共查询到10条相似文献，搜索用时 140 毫秒
1.
Adams—Cowell方法与KSG积分器的比较 总被引：2，自引：0，他引：2
在人造地球卫星精密定轨中,有摄星历等量的计算常采用Adams-Cowell方法,美国Texas大学空间研究中心(CSR)的定轨软件中则采用了一种有别于Adams-Cowell方法的KSG积分器。本文对这两种线性多步法作了全面比较,并用典型算例作了数值验证,列出了两种方法中卫星轨道沿迹误差的状况,以此表明为什么人们常采用Adams-Cowell方法。 相似文献
2.
简要介绍当前天体力学中常用的各种数值计算方法,结合同步卫星运动方程的特点和轨道解的性质,分析各种数值计算方法在同步卫星情况下使用的优劣,确定一次和分形式的Cowell方法是建立同步卫星精密星历表的最佳方法,最后通过有效的数值实验,给出不同精度要求下Cowell方法的最佳阶和相应的最大步长. 相似文献
3.
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. 相似文献
4.
V. A. Shefer 《Solar System Research》2008,42(5):405-413
A new method of computing the preliminary orbit of a celestial body based on four pairs of angle measurements has been suggested. The method makes use of preliminary orbit previously constructed by the author based on two position vectors and a corresponding time interval, taking into account the main part of the perturbations in the motion of the body under study. Using the example of constructing the orbit of the minor planet 1383 Limburgia, the results obtained using a four-position procedure of the Gaussian type based on the solution of a two-body problem have been compared with those of the new method. The comparison showed the new method to be highly efficient for perturbed motion studies. It is especially advantageous in the case of high-accuracy observation data on small orbital arcs. 相似文献
5.
V. A. Shefer 《Solar System Research》2003,37(4):326-332
A new method is suggested for finding the preliminary orbit from three complete measurements of the angular coordinates of a celestial body developed by analogy with the classic Lagrange–Gauss method. The proposed method uses the intermediate orbit that we had constructed in an earlier paper based on two position vectors and the corresponding time interval. This intermediate orbit allows for most of the perturbations in the motion of the body. Using the orbital motion of asteroid 1566 Icarus as an example, we compare the results obtained by applying the classic and the new method. The comparison shows the new method to be highly efficient for studying perturbed motion. It is especially efficient if applied to high-precision observational data covering short orbital arcs. 相似文献
6.
V. A. Shefer 《Solar System Research》2010,44(2):152-165
We propose a new method for the determination of the preliminary orbit of a small celestial body using three pairs of its
angular coordinates in three moments of time. The method is based on the use of the intermediate orbit we constructed earlier
using three position vectors and the corresponding time moments. This intermediate orbit accounts for the main part of the
perturbations of the motion of the body under study. We compare the results obtained by the classical Lagrange-Gauss method,
Herrick-Gibbs method, generalized Herrick-Gibbs method, and the new method by the examples of the determination of the orbit
of the small planet 1566 Icarus. The comparison showed that the new method is a highly efficient tool for the study of perturbed
motion. It is especially efficient when applied to high-precision observational data covering short arcs of the orbit. 相似文献
7.
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
8.
《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
9.
V. A. Shefer 《Astronomy Letters》2007,33(4):270-282
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. 相似文献
10.
V. A. Shefer 《Solar System Research》2010,44(3):252-266
The classic problem of finding the orbit of a celestial body from its two position vectors for two instants of time is considered.
A solution to the problem free from uncertainties is obtained which can be applied for all three kinds of Keplerian movement.
The main part of the computational procedure is reduced to solving one equation with one unknown. Formulas are derived for
the initial value of the equation root, which makes the application of the Newton-Raphson method successful. The efficiency
and reliability of the suggested algorithm is illustrated by examples of the orbit determination for the asteroids Adeona
and Icarus, as well as for Halley’s Comet and Bowell’s Comet. 相似文献