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1.
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
2.
The aim of this investigation is to present the secular and periodic perturbations of the six orbital elements of a close binary system due to rotational distortion. In our study we consider very small inclinationst of the orbital plane of the system, whereas the eccentricity of the orbit may assume any value between 0<e<1. The final formulae for the various elements have been expressed by means of the unperturbed true anomaly measured from the ascending node. 相似文献
3.
A second order atmospheric drag theory based on the usage of TD88 model is constructed. It is developed to the second order
in terms of TD88 small parameters K
n,j
. The short periodic perturbations, of all orbital elements, are evaluated. The secular perturbations of the semi-major axis
and of the eccentricity are obtained. The theory is applied to determine the lifetime of the satellites ROHINI (1980 62A),
and to predict the lifetime of the microsatellite MIMOSA. The secular perturbations of the nodal longitude and of the argument
of perigee due to the Earth’s gravity are taken into account up to the second order in Earth’s oblateness. 相似文献
4.
The variations of perturbations in perigee distance for different values of the orbital eccentricity for artificial Earth's satellites due to air drag have been studied. The analytical solution of deriving these perturbations, using the TD model (Total Density) have been applied, Helali (1987). The Theory is valid for altitudes ranging from 200 to 500 km above the Earth's surface and for solar 10.7 cm flux. Numerical examples are given to illustrate the variations of the perturbations in perigee distance with changing eccentricity (e < 0.2). A stronge perturbations in the perigee distance have been shown when the eccentricity in the range 0.001 <e < 0.05, especially for perigee distance 200 km. 相似文献
5.
Mohamed Adel Sharaf 《Astrophysics and Space Science》1984,104(2):267-284
In this paper of the series, elliptic expansions in terms of the sectorial variables
j
(i)
introduced recently in Paper IV (Sharaf, 1982) to regularize highly oscillating perturbations force of some orbital systems will be established analytically and computationally for the fifth and sixth categories. For each of the elliptic expansions belonging to a category, literal analytical expressions for the coefficients of its trigonometric series representation are established. Moreover, some recurrence formulae satisfied by these coefficients are also established to facilitate their computations; numerical results are included to provide test examples for constructing computational algorithms. 相似文献
6.
Using specialized codes for the search of periodic and linear components we show that direct solar radiation leads to short-period
variations of all the orbital elements of geosynchronous satellites. The variation period of the semimajor axis a, orbit inclination i and the longitude of the ascending node Ω is 1 day. Eccentricity e, the argument of perigee ω and the mean anomaly M vary with a period of 0.5 days. Direct solar radiation also leads to long-period variations in e, ω and M with a period of 1 year. The elements a, i and Ω undergo variations only in the amplitude of diurnal variations with a period of 1 or 0.5 years. Secular variability
(linear components) are not detected. To obtain the initial value array of the orbital elements we used the Lagrange equations
of perturbed motion in the form of a Gaussian with their subsequent integration via a special method of harmonics: the values
of the derived orbital elements, obtained from the Lagrange equations, were presented through the periodic functions that
are easy to integrate. 相似文献
7.
A. Carusi G. B. Valsechi R. Greenberg 《Celestial Mechanics and Dynamical Astronomy》1990,49(2):111-131
Öpik's assumptions on the geometry of particle trajectories leading to and through planetary close encounters are used to compute the distribution of changes in heliocentric orbital elements that result from such encounters for a range of initial heliocentric orbits. Behaviour at encounter is assumed to follow two-body (particle—planet) gravitational scattering, while before and after encounter particle motion is only governed by the force of the Sun. Derivation of these distributions allows precise analysis of the probability of various outcomes in terms of the physical characteristics of the bodies involved. For example, they allow an explanation and prediction of the asymmetry of the extreme energy perturbations for different initial orbits. The formulae derived here may be applied to problems including the original accumulation of planets and satellites, and the continuing evolution of populations of small bodies, such as asteroids and comets. 相似文献
8.
9.
Luis Floría 《Celestial Mechanics and Dynamical Astronomy》1993,57(1-2):203-223
Within the framework of the Canonical Formalism in the extended phase space,a general Hamiltonian is investigated that covers a wide class of radial intermediaries accounting for themajor secular effects due to a planet's oblateness perturbations.An analytical, closed-form solution for this generic Hamiltonian is developed in terms of elementary functions via the corresponding Hamilton-Jacobi equation. The analytical solution so obtained can be contemplated according to a simple geometrical and dynamical interpretation in Keplerian language by means of the usual relations characterizing elliptic elements along ahypothetic Keplerian motion.Appropriate choices for the terms appearing in the proposed Hamiltonian lead to recovering the analogues of some well-known, classical radial intermediaries (those introduced by Deprit and the one built by Alfriend and Coffey), but also certain new ones derived by Ferrándiz for the Main Problem in the Theory of Artificial Satellites of the Earth. In any case, the results are also applicable to problems dealing with orbital motion of other planetary satellites.The generality of this pattern leads to asystematic obtaining of solutions to the considered intermediaries: special choices of the Hamiltonian yield the correspondinganalytical solution to the respective intermediary problem. 相似文献
10.
