共查询到20条相似文献，搜索用时 46 毫秒
1.
2.
Sławomir Breiter 《Celestial Mechanics and Dynamical Astronomy》1997,67(3):237-249
The analytical solution for the perturbations of an artificial satellite due to the zonal part of the geopotential is presented.
The Hamiltonian is fully normalized up to the second order by a single averaging transformation and the generating function
is given explicitly. The formulas allow an arbitrarily high degree of geopotential harmonics to be included. The transformation
from mean to osculating variables or vice versa is performed by means of a numerical method proposed by the author in a previous
paper (Breiter,1997): periodic perturbations are computed by means of a Runge-Kutta method of order 2 instead of being explicitly
derived from a generator.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
The solution to the motion of a satellite in an eccentric orbit and in resonance with the second-degree sectorial harmonic of the potential field is developed. The method of solution used parallels the well known von Zeipel method of general perturbations. The solution consists of expressions for the variations of the Delaunay variables. These expressions are composed of the perturbations developed by Brouwer in 1959 for the motion of an artificial satellite plus first-order perturbations due to the second-degree sectorial harmonic (in terms of the Legendre normal elliptic integrals of the first and second kind).This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration. 相似文献
4.
Giorgio E. O. Giacaglia James P. Murphy Theodore L. Felsentreger 《Celestial Mechanics and Dynamical Astronomy》1970,3(1):3-66
A semi-analytical solution to the problem of the motion of a satellite of the moon is presented. Perturbative effects which are considered include those due to the attraction of the moon, earth, and sun, the non-sphericity of the moon's gravitational field, coupling of lower-order terms, solar radiation pressure, and physical libration. Short-period terms and intermediate-period terms, terms with the period of the moon's longitude, are produced by means of von Zeipel's method; it is proposed to obtain the secular perturbations, and those depending only on the argument of perilune, by numerical integration of the equations of motions. The short-period terms and intermediate-period terms are developed up to second order, where first order is 10–2. The secular perturbations and perturbations dependent on the argument of perilune are obtained to third order. 相似文献
5.
M. A. Vashkov’yak 《Astronomy Letters》2005,31(1):64-72
We describe an approximate numerical-analytical method for calculating the perturbations of the elements of distant satellite orbits. The model for the motion of a distant satellite includes the solar attraction and the eccentricity and ecliptic inclination of the orbit of the central planet. In addition, we take into account the variations in planetary orbital elements with time due to secular perturbations. Our work is based on Zeipel’s method for constructing the canonical transformations that relate osculating satellite orbital elements to the mean ones. The corresponding transformation of the Hamiltonian is used to construct an evolution system of equations for mean elements. The numerical solution of this system free from rapidly oscillating functions and the inverse transformation from the mean to osculating elements allows the evolution of distant satellite orbits to be studied on long time scales on the order of several hundred or thousand satellite orbital periods. 相似文献
6.
D. A. Lautman 《Celestial Mechanics and Dynamical Astronomy》1977,15(4):387-420
A semianalytic method has been developed to calculate the radiation-pressure perturbations of a close-Earth satellite due to sunlight reflected from the Earth. The assumptions made are that the satellite is spherically symmetric and that the solar radiation is reflected from the Earth according to Lambert's Law with uniform albedo. By using expressions for the components of the radiation-pressure force due to Lochry, the expressions for the perturbations of the elements were developed into series in the true anomalyv. The perturbations within a given revolution can be obtained analytically by integrating with respect tov while holding all slowly varying quantities constant. The long-range perturbations are then obtained by accumulating the net perturbations at the end of each revolution. 相似文献
7.
The motion of a lunar satellite 总被引：2，自引：0，他引：2
Claus Oesterwinter 《Celestial Mechanics and Dynamical Astronomy》1970,1(3-4):368-436
Presented in this theory is a semianalytical solution for the problem of the motion of a satellite in orbit around the moon. The principal perturbations on such a body are due to the nonspherical gravity field of the moon, the attraction of the earth, and, to a lesser degree, the attraction of the sun. The major part of the problem is solved by means of the celebrated von Zeipel Method, first successfully applied to the motion of an artificial earth satellite by Brouwer in 1959. After eliminating from the Hamiltonian all terms with the period of the satellite and those with the period of the moon, it is suggested to solve the remaining problem with the aid of numerical integration of the modified equations of motion.This theory was written in 1964 and presented as a dissertation to Yale University in 1965. Since then a great deal has been learned about the gravity field of the moon. It seems that quite a number of recently determined gravity coefficients would qualify as small quantities of order two. Hence, according to the truncation criteria employed, they should be considered in the present theory. However, the author has not endeavored to update the work accordingly. The final results, therefore, are incomplete in the lunar gravitational perturbations. Nevertheless, the theory does give the largest such variations and it does present the methods by which perturbations may be derived for any gravity terms not actually developed. 相似文献
8.
