共查询到20条相似文献，搜索用时 15 毫秒
1.
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
2.
G. Metris P. Exertier Y. Boudon F. Barlier 《Celestial Mechanics and Dynamical Astronomy》1993,57(1-2):175-188
The main effects of tesseral harmonics of a gravity potential expansion on the motion of a satellite, are short period variations as well as long period variations due to resonances. However, other smaller long period and secular variations can arise from interactions between tesseral terms of the same order. The analytical integration of these effects is developed, using numerical evaluation of Kaula eccentricity and inclination functions. Examples for some Earth's geodetic satellites show that secular effects can reach a few decameters per year. The secular variations can even reach several hundred of meters per year for the Mars natural satellite Phobos. 相似文献
3.
现代天王星卫星运动定量理论的研究和发展 总被引：1，自引：0，他引：1
1986年“旅行者2号”飞越天于星期间，由空间无线电和光学观测获得的卫星资料首次给出天王星5颗主要卫星质量的可靠估计，从而推动了现代天王星卫星运动定量理论的建立。Laskar于1986年建立了第一个相对完整的天王星主要卫星的(半）分析理论——GUST86，其高精度已被许多学者的实算证实。之后，对理论的改进作出贡献的学者有：Malhotra等人(1989）、Lazzaro等人(1987，1991)分析研究了天王星卫星系统中近共振项对长期摄动解的影响；Taylor(1998)采用数值积分拟合观测资料，以更精确地测定卫星质量；Christou和Murray(1997)则将一个2阶Laplace—Lagrange理论应用于天王星卫星系统。对这些学者的工作作一概述。 相似文献
4.
M. A. Vashkov’yak 《Solar System Research》2010,44(6):527-540
A new analytical solution of the system of differential equations describing secular perturbations and long-period solar perturbations
of mean orbits of outer satellites of giant planets was obtained. As distinct from other solutions, the solution constructed
using von Zeipel’s method approximately takes into account, in the secular part of the perturbing function, the totality of
fourth order with respect to the small parameter m of the ratio of the mean motions of the primary planet and the satellite. This enables us to describe more accurately the
evolution of satellite orbits with large apocentric distances, which in the course of evolution may exceed the halved radius
of the Hill sphere of the planet with respect to the Sun. Among these are the orbits of the two outermost Neptunian satellites
N10 (Psamathe) and N13 (Neso). For these satellites, the parameter m amounts to 0.152 and 0.165, respectively. Different from a purely analytical solution, the proposed solution requires preliminary
calculations for each satellite. More precisely, in doing so, we need to construct some simple functions to approximate more
complex ones. This is why we use the phrase “constructive analytical.” To illustrate the solution, we compare it with the
results of the numerical integration of the strict motion equations of the satellites N10 and N13 over time intervals 5–15
thousand years. 相似文献
5.
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
6.
A new theory for the calculation of proper elements, taking into account terms of degree four in the eccentricities and inclinations, and also terms of order two in the mass of Jupiter, has been derived and programmed in a self contained code. It has many advantages with respect to the previous ones. Being fully analytical, it defines an explicit algorithm applicable to any chosen set of orbits. Unlike first order theories, it takes into account the effect of shallow resonances upon the secular frequencies; this effect is quite substantial, e.g. for Themis. Short periodic effects are corrected for by a rigorous procedure. Unlike linear theories, it accounts for the effects of higher degree terms and can thus be applied to asteroids with low to moderate eccentricity and inclination; secular resonances resulting from the combination of up to four secular frequencies can be accounted for. The new theory is self checking : the proper elements being computed with an iterative algorithm, the behaviour of the iteration can be used to define a quality code. The amount of computation required for a single set of osculating elements, although not negligible, is such that the method can be systematically applied on long lists of osculating orbital elements, taken either from catalogues of observed objects or from the output of orbit computations. As a result, this theory has been used to derive proper elements for 4100 numbered asteroids, and to test the accuracy by means of numerical integrations. These results are discussed both from a quantitative point of view, to derive an a posteriori accuracy of the proper elements sets, and from a qualitative one, by comparison with the higher degree secular resonance theory. 相似文献
7.
