共查询到20条相似文献，搜索用时 31 毫秒
1.
The three-dimensional secular behavior of a system composed of a central star and two massive planets is modeled semi-analytically in the frame of the general three-body problem. The main dynamical features of the system are presented in geometrical pictures allowing us to investigate a large domain of the phase space of this problem without time-expensive numerical integrations of the equations of motion and without any restriction on the magnitude of the planetary eccentricities, inclinations and mutual distance. Several regimes of motion of the system are observed. With respect to the secular angle Δ?, possible motions are circulations, oscillations (around 0° and 180°), and high-eccentricity/inclination librations in secular resonances. With respect to the arguments of pericenter, ω1 and ω2, possible motions are direct circulation and high-inclination libration around ±90° in the Lidov-Kozai resonance. The regions of transition between domains of different regimes of motion are characterized by chaotic behavior. We apply the analysis to the case of the two outer planets of the υ Andromedae system, observed edge-on. The topology of the 3-D phase space of this system is investigated in detail by means of surfaces of section, periodic orbits and dynamical spectra, mapping techniques and numerical simulations. We obtain the general structure of the phase space, and the boundaries of the spatial secular stability. We find that this system is secularly stable in a large domain of eccentricities and inclinations. 相似文献
2.
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
3.
V.V. Kouprianov 《Icarus》2005,176(1):224-234
The problem of observability of chaotic regimes in the rotation of planetary satellites is studied. The analysis is based on the inertial and orbital data available for all satellites discovered up to now. The Lyapunov spectra of the spatial chaotic rotation and the full range of variation of the spin rate are computed numerically by integrating the equations of the rotational motion; the initial data are taken inside the main chaotic layer near the separatrices of synchronous resonance in phase space. The model of a triaxial satellite in a fixed elliptic orbit is adopted. A short Lyapunov time along with a large range of variation of the spin rate are used as criteria for observability of the chaotic motion. Independently, analysis of stability of the synchronous state with respect to tilting the axis of rotation provides a test for the physical opportunity for a satellite to rotate chaotically. Finally, a calculation of the times of despinning due to tidal evolution shows whether a satellite's spin could evolve close to the synchronous state. Apart from Hyperion, already known to rotate chaotically, only Prometheus and Pandora, the 16th and 17th satellites of Saturn, pass all these four tests. 相似文献
4.
In this paper, we use a semi-analytical approach to analyze the global structure of the phase space of the planar planetary 3/1 mean-motion resonance. The case where the outer planet is more massive than its inner companion is considered. We show that the resonant dynamics can be described using two fundamental parameters, the total angular momentum and the spacing parameter. The topology of the Hamiltonian function describing the resonant behaviour is investigated on a large domain of the phase space without time-expensive numerical integrations of the equations of motion, and without any restriction on the magnitude of the planetary eccentricities. The families of the Apsidal Corotation Resonances (ACR) parameterized by the planetary mass ratio are obtained and their stability is analyzed. The main dynamical features in the domains around the ACR are also investigated in detail by means of spectral analysis techniques, which allow us to detect the regions of different regimes of motion of resonant systems. The construction of dynamical maps for various values of the total angular momentum shows the evolution of domains of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. 相似文献
5.
Dionyssia Psychoyos John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》2005,92(1-3):135-156
A complete study is made of the resonant motion of two planets revolving around a star, in the model of the general planar three body problem. The resonant motion corresponds to periodic motion of the two planets, in a rotating frame, and the position and stability properties of the periodic orbits determine the topology of the phase space and consequently play an important role in the evolution of the system. Several families of symmetric periodic orbits are computed numerically, for the 2/1 resonance, and for the masses of some observed extrasolar planetary systems. In this way we obtain a global view of all the possible stable configurations of a system of two planets. These define the regions of the phase space where a resonant extrasolar system could be trapped, if it had followed in the past a migration process.The factors that affect the stability of a resonant system are studied. For the same resonance and the same planetary masses, a large value of the eccentricities may stabilize the system, even in the case where the two planetary orbits intersect. The phase of the two planets (position at perihelion or aphelion when the star and the two planets are aligned) plays an important role, and the change of the phase, other things being the same, may destabilize the system. Also, the ratio of the planetary masses, for the same total mass of the two planets, plays an important role and the system, at some resonances and some phases, is destabilized when this ratio changes.The above results are applied to the observed extrasolar planetary systems HD 82943, Gliese 876 and also to some preliminary results of HD 160691. It is shown that the observed configurations are close to stable periodic motion. 相似文献
6.
