共查询到19条相似文献,搜索用时 15 毫秒
1.
A symplectic mapping for Trojan-type motion has been developed in the secularly changing elliptic restricted three-body problem. The mapping describes well the characteristics of Trojan-type dynamics at small eccentricities. By using this mapping the boundary of the stability region has been studied for different values of the initial eccentricities of hypothetical Jupiter's Trojans. It has been found that in the secularly changing elliptic case the chaotic diffusion at the border of the stability region is stronger than simply in the elliptic case. An explanation of this observation might be the destruction of the chain of islands of the 13:1 secondary resonance between the short and long period component of the Trojan-like motion, caused possibly by the indirect perturbations of Saturn. 相似文献
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The purpose of this paper is to extend the study of the so called p-q resonant orbits of the planar restricted three-body problem to the spatial case. The p-q resonant orbits are solutions of the restricted three-body problem which have consecutive close encounters with the smaller primary. If E, M and P denote the larger primary, the smaller one and the infinitesimal body, respectively, then p and q are the number of revolutions that P gives around M and M around E, respectively, between two consecutive close approaches. For fixed values of p and q and suitable initial conditions on a sphere of radius around the smaller primary, we will derive expressions for the final position and velocity on this sphere for the orbits under consideration. 相似文献
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《Chinese Astronomy and Astrophysics》2019,43(4):549-562
The velocity scaling factor method based on the least squares principle is regarded as the most efficient, stable, and widely-used method among all the manifold correction methods. The stability of the restricted three-body problem where the primary body is a source of radiation and the secondary body is an oblate spheroid is discussed by using the velocity scaling factor method. The numerical simulations suggest that (1) the number of the chaotic orbits will increase if only the oblate spheroid perturbation is considered; (2) the number of the regular orbits will increase if only considering the radiation pressure; (3) when both the radiation and oblateness perturbation exist, the radiation plays a dominant role, and the probability of regular motion of the system will increase. 相似文献
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W. S. Koon M. W. Lo J. E. Marsden S. D. Ross 《Celestial Mechanics and Dynamical Astronomy》2001,81(1-2):27-38
A number of Jupiter family comets such as Otermaand Gehrels 3make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L
1and L
2, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L
1and L
2is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L
1and the other around L
2) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold tubes associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit. 相似文献
7.
The purpose of this paper is to study, for small values of , the three-dimensional p–q resonant orbits that are close to periodic second species solutions (SSS) of the restricted three-body problem. The work is based on an analytic study of the in- and out-maps. These maps are associated to follow, under the flow of the problem, initial conditions on a sphere of radius around the small primary, and consider the images of those initial points on the same sphere. The out-map is associated to follow the flow forward in time and the in-map backwards. For both mappings we give analytical expressions in powers of the mass parameter. Once these expressions are obtained, we proceed to the study of the matching equations between both, obtaining initial conditions of orbits that will be 'periodic' with an error of the order 1–, for some (1/3,1/2). Since, as 0, the inner solution and the outer solution will collide with the small primary, these orbits will be close to SSS. 相似文献
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研究了Coriolis力和离心力摄动对Robe限制性三体问题主要平动点位置及线性稳定性的影响,给出了Robe限制性三体问题主要平动点的摄动位置和Coriolis力和离心力摄动对主要平动点位置和线性稳定的影响量级.改进了Shrivastava的结果. 相似文献