The non-spherical gravitational potential of the planet Mars is sig- nificantly different from that of the Earth. The magnitudes of Mars’ tesseral harmonic coefficients are basically ten times larger than the corresponding val- ues of the Earth. Especially, the magnitude of its second degree and order tesseral harmonic coefficient J2,2 is nearly 40 times that of the Earth, and approaches to the one tenth of its second zonal harmonic coefficient J2. For a low-orbit Mars probe, if the required accuracy of orbit prediction of 1-day arc length is within 500 m (equivalent to the order of magnitude of 10−4 standard unit), then the coupled terms of J2 with the tesseral harmonics, and even those of the tesseral harmonics themselves, which are negligible for the Earth satellites, should be considered when the analytical perturbation solution of its orbit is built. In this paper, the analytical solutions of the coupled terms are presented. The anal- ysis and numerical verification indicate that the effect of the above-mentioned coupled perturbation on the orbit may exceed 10−4 in the along-track direc- tion. The conclusion is that the solutions of Earth satellites cannot be simply used without any modification when dealing with the analytical perturbation solutions of Mars-orbiting satellites, and that the effect of the coupled terms of Mars's non-spherical gravitational potential discussed in this paper should be taken into consideration. 相似文献
11.
火星非球形引力位田谐项联合摄动分析解 总被引：2，自引：0，他引：2
火星非球形引力场模型与地球有明显差别,其非球形引力位中的田谐项系数基本都要比地球的相应值大一个量级,尤其是J2,2项（赤道椭率项）的大小接近它的动力学扁率项J2.对于低轨探测器,若要使轨道外推1 d弧段的精度达到500 m(相当于标准单位10-4量级),在构造环火探测器的轨道分析解时,田谐项与J2项以及田谐项与田谐项之间的联合摄动不容忽视.根据摄动量级分析和构造的摄动分析解证实,上述联合摄动对轨道沿迹方向的影响可超过10-4,并给出了数值验证.结果表明,与地球低轨卫星不同,在类似的问题中,构造环火卫星摄动分析解时,必须考虑这些联合摄动项的影响. 相似文献
12.
D. V. Nikonchuk 《Astronomy Letters》2012,38(12):813-828
Anonlinear analytical theory of secular perturbations in the problem of the motion of a systemof small bodies around a major attractive center has been developed. Themutual perturbations of the satellites and the influence of the oblateness of the central body are taken into account in the model. In contrast to the classical Laplace-Lagrange theory based on linear equations for Lagrange elements, the third-degree terms in orbital eccentricities and inclinations are taken into account in the equations. The corresponding improvement of the solution turns out to be essential in studying the evolution of orbits over long time intervals. A program inC has been written to calculate the corrections to the fundamental frequencies of the solution and the third-degree secular perturbations in orbital eccentricities and inclinations. The proposed method has been applied to investigate the motion of the major Uranian satellites. Over time intervals longer than 100 years, allowance for the nonlinear terms in the equations is shown to give corrections to the coordinates of Miranda on the order of the orbital eccentricity, which is several thousand kilometers in linear measure. For other satellites, the effect of allowance for the nonlinear terms turns out to be smaller. Obviously, when a general analytical theory of motion for the major Uranian satellites is constructed, the nonlinear terms in the equations for the secular perturbations should be taken into account. 相似文献
13.
B. Zafiropoulos 《Astrophysics and Space Science》1987,137(1):139-149
The aim of this investigation is to present the periodic and secular perturbations of the orbital elements of close binary systems due to tidal lag in latitude. The variational equations of the problem of plane motion will be set up in terms of the rectengular componentsR, S, andW of the disturbing accelerations. These equations are highly nonlinear with respect to the orbital elements and we present analytic approximations to the effects produced by the perturbing acceleration due to dynamical tides lagging in latitude. The perturbed elements of the orbit have been expressed by means of Hansen coefficients in the compact form of summations. 相似文献
14.
Zdeněk Kopal 《Astrophysics and Space Science》1972,18(2):287-305
The aim of the present investigation will be to determine the explicit forms of differential equations which govern secular perturbations of the orbital elements of close binary systems in the plane of the orbit (i.e., of the semi-major axisA, eccentricitye, and longitude of the periastron ), arising from the lag of dynamical tides due to viscosity of stellar material. The results obtained are exact for any value of orbital eccentricity comprised between 0e<1; and include the effects produced by the second, third and fourth-harmonic dynamical tides, as well as by axial rotation with arbitrary inclination of the equator to the orbital plane.In Section 2 following brief introductory remarks the variational equations of the problem of plane motion will be set up in terms of the rectangular componentsR, S, W of disturbing accelerations with respect to a revolving system of coordinates. The explicit form of these coefficients will be established in Section 3 to the degree of accuracy to which squares and higher powers of quantities of the order of superficial distortion can be ignored. Section 4 will be devoted to a derivation of the explicit form of the variational equations for the case of a perturbing function arising from axial rotation; and in Section 5 we shall derive variational equations which govern the perturbation of orbital elements caused by lagging dynamical tides.Numerical integrations of these equations, which govern the tidal evolution of close binary systems prompted by viscous friction at constant mass, are being postponed for subsequent investigations.Prepared at the Lunar Science Institute, Houston, Texas, under the joint support of the Universities Space Research Association, Charlottesville, Virginia, and the National Aeronautics and Space Administration Manned Spacecraft Center, Houston, Texas, under Contract No. NSR 09-051-001. This paper constitutes Lunar Science Institute Contribution no. 100.Normally at the Department of Astronomy, University of Manchester, England. 相似文献
15.
