共查询到20条相似文献，搜索用时 31 毫秒
1.
田谐项摄动是分析法轨道预报中的重要部分,其中包含大量倾角函数及其偏导数的计算.由于具有精度更高、速度更快的优点,倾角函数一般通过递推方法计算.以文献中提出的改进Gooding方法为基础,将其给出的程序稍加改进,在计算2–50阶倾角函数时缩短了约24%的计算时间.考虑到分析法预报过程中轨道平倾角变化很小,以泰勒展开式计算倾角函数,可极大提高计算速度,较大程度地减小分析法预报耗时,且引力场阶次越高,减小幅度越大,取50阶时预报耗时缩短了48%.另一方面,以2阶展开式计算倾角函数时,与改进Gooding法相比,分析法预报星历偏差很小.对于500 km高度的低轨卫星,分别以改进Gooding法和2阶泰勒展开式计算倾角函数,预报3天,当地球引力场阶次不高于50时,二者预报星历偏差RMS (Root Mean Square)低于1 mm,且随着轨道高度的增加,预报星历偏差RMS逐渐减小. 相似文献
2.
Pasquale Sconzo 《Astronomische Nachrichten》1967,290(4):163-170
After reviewing the existing procedures for solving the three-body problem by convergent power series, the author develops two algebraic methods in terms of the independent variable which is either the time t or Levi-Civita's regularizing variable u. These power series solve in Weierstrass' and Painlevé's sense the problem formulated in its greatest generality, since no restrictions at all are made on the order of magnitude of masses and none of the three bodies is restricted to moving along a prescribed conic section. Besides, the reference system used is a tridimensional Cartesian one. In the t-domain, the expressions for the high-order derivatives of the coordinates are computed using repeatedly Leibnitz's rule for derivatives of products of functions. In the u-domain, an extremely simple successive approximation procedure is established by means of a single recursion formula which requires elementary operations to be performed on polynomials of increasing degrees. 相似文献
3.
Paolo Lanzano 《Astrophysics and Space Science》1976,42(2):425-440
This paper discusses a method for improving on the numerical evaluation of the light changes exhibited by a distorted eclipsing binary system.In the theory formulated by Kopal (1959), certain boundary integrals due to the distortion of both components have been calculated in terms of the Appell hypergeometric series of the first kind. The values of the four parameters appearing in these series differ according as to whether one is dealing with a partial or an annular eclipse.To accelerate the numerical evaluation of the light changes one should avoid recomputing such infinite series for contiguous values of the parameters. This can be achieved by making use of certain recursion formulae which hold for the foregoing series.We have provided here a procedure that yields forty-eight recursion formulae for the Appell hypergeometric series and have specifically calculated four new independent recursion formulae relevant to the astrophysical problem. 相似文献
4.
《Chinese Astronomy and Astrophysics》2013,37(3):315-327
In this paper, a method to calculate the inclination function with Jacobi polynomials is studied, the formulation of this method is very simple, it needs not to concern about whether k and l have the same parity, and to calcu- late the non-integral factorials, nor to concern about the conversion between the case of k < 0 and the case of k ≥ 0, and the recurrent formula can be the stan- dard recurrent formula for Jacobi polynomials. In addition, its computational accuracy and applicable order-numbers are equivalent to those of the Gooding method, but its calculating time is shorter than that of the Gooding method for 9%. 相似文献
5.
Paolo Lanzano 《Astrophysics and Space Science》1976,45(2):483-490
This is a third paper dealing with the numerical evaluation of the light changes exhibited by close binary systems; for previous communications, Lanzano, 1976a, b.TheJ-integrals which were introduced by Kopal for the purpose of this numerical evaluation can be expanded in terms of the Appell hypergeometric series of the first kind. This relationship has been instrumental in establishing a number of recursion formulae for theJ-integrals applicable to the case of an annular eclipse. It was found that some recursion formulae hold both for the case of a partial and annular eclipse.The appropriate use of these recursion formulae should facilitate any numerical computation for eclipsing binaries. 相似文献
6.
