共查询到20条相似文献，搜索用时 15 毫秒
1.
给出了以偏近点角为自变量的变引力常数的摄动方程组的解.解包括轨道半长轴的长期和周期变化项,其他轨道根数在一阶解中无长期项,只有周期项.近星点经度和平经度在二阶解中显示长期项变化.给出了由于引力常数变化对双星轨道演变情况的数值估计,对结果做了讨论并给出结论. 相似文献
2.
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
3.
Lin-Sen Li 《Astrophysics and Space Science》2012,340(2):323-330
Perturbative post-Newtonian variations of the standard osculating orbital elements are obtained by using the two-body equations of motion in the parameterized post-Newtonian theoretical framework. The results obtained are applied to the Einstein and Brans–Dicke theories. As a results, the semi-major axis and eccentricity exhibit periodic variation, but no secular changes. The longitude of periastron and mean longitude at epoch experience both secular and periodic shifts. The post-Newtonian effects are calculated and discussed for six extrasolar planets. 相似文献
4.
5.
Pavol Pástor 《Celestial Mechanics and Dynamical Astronomy》2014,120(1):77-104
Circumstellar dust particles can be captured in a mean-motion resonance (MMR) with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the MMR analytically using averaged resonant equations. We derive the averaged resonant equations from the equations of motion in near-canonical form. The secular variations of the particle orbit depending on the orientation of the orbit in space are taken into account. The averaged resonant equations can be derived/confirmed also from Lagrange’s planetary equations. We apply the derived theory to the case when the non-gravitational effects are the Poynting–Robertson effect, the radial stellar wind, and an interstellar wind. The analytical and numerical results obtained are in excellent agreement. We found that the types of orbits correspond to libration centers of the conservative problem. The averaged resonant equations can lead to a system of equations which holds for stationary points in a subset of resonant variables. Using this system we show analytically that for the considered non-gravitational effects, all stationary points should correspond to orbits which are stationary in interplanetary space after an averaging over a synodic period. In an exact resonance, the stationary orbits are stable. The stability is achieved by a periodic repetition of the evolution during the synodic period. Numerical solutions of this system show that there are no stationary orbits for either the exact or non-exact resonances. 相似文献
6.
Wei-Duo Hu Daniel J. Scheeres 《天体物理学报》2008,8(1):108-118
Periodic orbits in an arbitrary 2nd degree and order uniformly rotating gravity field are studied. We investigate the four equilibrium points in this gravity field. We see that close relation exists between the stability of these equilibria and the existence and stability of their nearby periodic orbits. We check the periodic orbits with non-zero periods. In our searching procedure for these periodic orbits, we remove the two unity eigenvalues from the state transition matrix to find a robust, non-singular linear map to solve for the periodic orbits. The algorithm converges well, especially for stable periodic orbits. Using the searching procedure, which is relatively automatic, we find five basic families of periodic orbits in the rotating second degree and order gravity field for planar motion, and discuss their existence and stability at different central body rotation rates. 相似文献
7.
Periodic orbits in an arbitrary 2nd degree and order uniformly rotating gravity field are studied. We investigate the four equilibrium points in this gravity field. We see that close relation exists between the stability of these equilibria and the existence and stability of their nearby periodic orbits. We check the periodic orbits with non-zero periods. In our searching procedure for these periodic orbits, we remove the two unity eigenvalues from the state transition matrix to find a robust, non-singular linear map to solve for the periodic orbits. The algorithm converges well, especially for stable periodic orbits. Using the searching procedure, which is relatively automatic, we find five basic families of periodic orbits in the rotating second degree and order gravity field for planar motion, and discuss their existence and stability at different central body rotation rates. 相似文献
8.
9.
In this work we reveal for the first time that in the three dipole problem only asymmetric periodic orbits exist.For these periodic orbits — planar and three dimensional — of a charged particle moving under the influence of the electromagnetic field of the three dipoles we give their symplectic relations using the Hamiltonian formulation which is related to the symplectic matrix. Also we study the properties of the symplectic matrix and we give the relations there are among the variations of a periodic solution. These relations have been used to check the accuracy of numerical integration of equations of first order variations. 相似文献
10.
