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1.
The secular terms of the planetary disturbing function are given, after elimination of short period terms by von Zeipel's transformation. The adequacy of this expansion up to terms of eighth order in the inclination and eccentricity is investigated by numerical processes, as a function of the Keplerian elementsa, e andi. The eccentricityé of the outer planet, is taken equal to zero. It is concluded that for values ofi which are not small the inclusion of additional terms in the expression for the disturbing function, results to drastic changes in its values, while larger values ofe do not have an equaly large effect on the disturbing function.  相似文献   

2.
The construction of a third order J-S theory is presented. The Hori theory of planetary perturbations is employed. No Critical J-S terms due to the 2:5 commensurabilities and its multiples exist, when we take into account the periodic terms of order 0, 1, 2 with respect to the eccentricity- inclination. In this case the Lie series transformation degenerates and is meaningless. The J-S equations of motion for secular perturbations are solved when we neglect in our treatment, the Poisson terms of degree > 2 in the Poincaré canonical variables H u , K u , P u Q u (u = 1, 2). The Jacobi-Radau referential is adopted, and the theory is expressed in terms of the canonical variables of H. Poincaré.Now at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, U.S.A.  相似文献   

3.
The in-plane motion of a Geosynchronous satellite under the gravitational effects of the sun, the moon and the oblate earth has been studied. The radial deviation (Δr) and the tangential deviation (r cΔθ) have been determined. Herer c represents the synchronous altitude. It has been seen that the sum of the oscillatory terms in Δr for different inclinations is a small finite quantity whereas the sum of the oscillatory terms inr cΔθ for different inclinations is quite large due to the presence of the low-frequency terms in the denominator  相似文献   

4.
We present a second order secular Jupiter-Saturn planetary theory through Poincaré canonical variables, von Zeipel's method and Jacobi-Radau referential. We neglect in our expansions terms of power higher than the fourth with respect to eccentricities and sines of inclinations. We assume that the disturbing function is composed of secular and critical terms only. We shall deriveF 2si and writeF 2s in terms of Poincaré canonical variables in Part II of this problem.  相似文献   

5.
We expand both parts, the principal and indirect, of the Hamiltonian function up to the third order in the masses for the four major planets Jupiter-Saturn-Uranus-Neptune. Accordingly we write down the secular terms ofF 1,F 2,F 3 and the critical terms ofF 1,F 2 in terms of the canonical variables of H. Poincaré neglecting powers higher than the second inH, K, P, Q.  相似文献   

6.
In a paper by the second author (Nacozy, 1981), various time elements are presented for use with the Sundman time transformation. In that paper, the time elements are given in terms of Keplerianorbital elements. We give here the corresponding time elements in terms ofrectangular coordinates. Extensive references are given in the previous paper and will be omitted here.We present additional numerical experiments comparing the use of time elementsand time transformationstogether with the use of time transformationsalone. The results indicate a reduction in computational error when time elements are used.  相似文献   

7.
The paper discusses the solution of a simple kinetic equation of thetype used for the computation of the change of the chemical compositionin stars like the Sun. Starting from the standard form of the kineticequation it is generalized to a fractional kinetic equation and itssolutions in terms of H-functions are obtained. The role of thermonuclearfunctions, which are also represented in terms of G- and H-functions,in such a fractional kinetic equation is emphasized. Results containedin this paper are related to recent investigations of possibleastrophysical solutions of the solar neutrino problem.  相似文献   

8.
The restricted three-body Hamiltonian is partitioned into a two-center type principal part and its accompanying perturbational part. The mathematical analysis, involving the Jacobian elliptic functions, is adapted for the case of figure-eight orbits winding around the two given mass points. For many such orbits the elliptic function modulusk is small and can serve as a small parameter.Fourier expansions in terms of a parameter related tot are obtained for the intermediate orbit functions which provide representations in terms of elementary functions.  相似文献   

9.
The comoving-frame equations of radiative transfer and moment equations to accurate terms of all orders inv/c are derived in the modified Lagrangian form. The equations exactly describe the interaction of radiation with matter in a relativistically moving medium in flat or curved spacetime. Two specialized sets of equations are presented: (1) the equation of radiative transfer and moment equations accurate to terms of second order (v 2/c 2), and (2) the transfer equation and moment equations for a radial flow in curved spacetime with the Schwarzschild-type metric.  相似文献   

10.
In radiative transfer, the intensities of radiation from the bounding faces of a scattering atmosphere of finite optical thickness can be expressed in terms of Chandrasekhar’s X- and Y-functions. The nonlinear nonhomogeneous coupled integral equations which the X- and Y-functions satisfy in the real plane are meromorphically extended to the complex plane to frame linear nonhomogeneous coupled singular integral equations. These singular integral equations are then transformed into nonhomogeneous Riemann–Hilbert problems using Plemelj’s formulae. Solutions of those Riemann–Hilbert problems are obtained using the theory of linear singular integral equations. New forms of linear nonhomogeneous decoupled expressions are derived for X- and Y-functions in the complex plane and real plane. Solutions of these two expressions are obtained in terms of one known N-function and two new unknown functions N 1- and N 2- in the complex plane for both nonconservative and conservative cases. The N 1- and N 2-functions are expressed in terms of the known N-function using the theory of contour integration. The unknown constants are derived from the solutions of Fredholm integral equations of the second kind uniquely using the new linear decoupled constraints. The expressions for the H-function for a semi-infinite atmosphere are obtained as a limiting case.  相似文献   

