Kuiper带天体的轨道动力学

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。     

Kuiper带天体的原始分布模拟

用包括太阳、8颗大行星、冥王星和UB313以及无质量实验粒子在内的N体问题的天体动力学模型,取当前观测的天体轨道根数为初始条件,对具有确定轨道根数的551个Kuiper主带内的小天体进行了10亿年的轨道反演数值模拟.结果显示:当前观测的这些Kuiper 天体中的1/3以上在10亿年前就位于该区域,少部分位于海王星轨道之内,其他在5OAU之外;在4.5亿年前,整个Kuiper主带内的天体呈较好的正态分布,海王星3:2共振带内没有像今天这样的天体聚集现象.     

Kuiper带小天体动力演化

Kuiper带是指太阳系内位于离太阳30－50AU一个区域。1992年该区域陆续发现了一群半径在几十到几百公里的小天体。这些小天体在Kuiper带的分布是极其不均匀的。Kuiper带小天体的发现对人们认识太阳系的形成与演化有重要的意义。本文回顾了近年来国际上在Kuiper带小天体动力演化方面的研究，着重分析了目前国际上几种用以解释其非均匀分布的动力学机制，并提出目前该领域的一些尚未解决的问题。     

Kuiper带小天体动力演化

Kuiper带是指太阳系内位于离太阳 30～ 50AU一个区域。 1 992年该区域陆续发现了一群半径在几十到几百公里的小天体。这些小天体在Kuiper带的分布是极其不均匀的。Kuiper带小天体的发现对人们认识太阳系的形成与演化有重要的意义。本文回顾了近年来国际上在Kuiper带小天体动力演化方面的研究 ,着重分析了目前国际上几种用以解释其非均匀分布的动力学机制 ,并提出目前该领域的一些尚未解决的问题。     

长期共振迁移对经典Kuiper带的影响

太阳星云气体的耗散可以引起长期共振迁移(secular resonance sweeping,SRS),当长期共振的位置扫过经典Kuiper带小天体(Kuiper Belt objects,KBOs),就会激发其轨道倾角.详细研究了在太阳系紧致构形中(指四个大行星轨道彼此相距较小的状态)SRS对经典KBOs轨道倾角的激发过程,发现KBOs轨道倾角受激发的程度敏感地依赖于星云气体中面与太阳系不变平面1的夹角δ:当星云气体中面与不变平面重合,即δ=0时,经典KBOs倾角受到的激发很小;而当星云气体中面与黄道面重合,即δ≈1.6°时,在合理的初始条件下,经典KBOs的倾角最高可以被激发到30°以上.另外,通过模拟木星具有较大轨道倾角的情形以及SRS和大行星轨道迁移同时发生的情形,发现对于经典KBOs倾角的受激发程度而言,它们两者的影响都远弱于δ.     

太阳系动力学中当前的重要课题

以当前太阳系动力学中的重要课题以及研究方法进行讨论，并提出一些看法，课题中主要讨论动力学模型，轨道共振，行星环，混沌和长期演化，近地天体运动，Kupiper带，太阳系中的引力理论，以及其他有关问题。     

两个可能存在大质量类冥王星的区域

1992年以来，在海王星外的太阳系发现了近千个小天体，称为Kuiper带天体(KBO)或Edgeworth—Kuiper带天体，其中有一部分偏心率和倾角较大的小天体与海王星之间存在3：2平运动共振，轨道特征类似冥王星，命名为类冥王星，自KBO发现以来，天文学家们进行了多次小天区的搜索，发现了几个质量较大的KBO，通过数值计算，在轨道参数空间发现了两个和冥王星一样同时具有3种共振的区域，在这两个区域里的小天体既避免了海王星的强摄动又不会与冥王星密切交会，轨道非常稳定，因此有可能在其中发现质量较大的类冥王星。     

卫星轨道预报的一种分析方法

人造地球卫星的轨道预报是空间环境监测和实时跟踪测量中一个重要环节，由于监测对象众多，要求精度也不太高，通常采用分析法预报．在已有分析法得到t时刻平均根数的基础上给出一种轨道预报方法，由t时刻的平均根数给出该时刻卫星的位置和速度，在此基础上将地球非球形引力摄动的周期项直接用卫星直角坐标的位置和速度分量表示，这样可以避免在计算轨道根数变化的周期项时出现的奇点问题，从而对根数的选择无特殊要求，可适用于各种轨道，简化预报程序和相应的软件，提高预报效率。     

月球卫星轨道力学综述

月球探测器的运动通常可分为3个阶段，这3个阶段分别对应3种不同类型的轨道：近地停泊轨道、向月飞行的过渡轨道与环月飞行的月球卫星轨道。近地停泊轨道实为一种地球卫星轨道；过渡轨道则涉及不同的过渡方式(大推力或小推力等)；环月飞行的月球卫星轨道则与地球卫星轨道有很多不同之处，它决不是地球卫星轨道的简单克隆。针对这一点，全面阐述月球卫星的轨道力学问题，特别是环月飞行中的一些热点问题，如轨道摄动解的构造、近月点高度的下降及其涉及的卫星轨道寿命、各种特殊卫星(如太阳同步卫星和冻结轨道卫星等)的轨道特征、月球卫星定轨等。     