We develop a semi-numerical perturbation method for problems with two critical arguments. We apply it to a truncated model of the restricted, elliptic three body problem in case of a resonance 2/1 We identify regions of the phase space where chaotic motion is expected because of the presence of homoclinic orbits. One of these regions, the largest one, sits at the entrance to the resonance zone and is associated with a 2/1 resonance between the two critical arguments. The results are compared with numerical results due to Murray (1986) 相似文献
7.
Massimiliano Guzzo Zoran Knežević Andrea Milani 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):121-140
We apply the spectral formulation of the Nekhoroshev theorem to investigate the long-term stability of real main belt asteroids. We find numerical indication that some asteroids are in the so-called Nekhoroshev stability regime, that is they are on chaotic orbits but their motion is stable over very long times. We have analyzed the motion of bodies in different regions of the belt, to assess the sensitivity of our method. We found that it allows us to clearly discriminate between different dynamical regimes, such as the one described by the Nekhoroshev stability, the one well described by the KAM theory, and the unstable chaotic regime in which diffusion in phase space can be detected over time spans much shorter than the age of the solar system. 相似文献
8.
The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom
respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps are observed
at specific values of the parameter which tunes the dynamics; these locations are approximated by the stability resonances.
The latter are defined by a resonant condition on the stability exponents of a central linearly stable periodic orbit. We
show that, for more than two degrees of freedom, these resonances can be excited opening up gaps, which effectively separate
and reduce the regions of trapped motion in phase space. Using the scattering approach to narrow rings and a billiard system
as example, we demonstrate that this mechanism yields rings with two or more components. Arcs are also obtained, specifically
when an additional (mean-motion) resonance condition is met. We obtain a complete representation of the phase-space volume
occupied by the regions of trapped motion. 相似文献
9.
近地小行星(10302) 1989 ML和(4660) Nereus作为下一代深空探测的候选目标一直备受关注. 在考虑太阳系主要天体的动力学背景下, 通过计算最大Lyapunov指数(MLE)及MEGNO (Mean Exponential Growth factor of Nearby Orbits)指数讨论它们的稳定性. 同时, 对每个小行星, 在其观测误差范围内按多元正态分布各选取1000个克隆粒子, 通过统计分析显示这两个小行星在10万年内可能的运动范围, 给出半长径-偏心率空间中的出现次数分布图, 并统计小行星与地球或其他大行星之间的密近交汇及碰撞的概率. 此外还对这两个小行星的标称轨道进行长期共振、Kozai共振及平运动共振的动力学分析. 综上得出结论, 1989 ML处在平运动共振主导的区域, 发生密近交汇的概率较小, 从而其轨道相对较稳定; 而Nereus处在地球的密近交汇区域, 轨道极不稳定. 相似文献
10.
Kuiper带天体的轨道动力学 总被引：1，自引：0，他引：1
主要评述太阳系动力学研究的一个新方向——Kuiper带的轨道动力学。早期的研究是为了探讨短周期彗星的起源。在发现第一颗Kuiper带小天体之后，人们开始将注意力转到Kuiper带共振区的相空间结构上，Morbidelli和Malhotra分别采用不同的模型研究了这些共振区的大小。其中主要研究对象是3:2共振区。冥王星也处在这一共振区中。从冥王星的轨道特性来看，冥王星应是一颗较大的Kuiper带天体，它还拥有另外两种共振——Kozai共振和1：1超级共振。正是由于这些共振的存在，冥王星的运动才得以长期保持稳定。观测表明许多Kuiper带天体也处的海王星的平运动共振中。早期的理论认为这些平运动共振起源于灾难性事件，如碰撞。然而这都是一些小概率事件，无法对共振的形成进行合理的解释。Malhotra通过行星迁移成功地解释了冥王星被共振俘获的机制。这一机制的概率非常大，同样可以用来解释Kuiper带天体共振的形成。 相似文献
11.