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D. Nesvorný F. Thomas S. Ferraz-Mello A. Morbidelli 《Celestial Mechanics and Dynamical Astronomy》2002,82(4):323-361
We develop a formalism of the non-singular evaluation of the disturbing function and its derivatives with respect to the canonical variables. We apply this formalism to the case of the perturbed motion of a massless body orbiting the central body (Sun) with a period equal to that of the perturbing (planetary) body. This situation is known as the co-orbital motion, or equivalently, as the 1/1 mean motion commensurability. Jupiter's Trojan asteroids, Earth's co-orbital asteroids (e.g., (3753) Cruithne, (3362) Khufu), Mars' co-orbital asteroids (e.g., (5261) Eureka), and some Jupiter-family comets are examples of the co-orbital bodies in our solar system. Other examples are known in the satellite systems of the giant planets. Unlike the classical expansions of the disturbing function, our formalism is valid for any values of eccentricities and inclinations of the perturbed and perturbing body. The perturbation theory is used to compute the main features of the co-orbital dynamics in three approximations of the general three-body model: the planar-circular, planar-elliptic, and spatial-circular models. We develop a new perturbation scheme, which allows us to treat cases where the classical perturbation treatment fails. We show how the families of the tadpole, horseshoe, retrograde satellite and compound orbits vary with the eccentricity and inclination of the small body, and compute them also for the eccentricity of the perturbing body corresponding to a largely eccentric exoplanet's orbit.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
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考虑周期解的数值延拓问题并提出基于Broyden拟牛顿法来延拓周期解的一种有效算法,先后以布鲁塞尔振子、平面圆型限制性三体问题(Planar Circular Restricted Three-Body Problem, PCRTBP)的周期解为例进行了验证.这里的Broyden方法包含线性搜索、正交三角分解求线性方程组的步骤.对一般的周期解,周期性条件方程组中含有周期作为待延拓参数,可用周期来决定积分时长,将解代入周期性条件得到积分型的非线性方程组,利用Broyden方法迭代延拓直至初值收敛.根据两次垂直通过一个超平面的轨道是对称周期轨道的性质,可采用插值的方法求得再次抵达超平面的解分量,得到周期性条件方程组,再用Broyden方法求解.结合哈密顿系统的对称性和PCRTBP周期轨道的一些分类,对2/1、3/1的内共振周期解族进行了数值研究.最后,对算法和计算结果做了总结和讨论. 相似文献
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Anne-Sophie Libert Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》2005,93(1-4):187-200
We analyse the secular interactions of two coplanar planets which are not in mean motion resonances. The analysis is based
on a high order (order 12) expansion of the perturbative potential in powers of the eccentricities. The model depends on only
two parameters (the ratio of semi-major axis and the mass ratio of the planets) and can be reduced to a one degree of freedom
system, allowing for an exhaustive parametric analysis. Following Pauwels [Pauwels T.: 1983, Celet. Mech. & Dyn. Astro. 30, 229–247] we map the phase space on a sphere, avoiding in this way the artificial singularities introduced by other mappings.
We show that the 12 order expansion is able to describe correctly most of the exosolar planetary systems discovered so far,
even if the eccentricities of these planets are considerably larger than the eccentricities of our own solar system. The expansion
is even able to reproduce, at moderate eccentricities, the secular resonances discovered numerically by Michtchenko and Malhotra
[Michtchenko, T. A. and Malhotra, R.: 2004, Icarus 168, 237–248] at moderate to large eccentricities.
FNRS Research Fellow. 相似文献
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V. S. Kalantonis C. N. Douskos E. A. Perdios 《Celestial Mechanics and Dynamical Astronomy》2006,94(2):135-153
Asymptotic motion to collinear equilibrium points of the restricted three-body problem with oblateness is considered. In particular,
homoclinic and heteroclinic solutions to these points are computed. These solutions depart asymptotically from an equilibrium
point and arrive asymptotically at the same or another equilibrium point and are important reference solutions. To compute
an asymptotic orbit, we use a fourth order local analysis, numerical integration and standard differential corrections. 相似文献
14.