用太阳系主要天体的位置建立特大地震的时间预测模型

根据某类事件发生时太阳系主要运动天体的位置，通过对其历史资料的归算，尝试并设计出一种具有普适性的事件时间预测模型．以1900-1980年间全球所有8级及以上的99次地震为例，定义与天体特征位置(视黄经)相关的发震率，初步建立预测发震时刻的概率曲线．指出这可能成为研究地震预报问题的新途径．     

The Effect of Sweeping Secular Resonances on the Classical Kuiper Belt

Abstract The Kuiper Belt is a disk of small icy objects orbiting the Sun beyond Neptune. The region between 40-48AU in this disk is supposed to consist of dynamical “cold” objects on low-inclination orbits and is called the “Classical Kuiper Belt”. Recent observations reveal that there is a “hot” population with inclinations being as large as 30? residing in this region. Secular resonance sweeping, which took place in the late stage of formation of the planetary system when the residual nebula gas was dispersing, is a possible mechanism that can excite the orbits in this region. In this paper, we investigate in detail the excitation of orbital inclination by this mechanism. It is shown that the excitation depends sensitively on the angle δ between the midplane of the nebula gas and the invariable plane of the solar system. The excitation is very small when δ = 0?, but if the gas midplane coincides with the ecliptic, i.e. if δ ≈ 1.6?, then objects in the region of classical Kuiper belt can be excited to orbital inclinations as high as 30?, provided the nebula gas has the proper initial density and disperses at a proper rate. We also considered the orbital excitation by secular resonance sweeping with Jupiter on an inclined orbit and with migrating Jovian planets, and found the excitation is only slightly affected.     

Formation of the Kuiper Belt by Long Time-Scale Migration of Jovian Planets

The orbital migration of Jovian planets is believed to have played an important role in shaping the Kuiper Belt. We investigate the effects of the long time-scale (2×107 yr) migration of Jovian planets on the orbital evolution of massless test particles that are initially located beyond 28 AU. Because of the slowness of the migration, Neptune's mean motion resonances capture test particles very efficiently. Taking into account the stochastic behavior during the planetary migration and for proper parameter values, the resulting concentration of objects in the 3:2 resonance is prominent, while very few objects enter the 2:1 resonance, thus matching the observed Kuiper Belt objects very well. We also find that such a long time-scale migration is favorable for exciting the inclinations of the test particles, because it makes the secular resonance possible to operate during the migration. Our analyses show that the v8 secular resonance excites the eccentricities of some test particles, so decreasing their perihelion distances, leading to close encounters with Neptune, which can then pump the inclinations up to 20℃.     

The Shape Distribution Of Kuiper Belt Objects

If we assume that the periodic brightness variations ina Kuiper Belt lightcurve are determined only by theiraspherical shapes and the observing geomtry, the fractionof detectable Kuiper Belt lightcurves and the lightcurveamplitude distribution can be used to constrain the shapesof Kuiper Belt objects. The results indicate that most KuiperBelt objects (～85%) have shapes that are close to spherical(a/b ≤ 1.5$), but there is a small but significant fraction(～12%) possessing highly aspherical shapes (a/b ≥ 1.7).The distribution cannot be well fitted by a gaussian and is betterapproximated by a power law.     

A stability study of Kuiper Belt binaries

The dynamical structure of the orbital element space of seven Kuiper Belt binary systems is studied by numerical methods in the model of the spatial elliptic restricted three‐body problem. It is shown that three systems have an extended region of stability where additional satellites could exist. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect on the Edgeworth–Kuiper Belt of a large distant tenth planet

We investigate the orbital evolution of both real and hypothetical Edgeworth–Kuiper Objects in order to determine whether any conclusions can be drawn regarding the existence, or otherwise, of the tenth planet postulated by Murray. We find no qualitative difference in the orbital evolution, and so conclude that the hypothetical planet has been placed on an orbit at such a large heliocentric distance that no evidence for the existence, or non-existence, can be found from a study of the known Edgeworth–Kuiper Objects.     

The Dynamics of Objects in the Inner Edgeworth–Kuiper Belt

Objects in 3:2 mean motion resonance with Neptune are protected from close encounters with Neptune by the resonance. Bodies in orbits with semi-major axis between 39.5 and about 42 AU are not protected by the resonance; indeed due to overlapping secular resonances, the eccentricities of orbits in this region are driven up so that a close encounter with Neptune becomes inevitable. It is thus expected that such orbits are unstable. The list of known Trans-Neptunian objects shows a deficiency in the number of objects in this gap compared to the 43–50 AU region, but the gap is not empty. We numerically integrate models for the initial population in the gap, and also all known objects over the age of the Solar System to determine what fraction can survive. We find that this fraction is significantly less than the ratio of the population in the gap to that in the main belt, suggesting that some mechanism must exist to introduce new members into the gap. By looking at the evolution of the test body orbits, we also determine the manner in which they are lost. Though all have close encounters with Neptune, in most cases this does not lead to ejection from the Solar System, but rather to a reduced perihelion distance causing close encounters with some or all of the other giant planets before being eventually lost from the system, with Saturn appearing to be the cause of the ejection of most of the objects.