限制性三體問(wèn)題中兩類特殊軌道的應(yīng)用研究
發(fā)布時(shí)間：2018-12-14 02:12
【摘要】：圓型限制性三體問(wèn)題描述不計(jì)質(zhì)量的第三體在兩個(gè)相互繞圓軌道運(yùn)行的大天體引力作用下的運(yùn)動(dòng)。由于其具有一個(gè)運(yùn)動(dòng)積分和五個(gè)平動(dòng)解,相空間結(jié)構(gòu)相對(duì)簡(jiǎn)單,廣泛的應(yīng)用在天文學(xué)的各個(gè)領(lǐng)域,是天體力學(xué)中最為重要的模型之一。本文分為兩部分,分別從應(yīng)用的角度研究了圓型限制性問(wèn)題兩類特殊軌道：發(fā)生Kozai效應(yīng)的軌道和彈道捕獲的軌道。第一部分中,我們主要研究氣體盤的引力和阻力對(duì)圓型限制性三體問(wèn)題中得到的經(jīng)典的Kozai效應(yīng)的影響。第二部分中,我們?cè)趫A型限制性三體問(wèn)題框架下,研究了月球附近發(fā)生彈道捕獲的區(qū)域-弱穩(wěn)定邊界的結(jié)構(gòu)和性質(zhì)。 如果第三體繞某個(gè)大天體運(yùn)動(dòng),且其軌道平面和兩個(gè)大天體平面存在比較大的傾角,則其偏心率將被周期性激發(fā)到很大的值,這種效應(yīng)即為Kozai效應(yīng)。本文以大傾角雙星系統(tǒng)中星子碰撞生長(zhǎng)過(guò)程為背景,研究了氣體盤的引力和阻力對(duì)Kozai效應(yīng)的影響。通過(guò)理論分析和數(shù)值模擬的方法,我們發(fā)現(xiàn)盤的引力一方面可以抑制系統(tǒng)內(nèi)部區(qū)域的Kozai效應(yīng),而另一方面可以對(duì)Kozai效應(yīng)起到增強(qiáng)的作用：傾角很小的系統(tǒng)中某些位置Kozai效應(yīng)也可以發(fā)生,并且發(fā)生Kozai效應(yīng)星子的最大偏心偏心率可以激發(fā)大很高的值(-1)。氣體盤的阻力的最大作用是使發(fā)生Kozai效應(yīng)的星子迅速內(nèi)遷并堆積在系統(tǒng)內(nèi)部,有利于行星形成。 另外本文在平面圓型限制性三體問(wèn)題框架下研究了航天器被月球彈道捕獲的軌道�？梢园l(fā)生彈道捕獲的區(qū)域可以用弱穩(wěn)定的邊界(Weak Stability Boundary, WSB)來(lái)描述。我們發(fā)現(xiàn)弱穩(wěn)定邊界主要有五種類型,即：(1)和流形相關(guān)的邊界,(2)和碰撞奇點(diǎn)相關(guān)的邊界,(3)和l(θ)相切的軌道對(duì)應(yīng)的邊界,(4)零開(kāi)普勒能量的軌道對(duì)應(yīng)的邊界。(5)與“偽穩(wěn)定軌道”相關(guān)的邊界。我們給出五種不同類型邊界的分布特征。其中弱穩(wěn)定邊界中心近圓形穩(wěn)定結(jié)構(gòu)的邊界大多為和流形相關(guān)的邊界,通過(guò)數(shù)值方法,我們發(fā)現(xiàn)月球附近穩(wěn)定流形上的軌道的第一個(gè)近月點(diǎn)為弱穩(wěn)定邊界中心近圓形穩(wěn)定結(jié)構(gòu)的上界。弱穩(wěn)定邊界的另一個(gè)特點(diǎn)是存在延伸很廣的臂狀結(jié)構(gòu)。本文發(fā)現(xiàn)這些大范圍的臂狀結(jié)構(gòu)和月球附近的C族,H1族和H2族周期軌道有關(guān)。周期軌道上近月點(diǎn)的位置決定了弱穩(wěn)定邊界臂狀的大致位置,周期軌道的穩(wěn)定性決定了弱穩(wěn)定邊界臂狀結(jié)構(gòu)的范圍大小。
[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.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2012
【分類號(hào)】：P132.2
，
本文編號(hào)：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.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2012
【分類號(hào)】：P132.2
，
本文編號(hào)：2377717
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