, the accuracy of such a determination can be reduced by more than an order of magnitude, if some of these free parameters involved in the simulation cannot be sufficiently constrained. One way to provide such constraints is through inputs (e.g. instantaneous plasma moments) from various Cassini instruments and updated magnetospheric field models. In that case, microsignature analysis may prove to be one of the best methods for attempting to measure or to at least constrain the magnitude of the very slow and global plasma outflow in Saturn’s magnetosphere that is driven by mass loading at Enceladus. 相似文献
13.
Marco Missana 《Astrophysics and Space Science》1979,61(2):277-286
The analysis of the Skylab measurements on the ultraviolet limb spectra confirm the presence of a generalized Compton effect in the solar spectrum which can be explained by Thomson scattering theory. The present measurements on the Orion spectrum and interstellar line towards -Arae give a large generalized Compton effect which could be explained by a resonance scattering theory. These numerical results cannot be due to random errors in the measurements, as follows from the statistical discussion. The need for further measurements is pointed out. 相似文献
14.
We have examined the effect on linear helioseismic inversions of correlations in data errors, taking an example from one-dimensional rotational splitting inversion. Artificial data with correlated errors were generated and then inverted with or without using the proper covariance matrix. The effects of using incorrect covariance matrices, on solutions as well as on trade-offs, are discussed. It is found that improper account of the correlations can be deleterious to the faithfulness of the inversions, and yields incorrect error estimates, which under some circumstances can lead to misleading inferences. 相似文献
15.
We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun–Jupiter–Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors. 相似文献
16.
L. Kahl Kristensen 《Astronomische Nachrichten》2001,322(1):47-56
The distribution of observations giving the smallest errors for specific purposes is found in the general case by a numerical procedure. Examples consider the minimum error ellipse for the recovery of a distant asteroid, a main belt object and the position in the target plane for a close approach to the Earth. The observations should be performed only on a few critical nights and inefficient times avoided. The methods are of interest for the optimum strategies for surveys and the determination of initial orbits. 相似文献
17.
Pablo M. Cincotta † 《Monthly notices of the Royal Astronomical Society》1999,307(4):941-948
In two recent papers a new method for searching for periodicity in time series was introduced. It takes advantage of the Shannon entropy to compute the amount of information contained in the light curve of a given signal as a function of a supposed period p . The basic result is that, if the signal is T -periodic, the entropy is then minimum when p T . Also, there is theoretical and numerical evidence that the minimum entropy method is more sensitive to the presence of periodicity and has a higher resolution power than other classical techniques. In the present work the discussion is focused on the way in which the observational errors have to be included in the method. The application of the resulting modified algorithm to real data and a performance comparison with the former algorithm are presented. The dependence of both periodograms on the size of the partition is also investigated. Analytical estimates are given only for the limiting case of small errors. The numerical results show that the new algorithm leads to a smoother periodogram and provides a higher significance for the minimum than the former algorithm. 相似文献
18.
The main limit to the time span of a numerical integration of the planetary orbits is no longer set by the availability of computer resources, but rather by the accumulation of the integration error. By the latter we mean the difference between the computed orbit and the dynamical behaviour of the real physical system, whatever the causes. The analysis of these causes requires an interdisciplinary effort: there are physical model and parameters errors, algorithm and discretisation errors, rounding off errors and reliability problems in the computer hardware and system software, as well as instabilities in the dynamical system. We list all the sources of integration error we are aware of and discuss their relevance in determining the present limit to the time span of a meaningful integration of the orbit of the planets. At present this limit is of the order of 108 years for the outer planets. We discuss in more detail the truncation error of multistep algorithms (when applied to eccentric orbits), the coefficient error, the method of Encke and the associated coordinate change error, the procedures used to test the numerical integration software and their limitations. Many problems remain open, including the one of a realistic statistical model of the rounding off error; at present, the latter can only be described by a semiempirical model based upon the simpleN
2 formula (N=number of steps, =machine accuracy), with an unknown numerical coefficient which is determined only a posteriori. 相似文献
19.
Sergei Nayakshin Seung-Hoon Cha Alexander Hobbs 《Monthly notices of the Royal Astronomical Society》2009,397(3):1314-1325
We present a new framework for radiation hydrodynamics simulations. Gas dynamics is modelled by smoothed particle hydrodynamics (SPH), whereas radiation transfer is simulated via a time-dependent Monte Carlo approach that traces photon packets. As a first step in the development of the method, in this paper we consider the momentum transfer between radiation field and gas, which is important for systems where radiation pressure is high. There is no fundamental limitation on the number of radiation sources, the geometry or the optical depth of the problems that can be studied with the method. However, as expected for any Monte Carlo transfer scheme, stochastic noise presents a serious limitation. We present a number of tests that show that the errors of the method can be estimated accurately by considering Poisson noise fluctuations in the number of photon packets that SPH particles interact with per dynamical time. It is found that, for a reasonable accuracy, the momentum carried by photon packets must be much smaller than the typical momentum of SPH particles. We discuss numerical limitations of the code, and future steps that can be taken to improve performance and applicability of the method. 相似文献
20.
S. Thomas T. Fusco A. Tokovinin M. Nicolle V. Michau G. Rousset 《Monthly notices of the Royal Astronomical Society》2006,371(1):323-336
Analytical theory is combined with extensive numerical simulations to compare different flavours of centroiding algorithms: thresholding, weighted centroid, correlation, quad cell (QC). For each method, optimal parameters are defined in function of photon flux, readout noise and turbulence level. We find that at very low flux the noise of QC and weighted centroid leads the best result, but the latter method can provide linear and optimal response if the weight follows spot displacements. Both methods can work with average flux as low as 10 photons per subaperture under a readout noise of three electrons. At high-flux levels, the dominant errors come from non-linearity of response, from spot truncations and distortions and from detector pixel sampling. It is shown that at high flux, centre of gravity approaches and correlation methods are equivalent (and provide better results than QC estimator) as soon as their parameters are optimized. Finally, examples of applications are given to illustrate the results obtained in the paper. 相似文献