T. V. Ivanova 《Solar System Research》2013,47(5):359-362
In order to generate an analytical theory of the motion of the Moon by considering planetary perturbations, a procedure of general planetary theory (GPT) is used. In this case, the Moon is considered as an addition planet to the eight principal planets. Therefore, according to the GPT procedure, the theory of the Moon’s orbital motion can be presented in the form of series with respect to the evolution of eccentric and oblique variables with quasi-periodic coefficients, which are the functions of mean longitudes for principal planets and the Moon. The relationship between evolution variables and the time is determined by a trigonometric solution for the independent secular system that describes the secular motion of a perigee and the Moon node by considering secular planetary inequalities. Principal planetary coordinates required for generating the theory of the motion of the Moon includes only Keplerian terms, the intermediate orbit, and the linear theory with respect to eccentricities and inclinations in the first order relative to the masses. All analytical calculations are performed by means of the specialized echeloned Poisson Series Processor EPSP. 相似文献
8.
An analytical theory of the rotation of a synchronous satellite is developed for the application to the rotation of the Galilean
satellites. The theory is developed in the framework of Hamiltonian mechanics, using Andoyer variables. Special attention
is given to the frequencies of libration as functions of the moments of inertia of the satellite.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
We propose a special representation for the secular part of the perturbing function describing the mutual attraction of satellites. In contrast to the known representations, it has a single analytical form for any ratio between the semimajor axes of the perturbed and perturbing satellites. The resulting expression is a partial sum of a power series with respect to the small eccentricities and planet-equatorial inclinations of the satellites’ orbits. This sum includes terms up to and including the fourth degree with respect to these small parameters. The proposed expansion is compared with one of the known expansions for the secular part of the perturbing function. 相似文献
10.
Bryan C. Brown 《Celestial Mechanics and Dynamical Astronomy》1981,23(3):203-221
This paper presents the results of an investigation into the secular behavior of the orbits of the Galilean satellites of Jupiter. Kamel's perturbation method is used to remove all the explicitly periodic variables from the differential equations that describe the long period behavior of the orbits to third order in the masses, and the resulting differential equations for the secular behavior are then solved. Several numerical examples are given to illustrate the sensitivity of the solution to variations in the masses of the satellites. 相似文献
11.
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
12.
David M. Lucchesi 《Celestial Mechanics and Dynamical Astronomy》2004,88(3):269-291
We propose a new analytical theory to explain the physical cause of the asymmetric reflectivity effect observed for the LAGEOS satellites. To achieve this result we have modelled the reflection of the Sun visible light from the four germanium Cube-Corner-Retroreflectors of these satellites. The position of the Cube-Corner-Retroreflectors play a crucial role in defining the characteristics of the effect and its impact in the satellites orbit. With this new approach we have been able to reproduce the temporal variation of the asymmetric reflectivity effect acceleration for LAGEOS, and to determine the main characteristic of the effect in the case of LAGEOS II. When considering the orbital elements, we have been able to reproduce the time evolution of LAGEOS eccentricity vector excitations and perigee rate. In the case of LAGEOS II, the asymmetric reflectivity effect need to be modelled with an analytical expression different from that previously introduced for LAGEOS.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
13.
Using a 12th order expansion of the perturbative potential in powers of the eccentricities and the inclinations, we study
the secular effects of two non-coplanar planets which are not in mean–motion resonance. By means of Lie transformations (which
introduce an action–angle formulation of the Hamiltonian), we find the four fundamental frequencies of the 3-D secular three-body
problem and compute the long-term time evolutions of the Keplerian elements. To find the relations between these elements,
the main combinations of the fundamental frequencies common to these evolutions are identified by frequency analysis. This
study is performed for two different reference frames: a general one and the Laplace plane. We underline the known limitations
of the linear Laplace–Lagrange theory and point out the great sensitivity of the 3-D secular three-body problem to its initial
values. This analytical approach is applied to the exoplanetary system Andromedae in order to search whether the eccentricities evolutions and the apsidal configuration (libration of ) observed in the coplanar case are maintained for increasing initial values of the mutual inclination of the two orbital
planes.
Anne-Sophie Libert is FNRS Research Fellow. 相似文献
14.
Carol A. Williams 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):395-410
Small divisors caused by certain linear combinations of frequencies appear in all analytical planetary theories. With the exception of the deep resonance between Neptune and Pluto, they can be removed at the expense of introducing secular and mixed secular terms, limiting the domain in which the solution is valid. Because of them classical solutions are known not to converge uniformly; Poincaré referred to them as asymptotic. The KAM theory shows that if one is far enough from exact commensurability and has small enough planetary masses, expansions exist which will converge to quasi-periodic orbits. Solutions showing very small divisors are excluded from this region of convergence. The question of whether they are intrinsic to the problem or are just manifestations of the method of solution is not settled. Problems with a single commensurabily that can be isolated from the rest of the Hamiltonian may have solutions with no small divisors. The problem of two or more commensurabilities remains unsolved. 相似文献
15.
