限制性三体问题中两类特殊轨道的应用研究
发布时间：2018-12-14 02:12
【摘要】：圆型限制性三体问题描述不计质量的第三体在两个相互绕圆轨道运行的大天体引力作用下的运动。由于其具有一个运动积分和五个平动解,相空间结构相对简单,广泛的应用在天文学的各个领域,是天体力学中最为重要的模型之一。本文分为两部分,分别从应用的角度研究了圆型限制性问题两类特殊轨道：发生Kozai效应的轨道和弹道捕获的轨道。第一部分中,我们主要研究气体盘的引力和阻力对圆型限制性三体问题中得到的经典的Kozai效应的影响。第二部分中,我们在圆型限制性三体问题框架下,研究了月球附近发生弹道捕获的区域-弱稳定边界的结构和性质。 如果第三体绕某个大天体运动,且其轨道平面和两个大天体平面存在比较大的倾角,则其偏心率将被周期性激发到很大的值,这种效应即为Kozai效应。本文以大倾角双星系统中星子碰撞生长过程为背景,研究了气体盘的引力和阻力对Kozai效应的影响。通过理论分析和数值模拟的方法,我们发现盘的引力一方面可以抑制系统内部区域的Kozai效应,而另一方面可以对Kozai效应起到增强的作用：倾角很小的系统中某些位置Kozai效应也可以发生,并且发生Kozai效应星子的最大偏心偏心率可以激发大很高的值(-1)。气体盘的阻力的最大作用是使发生Kozai效应的星子迅速内迁并堆积在系统内部,有利于行星形成。 另外本文在平面圆型限制性三体问题框架下研究了航天器被月球弹道捕获的轨道。可以发生弹道捕获的区域可以用弱稳定的边界(Weak Stability Boundary, WSB)来描述。我们发现弱稳定边界主要有五种类型,即：(1)和流形相关的边界,(2)和碰撞奇点相关的边界,(3)和l(θ)相切的轨道对应的边界,(4)零开普勒能量的轨道对应的边界。(5)与“伪稳定轨道”相关的边界。我们给出五种不同类型边界的分布特征。其中弱稳定边界中心近圆形稳定结构的边界大多为和流形相关的边界,通过数值方法,我们发现月球附近稳定流形上的轨道的第一个近月点为弱稳定边界中心近圆形稳定结构的上界。弱稳定边界的另一个特点是存在延伸很广的臂状结构。本文发现这些大范围的臂状结构和月球附近的C族,H1族和H2族周期轨道有关。周期轨道上近月点的位置决定了弱稳定边界臂状的大致位置,周期轨道的稳定性决定了弱稳定边界臂状结构的范围大小。
[Abstract]:The circular restricted three-body problem describes the motion of a third body without mass under the gravitational action of two large celestial bodies orbiting each other. Because it has a motion integral and five translational solutions, the phase space structure is relatively simple and widely used in various fields of astronomy. It is one of the most important models in celestial mechanics. This paper is divided into two parts. From the point of view of application, we study two kinds of special orbits of circular restricted problem: the orbit with Kozai effect and the trajectory with trajectory capture. In the first part, we mainly study the influence of the gravity and drag of the gas disk on the classical Kozai effect in the circular restricted three-body problem. In the second part, we study the structure and properties of the weakly stable boundary near the moon in the framework of circular restricted three-body problem. If the third body moves around a large celestial body and the orbital plane and the plane of two large celestial bodies have a relatively large inclination, the eccentricity of the third body will be periodically excited to a very large value, which is called the Kozai effect. In this paper, the influence of gravitational force and drag of gas disk on the Kozai effect is studied on the background of the collision growth process of star in a large dip binary system. By means of theoretical analysis and numerical simulation, we find that on the one hand, the gravitational force of the disk can suppress the Kozai effect in the internal region of the system. On the other hand, the Kozai effect can be enhanced: the Kozai effect can occur at some positions in the system with small inclination angle, and the maximum eccentricity of the star in the Kozai effect can excite a large and high value (-1). The greatest effect of the resistance of the gas disk is to make the stars of the Kozai effect move in quickly and accumulate inside the system, which is favorable to the formation of the planets. In addition, the orbit of spacecraft captured by lunar trajectory is studied in the framework of plane circular restricted three-body problem. The region where ballistic capture can occur can be described by a weakly stable boundary (Weak Stability Boundary, WSB). We find that there are five main types of weakly stable boundary, namely: (1) the boundary associated with the manifold, (2) the boundary associated with the collision singularity, (3) the boundary corresponding to the tangent orbit of l (胃), (4) the boundary corresponding to the orbit of zero Kepler energy. (5) the boundary related to the pseudo-stable orbit. We give the distribution characteristics of five different types of boundaries. The boundary of the weakly stable boundary center near the circular stable structure is mostly the boundary related to the manifold, and the numerical method is used. We find that the first near-moon point of the orbit on the stable manifold near the moon is the upper bound of the near-circular stable structure in the center of the weakly stable boundary. Another characteristic of the weak stable boundary is the existence of a wide range of arm-like structures. In this paper, it is found that these large range arm structures are related to the periodic orbits of C, H 1 and H 2 groups near the moon. The position of the near moon on the periodic orbit determines the approximate position of the weakly stable boundary arm, and the stability of the periodic orbit determines the range of the weakly stable boundary arm structure.