H. M. Srivástava 《Astrophysics and Space Science》1991,181(2):195-202
The multivariable hypergeometric function $$F_{q_0 :q_1 ;...;q_n }^{P_0 :P_1 ;...;P_n } \left( {\begin{array}{*{20}c} {x_1 } \\ \vdots \\ {x_n } \\ \end{array} } \right),$$ considered recently by A. W. Niukkanen and H.M. Srivastava, is known to provide an interesting unification of the generalized hypergeometric functionp F q of one variable, Appell and Kampé de Fériet functions of two variables, and Lauricella functions ofn variables, as also of many other hypergeometric series which arise naturally in various physical, astrophysical, and quantum chemical applications. Indeed, as already pointed out by Srivastava, this multivariable hypergeometric function is an obvious special case of the generalized Lauricella function ofn variables, which was first introduced and studied by Srivastava and M. C. Daoust. By employing such fruitful connections of this multivariable hypergeometric function with much more general multiple hypergeometric functions studied in the literature rather systematically and widely, Srivastava presented several interesting and useful properties of this function, most of which did not appear in the work of Niukkanen. The object of this sequel to Srivastava's work is to derive a further reduction formula for the multivariable hypergeometric function from substantially more general identities involving multiple series with essentially arbitrary terms. Some interesting connections of the results considered here with those given in the literature, and some indication of their applicability, are also provided. 相似文献
7.
A set of spherical harmonics is the most widely used representation of the Earth’s gravity potential. This series converges outside and on the surface of a reference sphere enveloping the Earth. However, the Earth’s surface is better approximated by the reference ellipsoid—a compressed ellipsoid of revolution that covers the entire Earth. The gravity potential can be expanded in a series over ellipsoidal harmonics on the surface of the reference ellipsoid and on the surface of other external confocal ellipsoids of revolution. In contrast to spherical harmonics, depending on the associated Legendre functions of the first kind, ellipsoidal harmonics depend also on the associated Legendre functions of the second kind. The latter contain the very slowly converging hypergeometric Gauss series. The number of series increases with increasing the order of their derivatives. In this work, we derived new series for the gravitational potential of the Earth and its derivatives over ellipsoidal harmonics. Starting from the first order derivative, all the series corresponding to higher order derivatives depend on the same two hypergeometric Gauss series. The latter converges considerably faster than that for the hypergeometric series previously used when computing the gravity potential and its derivatives. 相似文献
8.
H. M. Srivastava 《Astrophysics and Space Science》1988,150(2):251-266
Motivated by their potential for applications in several diverse fields of physical, astrophysical, and engineering sciences, this paper aims at presenting a unified study of various classes of polynomial expansions and multiplication theorems associated with the general multivariable hypergeometric function (studied recently by A. W. Niukkanen and H. M. Srivastava), which provides an interesting and useful unifiation of numerous families of special functions in one and more variables, encoutered naturally (and rather frequently) in many physical, quantum chemical, and quantum mechanical situations. Several interesting applications of these general polynomial expansions are considered, not only in the derivations of various Clebsch-Gordan type linearization relations involving products of several Jacobi or Laguerre polynomials, but also to associated Neumann expansions in series of the Bessel functionsJ
v
(z) andI
v
(z) (and of their suitable products). 相似文献
9.
Afaq Ahmad 《Astrophysics and Space Science》1974,27(2):343-350
A class of equilibrium solutions of the Vlasov equation for self-gravitating systems is discussed. The density and the potential are derived in form of Jacobi polynomials, which in a special case give rise to a model with uniform density. 相似文献
10.
This paper gives a de?nite integration method for calculating the inclination function and its derivative, which has a very simple expression, and the accuracies as high as 10-15 for the inclination function, and 10-13 for its derivative, comparable with the accuracy of Gooding's method. By through a lot of numerical simulations, it is proved that this method has a good stability and an wide applicable range of inclinations, hence it can be used to calculate the inclination function to the maximum order of Lmax ≤ 50. 相似文献
11.
Osman Demircan 《Astrophysics and Space Science》1977,52(1):189-199
New expressions for the fractional loss of light
l
0
have been derived in the simple forms of rapidly converging expansions to the series of Chebyshev polynomials, Jacobi polynomials, and Kopal'sJ-integrals. In these expansions, which are a supplement to those given by Kopal (1977b), variablesk andh occur in different products that simplify the numerical computation. The treatment follows the new definition of
l
0
which has been recently developed by Kopal (1977a). 相似文献
12.
