共查询到20条相似文献,搜索用时 531 毫秒
1.
Andrej G. Sokolsky Akmal A. Vakhidov Nickolay N. Vasiliev 《Celestial Mechanics and Dynamical Astronomy》1995,63(3-4):357-374
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. 相似文献
2.
Akmal A. Vakhidov 《Celestial Mechanics and Dynamical Astronomy》2001,81(3):177-190
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. 相似文献
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《Chinese Astronomy and Astrophysics》2022,46(1):137-151
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. 相似文献
5.
Richard L. Branham Jr. 《Celestial Mechanics and Dynamical Astronomy》1990,49(2):209-217
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. 相似文献
6.
It is shown that a sufficient condition for the stability of an incompressible sheared gravitationally stratified ideal magnetofluid with flow-aligned horizontal magnetic field is that there exists a Galilean frame in which the flow is nowhere super-Alfvénic (similarly, stability is assured in a compressible shear flow without gravity if there exists a frame in which the flow nowhere exceeds the cusp speed). Complex eigenvalue bounds are presented for unstable flows. The stability condition is applied to the solar tachocline; it suggests that any shear instabilities associated with radial gradients in flow speed should be stabilized by fields of above about 7 kG. 相似文献
7.
We introduce a class of fourth order symplectic algorithms that are ideal for doing long time integration of gravitational
few-body problems. These algorithms have only positive time steps, but require computing the force gradient in addition to
the force. We demonstrate the efficiency of these Forward Symplectic Integrators by solving the circular restricted three-body
problem in the space-fixed frame where the force on the third body is explicitly time-dependent. These algorithms can achieve
accuracy of Runge–Kutta, conventional negative time step symplectic and corrector symplectic algorithms at step sizes five
to ten times as large. 相似文献
8.
Yu. I. Morozov 《Astrophysics and Space Science》1987,133(1):107-148
This paper deals with the representation of relativistic equations of gas dynamics with due regard to the general relativity theory effects in the form accepted and widely applied in the special relativity theory. With this purpose, a strict formal definition of a non-inertial co-moving reference frame without rotation is carried out on the basis of a tetrad formalism by use of the Fermi—Walker rules of transport of 4-frame. The equations of physical kinetics, relativistic collapse, Einstein's equations, equations of relatiivistic radiation gas dynamics for ideal and dissipative gases, Taub's equations for a shock wave, which allow for radiation and electron-positron pairs, are obtained in this reference frame. On the basis of the local Lorentz transformation and the Ricci rotation coefficients, these equations are written in the laboratory reference frame, in order to illustrate the fact that the general relativity effects can be simply taken into account in the equations having a form accepted in the special relativity theory. 相似文献
9.
B. Zafiropoulos 《Astrophysics and Space Science》1987,136(1):149-165
This paper deals with the perturbations which tidal lag in longitude can produce to the orbital elements of a close binary system. The expressions obtained for the six elements of the orbit have been presented as functions of the unperturbed true anomaly, measured from the periastron. Our study includes the effects produced by the second, third, and fourth tidal harmonic distortions. In order to save space these extremely lengthy equations are given in the compact form of summations, by means of Hansen coefficients. Various recurrence relations, which hold good for Hansen coefficients, are also presented. Finally, this paper includes a second-order approximation only for the secular terms of first-order approximation. 相似文献
10.
Andre Deprit 《Celestial Mechanics and Dynamical Astronomy》1976,13(2):253-263
Cartan's exterior calculus is used to refer a perturbed Keplerian motion to an ideal frame by means of either the Eulerian parameters or the Eulerian angles, in which case the equations are given a Hamiltonian form. The results are compared with the corresponding systems in the orbital and nodal frames. 相似文献
11.
An end-to-end modelling program for an astrometric telescope employing a Ronchi ruling has been developed. The program models the aberrated images formed anywhere in the field-of-view. It then determines apparent centroids by simulating the motion of a Ronchi ruling across the field. Photo-electron statistics are included. A 6-term plate-constant model is used to determine the apparent motion of a target star within a reference frame as the object is re-observed through both ideal and perturbed optics. The modelling code is accurate at the submicroarcsecond level.Paper presented at the Conference on Planetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A. 相似文献
12.
