共查询到20条相似文献，搜索用时 31 毫秒
1.
The limitations on determining the masses of the outer planets from their mutual perturbations are investigated based on the magnitudes of the periodic perturbations given in general theories and the accuracy of the observational data. 相似文献
2.
Zoran Knežević 《Celestial Mechanics and Dynamical Astronomy》1993,55(4):387-404
Leverrier's development of the indirect part of the disturbing function has been extended to include terms up to degree 4 in eccentricity and inclination; the resulting series has been expressed with respect to a fixed plane, and in a computer readable form (a list of integers). Tests have been performed for the relative significance of the terms of degrees 2, 3 and 4, and estimates have been obtained for the accuracy of the short periodic perturbations of a minor planet, and of the corresponding mean orbital elements. It was found that: (i) even in extreme cases, the indirect part of the disturbing function gives rise to very small short periodic perturbations; (ii) bodies of very high eccentricity/inclination and those close to mean motion resonances are most significantly affected; (iii) indirect perturbations for minor planets can be computed up to the degree 2 terms only, without any significant loss of accuracy; and (iv) higher degree indirect perturbations appear to be important only for their contribution to the long periodic effects of higher order (with respect to the perturbing mass). 相似文献
3.
E. M. Gaposchkin 《Celestial Mechanics and Dynamical Astronomy》1981,25(2):181-183
The short periodic perturbations due to the Schwarzschild Metric can be ignored when analyzing earth satellite data. 相似文献
4.
We locate members of a one-parameter family of equal-mass four-body periodic orbits in the plane. The family begins and ends with the rectilinear four-body equal-mass Schubart interplay orbit and passes through a double choreography orbit. The first-order stability of these orbits is computed. Some members of this symmetric family are stable to symmetric perturbations; however, they are unstable when all perturbations are allowed. 相似文献
5.
Chaotic mixing in noisy Hamiltonian systems 总被引：1，自引：0，他引：1
Henry E. Kandrup Ilya V. Pogorelov Ioannis V. Sideris 《Monthly notices of the Royal Astronomical Society》2000,311(4):719-732
This paper summarizes an investigation of the effects of low-amplitude noise and periodic driving on phase-space transport in three-dimensional Hamiltonian systems, a problem directly applicable to systems like galaxies, where such perturbations reflect internal irregularities and/or a surrounding environment. A new diagnostic tool is exploited to quantify the extent to which, over long times, different segments of the same chaotic orbit evolved in the absence of such perturbations can exhibit very different amounts of chaos. First-passage-time experiments are used to study how small perturbations of an individual orbit can dramatically accelerate phase-space transport, allowing 'sticky' chaotic orbits trapped near regular islands to become unstuck on surprisingly short time‐scales. The effects of small perturbations are also studied in the context of orbit ensembles with the aim of understanding how such irregularities can increase the efficacy of chaotic mixing. For both noise and periodic driving, the effect of the perturbation scales roughly logarithmically in amplitude. For white noise, the details are unimportant: additive and multiplicative noise tend to have similar effects and the presence or absence of friction related to the noise by a fluctuation–dissipation theorem is largely irrelevant. Allowing for coloured noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time, which vanishes for white noise, becomes so large that there is little power at frequencies comparable with the natural frequencies of the unperturbed orbit. This suggests strongly that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. Potential implications for galaxies are discussed. 相似文献
6.
J. Chapront M. Chapront-Touzé G. Francou 《Celestial Mechanics and Dynamical Astronomy》1999,73(1-4):317-328
Analytical complements have been brought to Moons' lunar libration theory concerning tidal effects, direct perturbations due
to the Earth's figure, and indirect non periodic perturbations. Comparisons to JPL numerical integrations DE245 and DE403
have been performed and the residuals treated by frequency analysis, allowing the determination of fitted free libration parameters
and numerical complements.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
7.
The proposed method connects two unstable periodic orbits by employing trajectories of their associated invariant manifolds that are perturbed in two levels. A first level of velocity perturbations is applied on the trajectories of the discretized manifolds at the points where they approach the nominal unstable periodic orbit in order to accelerate them. A second level of structured velocity perturbations is applied to trajectories that have already been subjected to first level perturbations in order to approximately meet the necessary conditions for a low \(\varDelta \text {V}\) transfer. Due to this two-level perturbation approach, the number of the trajectories obtained is significantly larger compared with approaches that employ traditional invariant manifolds. For this reason, the problem of connecting two unstable periodic orbits through perturbed trajectories of their manifolds is transformed into an equivalent discrete optimization problem that is solved with a very low computational complexity algorithm that is proposed in this paper. Finally, the method is applied to a lunar observation mission of practical interest and is found to perform considerably better in terms of \(\varDelta \text {V}\) cost and time of flight when compared with previous techniques applied to the same project. 相似文献
8.
G. Contopoulos 《Celestial Mechanics and Dynamical Astronomy》2009,104(1-2):3-21
Spiral galaxies contain both ordered and chaotic orbits. In normal spirals the perturbations are weak (of order 2–10%) and most orbits are ordered. The density wave theory refers mainly to linear perturbations. Nonlinear effects appear in the outer parts of the open spirals (S_b, S_c) and produce the termination of these spirals near the 4/1 resonance. On the other hand in barred spirals the perturbations are relatively strong (of order 100%). Then the outer spirals and the envelope of the bar are composed mainly of chaotic orbits, while the main body of the bar is composed of ordered orbits. The chaotic orbits of the spiral arms of strong barred galaxies are sticky, i.e. they do not escape from the galaxy for at least a Hubble time. The forms of these spirals are delineated by the unstable manifolds of the unstable periodic orbits L_1, L_2 near the ends of the bar and of other unstable periodic orbits inside and outside corotation. 相似文献
9.