Anthony G. Lubowe 《Celestial Mechanics and Dynamical Astronomy》1970,2(1):88-102
The basic principles and equations of Hansen's method are briefly stated. These equations are integrated to first order accuracy by analytic quadratures for the case of perturbations due to the Earth's oblateness and the procedure for obtaining the position of a satellite acted upon by such a perturbation is described in detail. Comparison of accuracies of one day predictions made with this Hansen's method and a first order variation of parameters method indicates comparable accuracies can be achieved with approximately 1/10 of the computation time when using Hansen's method.Presented at the AIAA/AAS Astrodynamics Conference, Princeton, N.J., August 20–22, 1969 (AIAA Preprint No. 69-909). 相似文献
9.
Luni-solar perturbations of an Earth satellite 总被引：1，自引：0，他引：1
A. E. Roy 《Astrophysics and Space Science》1969,4(4):375-386
Luni-solar perturbations of the orbit of an artificial Earth satellite are given by modifying the analytical theory of an artificial lunar satellite derived by the author in recent papers. Expressions for the first-order changes, both secular and periodic, in the elements of the geocentric Keplerian orbit of the earth satellite are given, the moon's geocentric orbit, including solar perturbations in it, being found by using Brown's lunar theory.The effects of Sun and Moon on the satellite orbit are described to a high order of accuracy so that the theory may be used for distant earth satellites. 相似文献
10.
Some aspects for efficient computation of the tidal perturbation due to the ellipticity effects of the Earth, the luni-solar potential on an Earth-orbiting satellite and the perturbations of the satellite's radial, transverse and normal position components due to the effects of the Earth's gravitational and ocean tide fields are presented. A straightforward method for computing the spectrum of the geopotential and the tidal-induced perturbations of the orbit elements and the radial, transverse and normal components is described. 相似文献
11.
David R. Cok 《Celestial Mechanics and Dynamical Astronomy》1977,16(4):459-479
The lunar disturbing function for a close-Earth satellite is expressed as a sum of products of harmonics of the satellite's position and harmonics of the Moon's position, and the latter are expanded about a rotating and precessing elliptic orbit inclined to the ecliptic. The deviations of the Moon from this approximate orbit are computed from Brown's lunar theory andthe perturbations in satellite orbital elements due to these inequalities are derived. Numerical calculations indicate that several perturbations in the position of the satellite's node and perigee have magnitudes on the order of one meter.The author is supported in part by a National Science Foundation Graduate Fellowship. 相似文献
12.
Effects of motion of the equatorial plane on the orbital elements of an earth satellite 总被引：1，自引：0，他引：1
Exact differential equations relating the perturbations to satellite orbital elements by the motion of the Earth's equatorial plane are derived, and they are solved to second order in precession. The system proposed in a previous paper (Kozai, 1960), in which the inclination and the argument of perigee are referred to the equator of date and the longitude of the ascending node is measured from a fixed point along a fixed plane and then along the equator of date, can still be recommended for precise studies of satellite motion even when the second-order perturbations are taken into account. 相似文献
13.
Vladimir Martinusi Lamberto Dell’Elce Gaëtan Kerschen 《Celestial Mechanics and Dynamical Astronomy》2017,127(4):451-476
The paper offers the fully analytic solution to the motion of a satellite orbiting under the influence of the two major perturbations, due to the oblateness and the atmospheric drag. The solution is presented in a time-explicit form, and takes into account an exponential distribution of the atmospheric density, an assumption that is reasonably close to reality. The approach involves two essential steps. The first one concerns a new approximate mathematical model that admits a closed-form solution with respect to a set of new variables. The second step is the determination of an infinitesimal contact transformation that allows to navigate between the new and the original variables. This contact transformation is obtained in exact form, and afterwards a Taylor series approximation is proposed in order to make all the computations explicit. The aforementioned transformation accommodates both perturbations, improving the accuracy of the orbit predictions by one order of magnitude with respect to the case when the atmospheric drag is absent from the transformation. Numerical simulations are performed for a low Earth orbit starting at an altitude of 350 km, and they show that the incorporation of drag terms into the contact transformation generates an error reduction by a factor of 7 in the position vector. The proposed method aims at improving the accuracy of analytic orbit propagation and transforming it into a viable alternative to the computationally intensive numerical methods. 相似文献
14.
The short period luni-solar theory of Kozai is generalized for arbitrary obliquity of the ecliptic and inclination of the moon's orbit to the ecliptic. Analytic first order lunar perturbations to the elements are derived. The theory is illustrated by an application to the communication satellite Intelsat 3F3.Presently at the Department of Environmental Sciences, University of Tel Aviv, Ramat Aviv, Israel. 相似文献
15.