The discovery of extra-solar planetary systems with multiple planets in highly eccentric orbits (∼0.1-0.6), in contrast with our own Solar System, makes classical secular perturbation analysis very limited. In this paper, we use a semi-numerical approach to study the secular behavior of a system composed of a central star and two massive planets in co-planar orbits. We show that the secular dynamics of this system can be described using only two parameters, the ratios of the semi-major axes and the planetary masses. The main dynamical features of the system are presented in geometrical pictures that allows us to investigate a large domain of the phase space of this three-body problem without time-expensive numerical integrations of the equations of motion, and without any restriction on the magnitude of the planetary eccentricities. The topology of the phase space is also investigated in detail by means of spectral map techniques, which allow us to detect the separatrix of a non-linear secular apsidal resonance. Finally, the qualitative study is supplemented by direct numerical integrations. Three different regimes of secular motion with respect to the secular angle Δ? are possible: they are circulation, oscillation (around 0° and 180°), and high eccentricity libration in a non-linear secular resonance. The first two regimes are a continuous extension of the classical linear secular perturbation theory; the last is a new feature, hitherto unknown, in the secular dynamics of the three-body problem. We apply the analysis to the case of the two outer planets in the υ Andromedae system, and obtain its periodic and ordinary orbits, the general structure of its secular phase space, and the boundaries of its secular stability; we find that this system is secularly stable over a large domain of eccentricities. Applying this analysis to a wide range of planetary mass and semi-major axis ratios (centered about the υ Andromedae parameters), we find that apsidal oscillation dominates the secular phase space of the three-body coplanar system, and that the non-linear secular resonance is also a common feature. 相似文献
11.
Nina A. Solovaya 《Earth, Moon, and Planets》1995,71(3):273-279
Some peculiarities in the motion of retrograde satellites of Jupiter have been investigated. The intermediate orbits were obtained by approximated solution of differential equations before transformation by the Zeipel's method. These orbits are non-keplerian ellipses. For their construction the secular motion of nodes, perijoves, and essential periodic perturbations were taken into account.The eccentricities and inclinations of all the retrograte satellites change in a large range. The motion may happen in a region, which is located very near to the limit cases of our theory. For some satellites the sign of the constant, which characterizes the type of orbit, librating or circular, may change. In some cases the value of this constant may be close to zero. Then the motion of the longitude of perijove will reduce the speed and in some moment the circular orbit may change its direction. 相似文献
12.
In a previous publication (Tsiganis et al. 2000, Icarus146, 240-252), we argued that the occurrence of stable chaos in the 12/7 mean motion resonance with Jupiter is related to the fact that there do not exist families of periodic orbits in the planar elliptic restricted problem and in the 3-D circular problem corresponding to this resonance. In the present paper we show that nonexistence of resonant periodic orbits, both for the planar and for the 3-D problem, also occurs in other jovian resonances—namely the 11/4, 22/9, 13/6, and 18/7—where cases of real asteroids on stable-chaotic orbits have been identified. This property may provide a “protection mechanism”, leading to semiconfinement of chaotic orbits and extremely slow migration in the space of proper elements, so that diffusion is practically unrelated to the value of the Lyapunov time, TL, of chaotic orbits. However, we show that, in more complicated dynamical models, the long-term evolution of chaotic orbits initiated in the vicinity of these resonances may also be governed by secular resonances. Finally, we find that stable-chaotic orbits have a characteristic spectrum of autocorrelation times: for the action conjugate to the critical argument the autocorrelation time is of the order of the Lyapunov time, while for the eccentricity- and inclination-related actions the autocorrelation time may be longer than 103TL. This behavior is consistent with the trajectory being sticky around a manifold of lower-than-full dimensionality in phase space (e.g., a 4-D submanifold of the 5-D energy manifold in a three-degrees-of-freedom autonomus Hamiltonian system) and reflects the inability of these “flawed” resonances to modify secular motion significantly, at least for times of the order of 200 Myr. 相似文献
13.
14.
Lin-Sen Li 《Journal of Astrophysics and Astronomy》2014,35(2):189-200
The influence of the gravitational radiation damping on the evolution of the orbital elements of compact binary stars is examined by using the method of perturbation. The perturbation equations with the true anomaly as an independent variable are given. This effect results in both the secular and periodic variation of the semi-major axis, the eccentricity, the mean longitude at the epoch and the mean longitude. However, the longitude of periastron exhibits no secular variation, but only periodic variation. The effect of secular variation of the orbit would lead to collapse of the system of binary stars. The deduced formulae are applied to the calculation of secular variation of the orbital elements for three compact binary stars: PSR19 13 + 16, PSR J0737-3039 and M33X-7. The results obtained are discussed. 相似文献
15.