Maria Gousidou-Koutita 《Earth, Moon, and Planets》1985,32(1):21-45
The present study deals with numerical modeling of the elliptic restricted three-body problem as well as of the perturbed elliptic restricted three-body (Earth-Moon-Satellite) problem by a fourth body (Sun). Two numerical algorithms are established and investigated. The first is based on the method of the series solution of the differential equations and the second is based on a 5th-order Runge-Kutta method. The applications concern the solution of the equations and integrals of motion of the circular and elliptical restricted three-body problem as well as the search for periodic orbits of the natural satellites of the Moon in the Earth-Moon system in both cases in which the Moon describes circular or elliptical orbit around the Earth before the perturbations induced by the Sun. After the introduction of the perturbations in the Earth-Moon-Satellite system the motions of the Moon and the Satellite are studied with the same initial conditions which give periodic orbits for the unperturbed elliptic problem. 相似文献
10.
B. Érdi 《Celestial Mechanics and Dynamical Astronomy》1987,43(1-4):303-308
The motion of the Trojan asteroids is studied in the elliptic restricted three-body problem of the Sun-Jupiter-asteroid system. Long periodic perturbations of the orbital elements are discussed. Relations between dynamical parameters are considered and comparisons are made with Bien's and Schubart's results. 相似文献
11.
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
12.
Claudio Vidal 《Celestial Mechanics and Dynamical Astronomy》2001,80(2):119-132
We consider perturbations of the Kepler problem that are symmetric with respect to the origin and admit a first integral of motion which is also symmetric with respect to the origin. It has been proved that each circular solution of the unperturbed problem gives rise to a periodic solution of the perturbed system. 相似文献
13.
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
14.
K. V. Krasnobaev 《Astronomy Letters》2001,27(9):568-573
We consider the interaction of an ionization-shock front with isothermal waves in an H I region. Based on a two-front model in the linear approximation, we have detected a significant (approximately by an order of magnitude) periodic amplification of perturbations as they penetrate from the interstellar medium into an H II region. Numerical simulations have revealed that even when the shock-and ionization-front velocities differ and the relative density perturbations in the interstellar medium are ～10?1, the variations in gas parameters near the ionization front are comparable to those observed at the boundaries of H II regions. 相似文献
15.
P. J. Message 《Celestial Mechanics and Dynamical Astronomy》1973,8(2):217-217
Saturn's satellite Hyperion experiences large perturbations by Titan, the largest of Saturn's satellites, because of the closeness of Hyperion's orbital period to three-quarters of that of Titan.The motion of Hyperion is a superposition of periodic fluctuations (both free and forced) onto a motion which is periodic in a suitable uniformly rotating frame of reference, and in which Hyperion would be at a maximum distance from Saturn at each conjunction with Titan.Successive attempts to determine the mass of Titan from observed perturbations of Hyperion have suffered from omissions in the theory of terms subsequently found to be significant.An attempt is in progress which, it is believed, comprises all long-period changes in the osculating elements which are of second degree in the mass of Titan, and of third degree in the eccentricity of its orbit. Results so far obtained indicate that the period of the free motion of the orbit plane of Hyperion is better determined by Woltjer's reduction of the observations than by his theoretical calculations.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 27–September 2, 1972. 相似文献
16.
A method is presented for the numerical study of the temporal evolution of nonlinear periodic waves in solar coronal loops which are approximated by smoothed slabs of enhanced gas density embedded within a uniform magnetic field. This method uses a fast Fourier transform technique to calculate spatial derivatives and a modified Euler algorithm for the time scheme for solving cold magnetohydrodynamic equations that govern nonlinear perturbations. The numerical results show that nonlinearity can play a significant role, leading to wave breaking of the kink wave and slab demolition for the sausage one. The kink periodic wave adjusts better to the smoothed slab than the sausage wave. 相似文献
17.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1987,43(1-4):371-390
A review is presented of periodic orbits of the planetary type in the general three-body problem and fourbody problem and the restricted circular and elliptic tnreebody problem. These correspond to planetary systems with one Sun and two or three planets (or a planet and its satellites), the motion of asteoids and also planetary systems with two Suns. The factors which affect the stability of the above configurations are studied in connection with resonance or additional perturbations. Finally, the correspondence of the periodic orbits in the restricted three-body problem with the fixed points obtained by the method of averaging or the method of surface of section is indicated. 相似文献
18.
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
19.
P. Delibaltas 《Astrophysics and Space Science》1976,45(1):207-233
Several families of planar planetary-type periodic orbits in the general three-body problem, in a rotating frame of reference, for the Sun-Jupiter-Saturn mass-ratio are found and their stability is studied. It is found that the configuration in which the orbit of the smaller planet is inside the orbit of the larger planet is, in general, more stable.We also develop a method to study the stability of a planar periodic motion with respect to vertical perturbations. Planetary periodic orbits with the orbits of the two planets not close to each other are found to be vertically stable. There are several periodic orbits that are stable in the plane but vertically unstable and vice versa. It is also shown that a vertical critical orbit in the plane can generate a monoparametric family of three-dimensional periodic orbits. 相似文献
20.
M. Soffel R. Wirrer J. Schastok H. Ruder M. Schneider 《Celestial Mechanics and Dynamical Astronomy》1987,42(1-4):81-89
The motion of artificial satellites in the gravitational field of an oblate body is discussed in the parametrized-post-Newtonian (PPN) framework with parameters and . Analytical expressions for first order post-Newtonian short periodic, long periodic and secular perturbations of orbital elements are given. 相似文献