The orbit of the balloon satellite, Explorer 19, is analysed to determine the effects of direct solar radiation pressure over one revolution of the satellite (111 min) for MJD 42822 and MJD 42966. At the earlier date, the satellite entered the Earth's shadow, presenting an opportunity to examine the effectiveness of two different shadow models. The reflectivity of the surface of the satellite was estimated from analysis of the variations in orbital eccentricity over a period of 236 days.Although many of the parameters associated with the shape and orientation of the satellite are unknown, the theory for a non-spherical satellite is applied using trial and error methods to determine the parameters of best fit. The paper concludes with an examination of the perturbations in orbital eccentricity and inclination due to incident, specularly reflected, and diffusely reflected radiation. 相似文献
16.
Position and velocity perturbations for the determination of geopotential from space geodetic measurements 总被引：10，自引：0，他引：10
Peiliang Xu 《Celestial Mechanics and Dynamical Astronomy》2008,100(3):231-249
Although space geodetic observing systems have been advanced recently to such a revolutionary level that low Earth Orbiting
(LEO) satellites can now be tracked almost continuously and at the unprecedented high accuracy, none of the three basic methods
for mapping the Earth’s gravity field, namely, Kaula linear perturbation, the numerical integration method and the orbit energy-based
method, could meet the demand of these challenging data. Some theoretical effort has been made in order to establish comparable
mathematical modellings for these measurements, notably by Mayer-Gürr et al. (J Geod 78:462–480, 2005). Although the numerical
integration method has been routinely used to produce models of the Earth’s gravity field, for example, from recent satellite
gravity missions CHAMP and GRACE, the modelling error of the method increases with the increase of the length of an arc. In
order to best exploit the almost continuity and unprecedented high accuracy provided by modern space observing technology
for the determination of the Earth’s gravity field, we propose using measured orbits as approximate values and derive the
corresponding coordinate and velocity perturbations. The perturbations derived are quasi-linear, linear and of second-order
approximation. Unlike conventional perturbation techniques which are only valid in the vicinity of reference mean values,
our coordinate and velocity perturbations are mathematically valid uniformly through a whole orbital arc of any length. In
particular, the derived coordinate and velocity perturbations are free of singularity due to the critical inclination and
resonance inherent in the solution of artificial satellite motion by using various types of orbital elements. We then transform
the coordinate and velocity perturbations into those of the six Keplerian orbital elements. For completeness, we also briefly
outline how to use the derived coordinate and velocity perturbations to establish observation equations of space geodetic
measurements for the determination of geopotential. 相似文献
17.
The formulae for the perturbations in radial, transverse and binormal components of the Earth artificial satellite motion have been derived. Perturbations due to the tesseral part of the geopotential are considered. The geopotential expressed in terms of the orbital elements has the form proposed by Wnuk (1988). The formulae for the perturbations have been obtained using the Hori (1966) method. They can be effectively applied in calculation of the perturbations in the components including the coefficients of the high order and degree tesseral harmonics. The derived formulae reveal no singularities at zero eccentricity. 相似文献
18.
David Vokrouhlický 《Celestial Mechanics and Dynamical Astronomy》1989,46(1):85-104
The orbital effects of the Lorentz force on the motion of an electrically charged artificial satellite moving in the Earth's
magnetic field are determined. The geomagnetic field is considered as a multipole potential field and the satellite electrical
charge is supposed to be constant. The relativistic perturbations of the main geomagnetic field are discussed briefly. The
results are concentrated on the determination of the secular changes, and numerical values are computed for the case of the
LAGEOS satellite. The results are discussed in the context of a possible detection of the Lense-Thirring effect analyzing
the orbital perturbations of the LAGEOS and LAGEOS X satellites. 相似文献
19.
S. Ferraz Mello 《Celestial Mechanics and Dynamical Astronomy》1972,5(1):80-101
In this paper a new mathematical model is proposed for the study of the effects of the direct solar radiation pressure on the orbit of an artificial Earth satellite. The equations for the first order effects become canonical when a different definition for the orders of magnitude is adopted. This enables us the utilization of the method of Von Zeipel to eliminate all periodic terms. The model leads to the non-existence of pure secular perturbations owing to the direct solar radiation pressure on the metric elements: semi-major axis, eccentricity and inclination. Numerical examples built with an approximation for the shadow function show that the secular inequalities on the angle variables—longitude, perigee and node—are very small. 相似文献
20.
Radial,transverse and normal satellite position perturbations due to the geopotential 总被引：1，自引：0，他引：1
Perturbations in the position of a satellite due to the Earth's gravitational effects are presented. The perturbations are given in the radial, transverse (or alongtrack) and normal (or cross-track) components. The solution is obtained by projecting the Kepler element perturbations obtained by Kaula [Kaula, 1966] into each of the three components. The resulting perturbations are presented in a form analogous to the form of Kaula's solution which facilitates implementation and interpretation. 相似文献