M. T. Edalati 《Astrophysics and Space Science》1978,59(2):333-345
The theoretical values of the momentsA
2m
for any type of eclipses, expressed in terms of the elementsL
1,a andc
0, have been derived in the simple forms of rapidly convergent expansions to the series of Chebyshev polynomials, Jacobi polynomials and KopalJ-integrals (Kopal, 1977c) and hold good for any real (not necessarily integral) value ofm0.The aim of the present paper has been to establish explicit expressions for the Jacobian and its fast enough computation in the light changes of close eclipsing systems, arising from the partial derivative of different pairs ofg-functions (Kopal and Demircan, 1978, Paper XIV) with respect toa andc
0
2
, for any type of eclipses (be these occultations or transit, partial, total or annular) and for any arbitrary degreel of the adopted law of limb-darkening. The functional behaviour of this Jacobian would determine the reasonable light curve in connection with geometrical determinacy of the parametersa andc
0. In the expansion of Jacobian, the terms consist of two polynomials which satisfy certain three-term recursion relations having the eclipse parametersa andc
0, as their arguments.Closed form expressions forf-functions, as well as of the Jacobian (e.g.,m=1, 2, 3), obtaining in the case of total eclipses, are given for a comparative discussion with the theoretical values of Jacobian derived from partial derivative of different pairs ofg-functions.The numerical magnitude of Jacobian would determine the best combination of the momentsA
2m
in the different pairs ofg-functions and definite results would follow in the subsequent paper of this series (Edalati, 1978c, Paper XXIV). 相似文献
13.
Paolo Lanzano 《Astrophysics and Space Science》1976,45(2):419-431
The integralsJ
,
m
were introduced by Kopal for the numerical evaluation of the light changes exhibited by eclipsing binaries when both the tidal and rotational distrotions are taken into account.This paper is a sequel to a previous one to appear in this journal and aims at ascertaining some recursion formulae for these integrals to alleviate the computational complexity of the problem.Using a relationship existing between theJ-integrals and the Appell hypergeometric series of the first kind, we have been able to obtain recursion formulae affecting all three parametersm , of these integrals. The present stage of development has also allowed for a complete enumeration of all independent recursion formulae applicable to the case of partial eclipses.Various recursion formulae, given here for the first time, generalize previous results by Kopal which were valid form=0 ory=0. 相似文献
14.
New expansions of elliptic motion based on considering the eccentricitye as the modulusk of elliptic functions and introducing the new anomalyw (a sort of elliptic anomaly) defined byw=u/2K–/2,g=amu–/2 (g being the eccentric anomaly) are compared with the classic (e, M), (e, v) and (e, g) expansions in multiples of mean, true and eccentric anomalies, respectively. These (q,w) expansions turn out to be in general more compact than the classical ones. The coefficients of the (e,v) and (e,g) expansions are expressed as the hypergeometric series, which may be reduced to the hypergeometric polynomials. The coefficients of the (q,w) expansions may be presented in closed (rational function) form with respect toq, k, k=(1–k
2)1/2,K andE, q being the Jacobi nome relatedk whileK andE are the complete elliptic integrals of the first and second kind respectively. Recurrence relations to compute these coefficients have been derived.on leave from Institute of Applied Astronomy, St.-Petersburg 197042, Russia 相似文献
15.
In this paper, the expression of V klm(I) in the Gooding method is rewritten to be the form convenient for calculation, and a standard recursive lm procedure is used to calculate Aklm(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. 相似文献
16.
Andre Deprit 《Celestial Mechanics and Dynamical Astronomy》1975,12(4):489-493
The geodetic latitude and the height of a satellite are obtained as power series in the ellipsoid's eccentricity, the terms being Fourier sums in the geocentric latitude with polynomials in 1/r as coefficients, with a view of determining the height to the fullest accuracy required by altimetry and geodesy from satellites. 相似文献
17.
18.
E. I. Burstein 《Celestial Mechanics and Dynamical Astronomy》1975,11(1):79-94
In this paper it is confirmed once more that there exists the general solution of Laplace's equation in ellipsoidal coordinates which satisfies the Stäckel theorem and which was derived earlier by M. Jarov-Jarovoi and S. J. Madden. The author interprets physically the general solution in real space as potentials of layers of charge and double layers in which the distribution of densities is defined by Green's formula. 相似文献
19.
A new formula is derived for the mass of spherically symmetric stellar configurations. An expression will be given where the mass square is connected to an integral over the pressure of gravitating matter. This formula turns out to hold for Newtonian gravity, for Einstein's GRT, for projective and bimetric scalar-tensor and further theories of gravitation. 相似文献
20.
《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