The motion of asteroids near the 3:1 Jovian resonance in the restricted planar case is studied using three numerical methods: (a) integrating the full equations of motion, (b) integrating the averaged equations of motion, and (c) using an algebraic mapping recently developed by Wisdom (1982, Astron. J.87, 577–593). The relative merits of each method are investigated. It is concluded that in the regular regions of the phase space, methods b and c give excellent agreement with each other and that provided the maximum eccentricity emax < 0.4 differences with the exact solution (method a) are <6% in emax and <27% in the period of the oscillations. The additions of higher order terms in the expansion of the averaged Hamiltonian provides marginally better agreement with the full integration. This is probably due to the slow convergence of the expansion of the disturbing function at large eccentricities (e > 0.3). In chaotic regions of the phase there is little agreement between the orbital elements at any given time calculated by each method. However, all methods reflect the qualitative behavior of the chaotic trajectories and give good agreement on the bounds of the motion. Since the map is at least 200 times faster than solving the full equations of motion it is an efficient method of rapidly exploring accessible regions of the chaotic phase space. 相似文献
12.
In a previous work (Callegari and Yokoyama, Celest. Mech. Dyn. Astr. 98:5–30, 2007), the main features of the motion of the
pair Enceladus–Dione were analyzed in the frozen regime, i.e., without considering the tidal evolution. Here, the results
of a great deal of numerical simulations of a pair of satellites similar to Enceladus and Dione crossing the 2:1 mean-motion
resonance are shown. The resonance crossing is modeled with a linear tidal theory, considering a two-degrees-of-freedom model
written in the framework of the general three-body planar problem. The main regimes of motion of the system during the passage
through resonance are studied in detail. We discuss our results comparing them with classical scenarios of tidal evolution
of the system. We show new scenarios of evolution of the Enceladus–Dione system through resonance not shown in previous approaches
of the problem. 相似文献
13.
Comparative Study of the 2:3 and 3:4 Resonant Motion with Neptune: An Application of Symplectic Mappings and Low Frequency Analysis 总被引：2，自引：1，他引：1
The 2:3 and 3:4 exterior mean motion resonances with Neptune are studied by applying symplectic mapping models. The mappings
represent efficiently Poincaré maps for the 3D elliptic restricted three body problem in the neighbourhood of the particular
resonances. A large number of trajectories is studied showing the coexistence of regular and chaotic orbits. Generally, chaotic
motion depletes the small bodies of the effective resonant region in both the 2:3 and 3:4 resonances. Applying a low frequency
spectral analysis of trajectories, we determined the phase space regions that correspond to either regular or chaotic motion.
It is found that the phase space of the 3:4 resonant motion is more chaotic than the 2:3 one. 相似文献
14.
The dynamics of a pair of satellites similar to Enceladus–Dione is investigated with a two-degrees-of-freedom model written
in the domain of the planar general three-body problem. Using surfaces of section and spectral analysis methods, we study
the phase space of the system in terms of several parameters, including the most recent data. A detailed study of the main
possible regimes of motion is presented, and in particular we show that, besides the two separated resonances, the phase space
is replete of secondary resonances. 相似文献
15.
Zsolt Sándor Bálint Érdi Carl D. Murray 《Celestial Mechanics and Dynamical Astronomy》2002,84(4):355-368
The dynamics of co-orbital motion in the restricted three-body problem are investigated by symplectic mappings. Analytical and semi-numerical mappings have been developed and studied in detail. The mappings have been tested by numerical integration of the equations of motion. These mappings have been proved to be useful for a quick determination of the phase space structure reflecting the main characteristics of the dynamics of the co-orbital problem. 相似文献
16.
John Hadjidemetriou George Voyatzis 《Celestial Mechanics and Dynamical Astronomy》2000,78(1-4):137-150
A comparative study is made between the 2/1 and the 3/2 resonant asteroid motion, with the aim to understand their different behaviour (gap in the 2/1 resonance, group in the 3/2 resonance). A symplectic mapping model is used, for each of these two resonances, assuming the asteroid is moving in the three-dimensional space under the gravitational perturbation of Jupiter. It is found that these resonances differ in several points, and although there is, in general, more chaos in the phase space close to the 3/2 resonance, even in the model of circular orbit of Jupiter, there are regions, close to the secondary resonances, which are less chaotic in the 3/2 resonance compared to the 2/1 resonance, and consequently trapping can take place. 相似文献
17.