P. Moore 《Celestial Mechanics and Dynamical Astronomy》1979,20(2):125-142
The orbital accelerations of certain balloon satellites exhibit marked oscillations caused by solar radiation impinging on the surface of the satellites, which, once spherical, have assumed a spheroidal shape producing a component of force at right-angles to the Sun-satellite direction. Given the characteristics and orientation of the satellite, the equations of force are determined by the formulae of Lucas. Otherwise the phase-angle and magnitude of the right-angle force are determined by trial and error, or best-fit techniques. Using a variation of the approach developed by Aksnes, a semi-analytical algorithm is presented for evaluating the perturbations of the Keplerian elements by direct solar radiation pressure on a spheroidal satellite. The perturbations are obtained by summing over the sunlit part of each orbit and allow for a linear variation in the phase-angle. The algorithm is used to determine the orbital accelerations of 1963-30D due to direct solar radiation pressure, and these results are compared to the observed values over two separate periods of the satellite's lifetime. 相似文献
16.
Alan H. Jupp 《Celestial Mechanics and Dynamical Astronomy》1976,14(3):335-339
This paper calls into question the validity of the well-known formulae for the perturbations in the Keplerian elements, over one revolution of an orbit, for the motion of a drag-perturbed artificial satellite. These formulae are derived from Gauss's form of the planetary equations, by averaging over a single revolution of the orbit, and using the eccentric anomaly as the independent variable.It is shown that for light balloon-type satellites in near-circular orbits neither the eccentric anomaly nor the true longitude is a suitable choice of independent variable for the averaging procedure. Under these circumstances, it would seem that simple formulae for the variations in the elements cannot be derived from Gauss's equations. 相似文献
17.
Leland E. Cunningham 《Celestial Mechanics and Dynamical Astronomy》1970,2(2):207-216
A method is presented for the accurate and efficient computation of the forces and their first derivatives arising from any number of zonal and tesseral terms in the Earth's gravitational potential. The basic formulae are recurrence relations between some solid spherical harmonics,V
n,m, associated with the standard polynomial ones. 相似文献
18.
Bruce C. Douglas Chreston F. Martin Ronald G. Williamson Carl A. Wagner 《Celestial Mechanics and Dynamical Astronomy》1969,1(2):252-270
An error analysis of resonant orbits for geodesy indicates that attempts to use resonance to recover high order geopotential coefficients may be seriously hampered by errors in the geopotential. This effect, plus the very high correlations (up to .99) of the resonant coefficients with each other and the orbital period in single satellite solutions, makesindividual resonant orbits of limited value for geodesy. Multiple-satellite, single-plane solutions are only a slight improvement over the single satellite case. Accurate determination of high order coefficients from low altitude resonant satellites requires multiple orbit planes and small drift-periods to reduce correlations and effects of errors of non-resonant geopotential terms. Also, the effects of gravity model errors on low-altitude resonant satellites make the use of tracking arcs exceeding two to three weeks of doubtful validity. Because high-altitude resonant orbits are less affected by non-resonant terms in the geopotential, much longer tracking arcs can be used for them. 相似文献
19.
This paper deals with the perturbations which rotation can produce to the orbital elements of a close binary system. The rectangular components,R, S andW of the disturbing accelerations due to rotation have been substituted to the Gauss form of Lagrange's planetary equations to yield the first order approximation. The results obtained are exact for any value of orbital eccentricity between the values 0<e<1 and for arbitrary inclinations of the rotational axes to the orbital plane.First and second order approximations are given for the special case when equators are coplanar to the orbit. 相似文献
20.
András Pál 《Celestial Mechanics and Dynamical Astronomy》2014,119(1):45-54
Lie-integration is one of the most efficient algorithms for numerical integration of ordinary differential equations if high precision is needed for longer terms. The method is based on the computation of the Taylor coefficients of the solution as a set of recurrence relations. In this paper, we present these recurrence formulae for orbital elements and other integrals of motion for the planar $N$ -body problem. We show that if the reference frame is fixed to one of the bodies—for instance to the Sun in the case of the Solar System—the higher order coefficients for all orbital elements and integrals of motion depend only on the mutual terms corresponding to the orbiting bodies. 相似文献