Giacomo Lari 《Celestial Mechanics and Dynamical Astronomy》2018,130(8):50
The Galilean satellites’ dynamics has been studied extensively during the last century. In the past it was common to use analytical expansions in order to get simple models to integrate, but with the new generation of computers it became prevalent the numerical integration of very sophisticated and almost complete equations of motion. In this article we aim to describe the resonant and secular motion of the Galilean satellites through a Hamiltonian, depending on the slow angles only, obtained with an analytical expansion of the perturbing functions and an averaging operation. In order to have a model as near as possible to the actual dynamics, we added perturbations and we considered terms that in similar studies of the past were neglected, such as the terms involving the inclinations and the Sun’s perturbation. Moreover, we added the tidal dissipation into the equations, in order to investigate how well the model captures the evolution of the system. 相似文献
16.
When Kozai (1962) studied the secular resonance of asteroids, he found the so-called Kozai resonance and expressed the analytical
solution with the use of Weierstrass ℘. Here we discuss the case where the disturber is outside a disturbed body and give
the analytical solution of the eccentricity, the inclination and the argument of pericenter with the use of the Jacobi elliptic
functions, which are more familiar than the Weierstrass ℘. Then we derive the Fourier expansion of the longitude of node and
the mean anomaly. The analytical expressions obtained here can be used for any value of the eccentricity and the inclination.
Finally we applied these analytical expressions to several dynamical systems – Nereid, that is a highly eccentric satellite
of Neptune, and newly discovered retrograde satellites of Uranus.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
17.
A special presentation of secular part of the perturbing function of mutual attraction in the satellite system is presented. In contrast to known ones, it is given in general analytical form for any ratio between semimajor axes for perturbed and perturbing satellites. 相似文献
18.
José Manuel Ferrándiz Ana Fernández-Ferreiros 《Celestial Mechanics and Dynamical Astronomy》1991,52(1):1-12
In this paper we consider the reduction of the equations of motion for non-planar perturbed two body problems into linear form. It is seen that this can be easily accomplished for any element of the class of radial intermediaries to the satellite problem proposed by Deprit in 1981, since they have a functional dependence suitable for linearization. The transformation is worked out by using an adequate set of redundant variables. Four harmonic oscillators are obtained, of which two are coupled through gyroscopic terms. Their constant frequencies contain the secular contribution of the main problem of artificial satellite theory up to the order of the considered intermediary. Therefore, this result may well be interesting in relation to the study and prediction of accurate long-term solutions to satellite problems. 相似文献
19.
The method applied since 1996 for the analysis of the orbital residuals of the LAGEOS satellites in order to measure the Lense-Thirring effect has been the subject of the present work. This method, based on the difference between the orbital elements of consecutive arcs, is explained and analysed also from the analytical point of view. It is proved that this “difference method” works well for the determination of the secular effects, as in the case of the relativistic precession induced by the Earth's angular momentum, but also very useful for the determination and study of the long-term periodic effects. Indeed, the only limitation in the determination of the periodic effects is the possibility of the reduction of their amplitude by a factor which depends from the periodicity of the given perturbation and from the orbital arc length chosen for the satellite during the data analysis. In the case of the Yarkovsky-Schach effect, the main non-gravitational perturbation seen in the LAGEOS satellites orbital residuals, in particular in its perigee rate and eccentricity vector excitation residuals, we show that the “difference method” is quite good also for the determination of the long-period perturbations induced by this subtle non-conservative force. 相似文献
20.
M. Burša 《Earth, Moon, and Planets》1988,43(3):261-265
The secular Love and the secular tidal numbers have been computed for eight synchronously orbiting satellites in the solar system for which the triaxiality parameters and satellite-centric gravitational constant are available. Excepting Deimos the total mass of which should be first refined, the secular Love and tidal numbers are rather close to unity, as a rule. That is why, the centrifugal and tidal distortions can be assumed responsible for the actual figures of the synchronously orbiting satellites resulting from the primordial spheres, as well as, their static equilibrium nearly satisfied. The hypothesis of the origin of synchronously orbiting satellites by accretion in orbits is supported by the results obtained. 相似文献