11.
A recurrence relation for inclination functions   总被引：2，自引：2，他引：0  
When the terms of the series expansion for the gravitational potential of the Earth are expressed in terms of the orbital elements of an arbitrary Earth satellite, the orbital inclination,i, appears in each, term as the argument of a function of inclination only. For the special case when the field is axi-symmetric, studied in an earlier paper, a recurrence relation was given for a normalized inclination function,A k l(i), with two parameters. The present paper gives a recurrence relation for a general normalized function,K k lm(i), with three parameters.  相似文献   

12.
In this paper, the classical and generalized Sundman time transformations are used to establish new generating set of differential equations of motion in terms of the Eulerian redundant parameters. The implementation of this set on digital computers for the commonly used independent variables is developed once and for all. Motion prediction algorithms based on these equations are developed in a recursive manner for the motions in the Earth's gravitational field with axial symmetry whatever the number of the zonal harmonic terms may be. Applications for the two types of short and long term predictions are considered for the perturbed motion in the Earth's gravitational field with axial symmetry with zonal harmonic terms up to J 36 . Numerical results proved the very high efficiency and flexibility of the developed equations.  相似文献   

13.
A Laplace and a Hankel transform of the light curves of eclipsing binary star systems have been expressed in terms of the eclipse elements (L 1,r 1,2 andi) of the spherical basic model. These general expressions can be used for the solution of the eclipse elements of the systems in terms of the observed quantities.  相似文献   

14.
The equation for radiative transfer in the case of resonance radiation for isotropic scattering has been solved by the method of the Laplace transformation and linear singular operators. The solution for emergent intensities have come out in terms ofX- andY-functions.  相似文献   

15.
The aim of the present paper will be to develop methods for computation of the Fourier transforms of the light curves of eclipsing variables — due to any type of eclipses — as a function of a continuous frequency variablev. For light curves which are symmetrical with respect to the conjunctions (but only then) these transforms prove to be real functions ofv, and expressible as rapidly convergent expansions in terms of the momentsA 2m+1 of the light curves of odd orders. The transforms are found to be strongly peaked in the low-frequency domain (attaining a maximum forv=0), and become numerically insignificant forv>3. This is even more true of their power spectra.The odd momentsA 2m+1 — not encountered so far in our previous papers — are shown in Section 3 of the present communication to be expressible as infinite series in terms of the even momentsA 2m well known to us from Papers I–IV; and polynomial expressions are developed for approximating them to any desired degree of accuracy. The numerical efficiency of such expressions will be tested in Section 4, by application to a practical case, with satisfactory results.Lastly, in Section 5, an appeal to the Wiener-Khinchin theorem (relating the power spectra with autocorrelation function of the light curves) and Parseval's theorem on Fourier series will enable us to extend our previous methods for a specification of quadratic moments of the light curves in terms of the linear ones.  相似文献   

16.
A conformally coupled Abelian gauged Q ball is studied in curved space. The mass of the Q ball is calculated in terms of the conserved Q charge and the parameters in the lagrangian and a brief discussion is given on the effects produced by the conformal couplings.  相似文献   

17.
The colors of giant elliptical (gE) galaxies in clusters out to redshiftz=0.2, observed by Oke and Sandage (1968), are studied for systematic color-redshift effects. To reveal any intrinsic changes, theK term is subtracted from each color, after correction for galactic reddening and the resulting (B-V) c -K B-V versus z relation analysed. If the Oke and SandageK terms (relevant to nuclear colors) are used, the best fitting linear relation shows negligible change withz. But if the Whitford (1970)K terms (relevant to integrated colors) are used, there is a trend to bluer colors, by 0.07 mag.atz=0.2 if higher weight is given the better observed clusters. An upper limit, of ±0.08 mag. atz=0.2, is set to possible systematic aperture effects, by the total change between nuclear and integrated B-V and U-B of nearbygE galaxies.The color-redshift trends, interpreted as evolutionary changes, are related to evolution in the magnitude-redshift relation by means of models of stellar evolution in agE galaxy. If one uses the linear fit to the color-redshift relation obtained with WhitfordK terms and neglect of any aperture effects (which is the appropriate case if Oke and Sandage used large enough apertures), and if one adopts plausible limits to the ratio between color and magnitude evolution, the effect of evolution in the magnitude-redshift relation results in a negative value ofq 0. There are still substantial observational and theoretical uncertainties affecting this conclusion.  相似文献   

18.
The application of the Wiener-Hopf technique to the coupled linear integral equation ofX- andY-equations gives rise to the Fredholm equations with simpler kernels.X-equation is expressed in terms ofY-equation and vice-versa. These are unique in representation with respect to coupled linear constraints.  相似文献   

19.
A new formula has been derived for geopotential expressed in terms of orbital elements. The summation sequence was changed so that the terms of the same frequencies would be grouped and the generalized lumped coefficients were derived. The proposed formula has the same form for both odd and evenl-m.Applying Hori's perturbation method, new formulae were derived for tesseral harmonic perturbations in nonsingular orbital elements:l+g, h, e cosg,e sing, L, andH. We show the possibility of effective application of the derived formulae to the calculation of orbits of very low satellites taking into account the coefficients of tesseral harmonics of the Earth's gravitational field up to high orders and degrees. As an example the perturbations up to the order and degree of 90 for the orbit of GRM satellites were calculated. The calculations were carried out on an IBM AT personal computer.  相似文献   

20.
The comoving-frame equation of radiative transfer and moment equations are derived in orthogonal, curvilinear coordinates, inclusive of terms of orderv/c. The equation of radiative transfer, which contains the terms due to the effect of curvature of coordinate lines explicitly as well as those of Doppler shift and aberration, is the generalization of Castor's equation for spherical symmetry and of Buchler's equation for Cartesian coordinates. The moment equations agree with Buchler's.  相似文献   

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