Pavol Pástor Jozef Klačka Ladislav Kómar 《Celestial Mechanics and Dynamical Astronomy》2009,103(4):343-364
Effect of stellar electromagnetic radiation on the motion of spherical dust particle in mean motion orbital resonances with
a planet is investigated. Planar circular restricted three-body problem with the Poynting–Robertson (P–R) effect yields monotonic
secular evolution of eccentricity when the particle is trapped in the resonance. Planar elliptic restricted three-body problem
with the P–R effect enables nonmonotonous secular evolution of eccentricity and the evolution of eccentricity is qualitatively
consistent with the published results for the complicated case of interaction of electromagnetic radiation with nonspherical
dust grain. Thus, it is sufficient to allow either nonzero eccentricity of the planet or nonsphericity of the grain and the
orbital evolutions in the resonances are qualitatively equal for the two cases. This holds both for exterior and interior
mean motion orbital resonances. Evolutions of argument of perihelion in the planar circular and elliptical restricted three-body
problems are shown. Numerical integrations show that an analytic expression for the secular time derivative of the particle’s
argument of perihelion does not exist, if only dependence on semimajor axis, eccentricity and argument of perihelion is admitted.
Connection between the shift of perihelion and oscillations in secular eccentricity is presented for the planar elliptic restricted
three-body problem with the P–R effect. Period of the oscillations corresponds to the period of one revolution of perihelion.
Change of optical properties of the spherical grain with the heliocentric distance is also considered. The change of the optical
properties: (i) does not have any significant influence on the secular evolution of eccentricity, (ii) causes that the shift
of perihelion is mainly in the same direction/orientation as the particle motion around the Sun. The statements hold both
for circular and noncircular planetary orbits. 相似文献
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We deal with the study of the spatial restricted three-body problem in the case where the small particle is far from the primaries, that is, the so-called comet case. We consider the circular problem, apply double averaging and compute the relative equilibria of the reduced system. It appears that, in the circular problem, we find not only part of the equilibria existing in the elliptic case, but also new ones. These critical points are in correspondence with periodic and quasiperiodic orbits and invariant tori of the non-averaged Hamiltonian. We explain carefully the transition between the circular and the elliptic problems. Moreover, from the relative equilibria of elliptic type, we obtain invariant 3-tori of the original system. 相似文献
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用直接数值积分方法通过模拟不同的行星构型探讨了HD82943行星系统(由两颗共振的巨行星组成)的长期动力演化,同时,还研究了在相空间的轨道运动.在对系统长达107年数值积分中,发现所有的稳定轨道均与2:1共振相关联.典型地,在相同的时标内,两个共振幅角θ1和θ2同时(或其中之一)存在秤动.由于共振幅角在一定范围内的秤动,因而使两颗行星轨道半长径被约束而表现为规则运动模式.另外,利用分析模型(包含了外行星偏心率e2的因素),还讨论了对于不同取值的e2和相对近星点经度θ时,内行星在相空间的运动,并发现2:1轨道共振对于相对较小的e2以及当θ=0°时易于保持.此外,适中的e2将导致系统的两颗行星进入深度共振状态.再者,分析模型和数值计算的结果吻合得很好,两者都揭示了行星系统的2:1共振结构. 相似文献
17.
Two asteroids 2001 QQ199 and 2004 AE9 and two comets P/LINEAR-Catalina and P/LINEAR are found to be quasi-satellites of Jupiter
at present time. The Tisserand parameters of these four bodies lie between 2.3 and 2.5, which means two asteroids might be
Jupiter family comets and will show a cometary’s activity in the near future. 相似文献
18.
K. E. Papadakis 《Astrophysics and Space Science》2006,305(1):57-66
We study numerically the asymptotic homoclinic and heteroclinic orbits associated with the triangular equilibrium points L
4 and L
5, in the gravitational and the photogravitational restricted plane circular three-body problem. The invariant stable-unstable manifolds associated to these critical points, are also presented. Hundreds of asymptotic orbits for equal mass of the primaries and for various values of the radiation pressure are computed and the most interesting of them are illustrated. In the Copenhagen case, which the problem is symmetric with respect to the x- and y-axis, we found and present non-symmetric heteroclinic asymptotic orbits. So pairs of heteroclinic connections (from L
4 to L
5 and vice versa) form non-symmetric heteroclinic cycles. The termination orbits (a combination of two asymptotic orbits) of all the simple families of symmetric periodic orbits, in the Copenhagen case, are illustrated. 相似文献