The dynamics of the 2/1 mean-motion asteroidal resonance with Jupiter is studied by numerical integration of the equations of motion of the Sun-Jupiter-Saturn-asteroid system. The measurement of the fundamental asteroidal frequencies by means of Fourier and wavelet analyses allows us to construct the web of the secular, secondary and Kozai resonances inside the 2/1-resonance boundaries. The structure of the phase space of the 2/1 resonance is discussed with emphasis on the acting depletion mechanisms due to presence of these inner resonances. Special attention is paid to the study of the middle-eccentricity depleted region. The importance of the great inequality of the Jupiter-Saturn system in the acceleration of the diffusion processes in this region is pointed out. The existence of a group of asteroids like (3789) Zhongguo, inside the 2/1 resonance, is also discussed. 相似文献
18.
Applying the method of analytical continuation of periodic orbits, we study quasi-satellite motion in the framework of the three-body problem. In the simplest, yet not trivial model, namely the planar circular restricted problem, it is known that quasi-satellite motion is associated with a family of periodic solutions, called family f, which consists of 1:1 resonant retrograde orbits. In our study, we determine the critical orbits of family f that are continued both in the elliptic and in the spatial models and compute the corresponding families that are generated and consist the backbone of the quasi-satellite regime in the restricted model. Then, we show the continuation of these families in the general three-body problem, we verify and explain previous computations and show the existence of a new family of spatial orbits. The linear stability of periodic orbits is also studied. Stable periodic orbits unravel regimes of regular motion in phase space where 1:1 resonant angles librate. Such regimes, which exist even for high eccentricities and inclinations, may consist dynamical regions where long-lived asteroids or co-orbital exoplanets can be found. 相似文献
19.
《Chinese Astronomy and Astrophysics》2022,46(1):109-136
Near-Earth asteroids (10302) 1989 ML and (4660) Nereus have attracted much attention as candidates for the next generation of deep space explorations. In the study, the maximum Lyapunov exponent (MLE) and MEGNO (Mean Exponential Growth factor of Nearby Orbits) index are calculated after considering the effects of major objects in the Solar system, and the stabilities of these two asteroids are discussed. For each asteroid, 1000 clonal particles consistent with the observational uncertainties are generated from a multivariate normal distribution. Statistical results display probably emerging regions of each asteroid within 0.1 million years, and provide distributions of occurrence times in the phase space of semi-major axis versus eccentricity. We estimate the probability of close encounters and collisions between the asteroid and Earth or other planets. Furthermore, secular resonances, Kozai resonance, and mean motion resonances are analyzed for nominal orbits of the two asteroids. We conclude that 1989 ML is in the region dominated by mean motion resonances with terrestrial planets. The probability of close encounters with them is relatively small, therefore its orbit is relatively stable. Nereus is located in a region that can have close-encounters with the Earth, and it has an extremely unstable orbit. 相似文献
20.
P. M. Cincotta C. M. Giordano J. G. Martí C. Beaugé 《Celestial Mechanics and Dynamical Astronomy》2018,130(1):7
We present numerical evidence that diffusion in the herein studied multidimensional near-integrable Hamiltonian systems departs from a normal process, at least for realistic timescales. Therefore, the derivation of a diffusion coefficient from a linear fit on the variance evolution of the unperturbed integrals fails. We review some topics on diffusion in the Arnold Hamiltonian and yield numerical and theoretical arguments to show that in the examples we considered, a standard coefficient would not provide a good estimation of the speed of diffusion. However, numerical experiments concerning diffusion would provide reliable information about the stability of the motion within chaotic regions of the phase space. In this direction, we present an extension of previous results concerning the dynamical structure of the Laplace resonance in Gliese-876 planetary system considering variations of the orbital parameters accordingly to the error introduced by the radial velocity determination. We found that a slight variation of the eccentricity of planet c would destabilize the inner region of the resonance that, though chaotic, shows stable when adopting the best fit values for the parameters. 相似文献