V. A. Brumberg 《Celestial Mechanics and Dynamical Astronomy》1994,59(1):1-36
It is shown that the first-order general planetary theory, i.e. the theory without secular terms, developed in (Brumberg and Chapront, 1973) may be re-constructed and presented by the series in powers of the eccentricity and inclination variables with the closed form coefficients expressed in terms of elliptic functions. The intermediate solution of the zero degree in eccentricities and inclinations has been given explicitly with the aid of elliptic functions and the Hansen type quadratures with trigonometric function kernels. In determining the first and higher degree terms in eccentricities and inclinations one meets the Hansen type quadratures with elliptic function kernels. The secular evolution is described by the autonomous polynomial differential system. 相似文献
13.
本文评述了在建立历表参考架和恒星参考架过程中所面临的问题和困难,回顾了建立河外射电天球参考架的发展历史,并介绍了其目前状况,讨论了河外射电天球参考架在与其他天球参考架连接过程中所遇到的问题及其可能的解决途径。 相似文献
14.
A phenomenological model of the interplay between the polar magnetic fields of the Sun and the solar sector structure is discussed. Current sheets separate regions of opposite polarity and mark the sector boundaries in the corona. The sheets are visible as helmet streamers. The solar sector boundary is tilted with respect to central meridian, and boundaries with opposite polarity change are oppositely tilted. The tilt of a given type of boundary [(+, ?) or (?, +)] changes systematically during the sunspot cycle as the polarity of the polar fields reverses. Similar reversals of the position of the streamers at the limbs takes place. If we consider (a) a sunspot cycle where the northern polar field is inward (?) during the early part of the cycle and (b) a (+, ?) sector boundary at central meridian then the model predicts the following pattern; a streamer at high northern latitudes should be observed over the west limb together with a corresponding southern streamer over the east limb. The current sheet runs now NW-SE. At sunspot maximum the boundary is more in the N-S direction; later when the polar fields have completed their reversal the boundary runs NE-SW and the northern streamer should be observed over the east limb and the southern streamer over the west limb. Observational evidence in support of the model is presented, especially the findings of Hansen, Sawyer and Hansen and Koomen and Howard that the K-corona is highly structured and related to the solar sector structure. 相似文献
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Martin Lara 《Celestial Mechanics and Dynamical Astronomy》2017,129(1-2):137-151
An implementation of the ideal frame formulation of perturbed Keplerian motion is presented which only requires the integration of a differential system of dimension 7, contrary to the 8 variables traditionally integrated with this approach. The new formulation is based on the integration of a scaled version of the Eulerian set of redundant parameters and slightly improves runtime performance with respect to the 8-dimensional case while retaining comparable accuracy. 相似文献
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In a previous paper (Zafiropoulos and Kopal, 1982; hereafter referred to as Paper I) we have studies the effects of rotational distortion on the orbital elements. The aim of the present paper is to investigate the secular and periodic perturbations of the orbital elements due to tidal distortion. For tidal distortion when tides do not lag, the Gaussian form of Lagrange's planetary equations has been employed to yield the first- and second-order approximations. The results obtained include the effects produced by the second, third and fourth harmonic distortions. The first order approximation for non-lagging tides has been expressed by means of Hansen coefficients. 相似文献
19.
N. Tomimura 《Astrophysics and Space Science》1993,201(2):223-228
The gravitational collapse of a slowly rotating star with small deviations from spherical symmetry is studied. The exterior metric is chosen to be the Kerr metric in synchronous coordinates discarding terms of order (a/r)2. Interior geometry is constructed by adding an off-diagonal term in first order ofa to the exact solution of the non-rotating case. This term is determined in part by requiring the validity of the junction conditions at the star's surface and by demanding that the angular momentum of the source is equal toM A, in agreement with the value measured by a distant observer. The resulting stress-energy tensor describes a homogeneous, pressureless, ideal fluid which rotates nonuniformly relative to the synchronous frame which is no longer comoving the stellar matter. 相似文献
20.
Dieter J. Lelgemann 《Celestial Mechanics and Dynamical Astronomy》1983,30(3):309-321
Using Hill's variables, an analytical solution of a canonical system of six differential equations describing the motion of a satellite in the gravitational field of the earth is derived. The gravity field, expanded into spherical harmonics, has to be expressed as a function of the Hill variables. The intermediary is chosen to include the main secular terms. The first order solution retains the highly practical formal structure of Kaula's linear solution, but is valid for circular orbits and provides of course a spectral decomposition of radius vector and radial velocity. The resulting eccentricity functions are much simpler than the Hansen functions, since a series evaluation of the Kepler equation is avoided. The present solution may be extended to higher order solutions by Hori's perturbation method. 相似文献