【学位授予单位】：南京大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：P132.2
，
本文编号：2377717
[Abstract]:The circular restricted three-body problem describes the motion of a third body without mass under the gravitational action of two large celestial bodies orbiting each other. Because it has a motion integral and five translational solutions, the phase space structure is relatively simple and widely used in various fields of astronomy. It is one of the most important models in celestial mechanics. This paper is divided into two parts. From the point of view of application, we study two kinds of special orbits of circular restricted problem: the orbit with Kozai effect and the trajectory with trajectory capture. In the first part, we mainly study the influence of the gravity and drag of the gas disk on the classical Kozai effect in the circular restricted three-body problem. In the second part, we study the structure and properties of the weakly stable boundary near the moon in the framework of circular restricted three-body problem. If the third body moves around a large celestial body and the orbital plane and the plane of two large celestial bodies have a relatively large inclination, the eccentricity of the third body will be periodically excited to a very large value, which is called the Kozai effect. In this paper, the influence of gravitational force and drag of gas disk on the Kozai effect is studied on the background of the collision growth process of star in a large dip binary system. By means of theoretical analysis and numerical simulation, we find that on the one hand, the gravitational force of the disk can suppress the Kozai effect in the internal region of the system. On the other hand, the Kozai effect can be enhanced: the Kozai effect can occur at some positions in the system with small inclination angle, and the maximum eccentricity of the star in the Kozai effect can excite a large and high value (-1). The greatest effect of the resistance of the gas disk is to make the stars of the Kozai effect move in quickly and accumulate inside the system, which is favorable to the formation of the planets. In addition, the orbit of spacecraft captured by lunar trajectory is studied in the framework of plane circular restricted three-body problem. The region where ballistic capture can occur can be described by a weakly stable boundary (Weak Stability Boundary, WSB). We find that there are five main types of weakly stable boundary, namely: (1) the boundary associated with the manifold, (2) the boundary associated with the collision singularity, (3) the boundary corresponding to the tangent orbit of l (胃), (4) the boundary corresponding to the orbit of zero Kepler energy. (5) the boundary related to the pseudo-stable orbit. We give the distribution characteristics of five different types of boundaries. The boundary of the weakly stable boundary center near the circular stable structure is mostly the boundary related to the manifold, and the numerical method is used. We find that the first near-moon point of the orbit on the stable manifold near the moon is the upper bound of the near-circular stable structure in the center of the weakly stable boundary. Another characteristic of the weak stable boundary is the existence of a wide range of arm-like structures. In this paper, it is found that these large range arm structures are related to the periodic orbits of C, H 1 and H 2 groups near the moon. The position of the near moon on the periodic orbit determines the approximate position of the weakly stable boundary arm, and the stability of the periodic orbit determines the range of the weakly stable boundary arm structure.
【学位授予单位】：南京大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：P132.2
，
本文编号：2377717
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