At critical mass the triangular equilibria in the planar restricted three-body problem, when the more massive primary is an oblate spheroid with its equatorial plane coincident with the plane of motion, are in general unstable due to the presence of secular terms in the solutions of linearized equations of motion in the vicinity of these points. Existence of retrograde elliptic periodic orbits is established through suitable velocity components. The eccentricity of these orbits increases with the oblateness. 相似文献
16.
An analytical expansion of the disturbing function arising from direct planetary perturbations on the motion of satellites is derived. As a Fourier series, it allows the investigation of the secular effects of these direct perturbations, as well as of every argument present in the perturbation. In particular, we construct an analytical model describing the evection resonance between the longitude of pericenter of the satellite orbit and the longitude of a planet, and study briefly its dynamic. The expansion developed in this paper is valid in the case of planar and circular planetary orbits, but not limited in eccentricity or inclination of the satellite orbit. 相似文献
17.
We have extend Stormer’s problem considering four magnetic dipoles in motion trying to justify the phenomena of extreme “orderlines”
such as the ones observed in the rings of Saturn; the aim is to account the strength of the Lorentz forces estimating that
the Lorentz field, co-acting with the gravity field of the planet, will limit the motion of all charged particles and small
size grains with surface charges inside a layer of about 200 m thickness as that which is observed in the rings of Saturn.
For this purpose our interest feast in the motion of charged particles with neglected mass where only electromagnetic forces
accounted in comparison to the weakness of the Newtonian fields. This study is particularly difficult because in the regions
we investigate these motions there is enormous three dimensional instability. Following the Poincare’s hypothesis that periodic
solutions are ‘dense’ in the set of all solutions in Hamiltonian systems we try to calculate many families of periodic solutions
and to study their stability. In this work we prove that in this environment charged particles can trace planar symmetric
periodic orbits. We discuss these orbits in details and we give their symplectic relations using the Hamiltonian formulation
which is related to the symplectic matrix. We apply numerical procedures to find families of these orbits and to study their
stability. Moreover we give the bifurcations of these families with families of planar asymmetric periodic orbits and families
of three dimensional symmetric periodic orbits. 相似文献
18.
In this paper we develop and implement an explicit numerical technique for studying stability of equilibrium solutions concerning the secular variations in the restricted problem. In our implementation, we use fourth-order expansions for the secular terms, but the method itself is independent of the particular order used as upper limit in the required expansions. 相似文献
19.
V. Kudielka 《Celestial Mechanics and Dynamical Astronomy》1994,60(4):455-470
An analytic model for third-body perturbations and for the second zonal harmonic of the central body's gravitational field is presented. A simplified version of this model applied to the Earth-Moon-Sun system indicates the existence of high-altitude and highly-inclined orbits with their apsides in the equator plane, for which the apsidal as well as the nodal motion ceases. For special positions of the node, secular changes of eccentricity and inclination disappear too (balanced orbits). For an ascending node at vernal equinox, the inclination of balanced orbits is 94.56°, for a node at autumnal equinox 85.44°, independent of the eccentricity of the orbit. For a node perpendicular to the equinox, there exist circular balanced orbits at 90° inclination. By slightly adjusting the initial inclination as suggested by the simplified model, orbits can be found — calculated by the full model or by different methods — that show only minor variations in eccentricity, inclination, argument of perigee, and longitude of the ascending node for 105 revolutions and more. Orbits near the unstable equilibria at 94.56° and 85.44° inclination show very long periodic librations and oscillations between retrogade and prograde motion.Retired from IBM Vienna Software Development Laboratory. 相似文献
20.
Cezary Migaszewski Krzysztof Go&#;dziewski 《Monthly notices of the Royal Astronomical Society》2009,395(4):1777-1794
We investigate the secular dynamics of a planetary system composed of the parent star and two massive planets in mutually inclined orbits. The dynamics are investigated in wide ranges of semimajor axes ratios (0.1–0.667) and planetary masses ratios (0.25–2), as well as in the whole permitted ranges of the energy and total angular momentum. The secular model is constructed by semi-analytic averaging of the three-body system. We focus on equilibria of the secular Hamiltonian (periodic solutions of the full system) and we analyze their stability. We attempt to classify families of these solutions in terms of the angular momentum integral. We identified new equilibria, yet unknown in the literature. Our results are general and may be applied to a wide class of three-body systems, including configurations with a star and brown dwarfs and substellar objects. We also describe some technical aspects of the seminumerical averaging. The HD 12661 planetary system is investigated as an example configuration. 相似文献