海王星特洛伊:回顾与新成员

目前观测到的海王星特洛伊天体已有17颗并已积累了较为精确的轨道数据,系统分析了这些天体轨道的动力学稳定性.数值结果表明:除去两个寿命短到只有数万年和百万年的临时海王星特洛伊,大部分天体在其轨道根数不确定范围内都可以存活至45亿年.大约有一半的海王星特洛伊在45亿年的时间内离开共振区,而逃离的途径是复杂动力学机制下轨道根数空间内缓慢的扩散.在半人马小行星群中识别并证认了一个新的海王星特洛伊天体2012 UW177,数值模拟表明该天体目前正在围绕海王星L4点的蝌蚪形轨道上运动.该天体大约在23万年前进入当前轨道,且未来将在该轨道停留至少130万年.约54°的倾角使得它的轨道成为最倾斜的轨道,并且使得该天体展现经由拟卫星轨道的复杂有趣的共轨轨道转换.     

地球特洛伊天体稳定区域研究

第1颗地球特洛伊天体2010 TK7的发现暗示了可能存在大量未发现的地球特洛伊天体.进行了大量数值模拟并结合频谱分析方法,在初始轨道根数(a,i)平面上,给出了日地系L_4拉格朗日点附近特洛伊天体的稳定分布区域.得到的地球特洛伊天体稳定区域相对前人的结果偏小,完全排除了初始轨道倾角超过37o的稳定区域.细致分析了该稳定区域分布图中的精细结构,发现多种长期共振包括近日点进动ν_2-ν_8长期共振均对地球特洛伊天体的稳定性区域分布具有重要影响,少数轨道还受升交点共振ν_(14)的影响,导致轨道倾角的激发.在(a,i)平面的不同位置处,不同共振的影响程度和影响方式并不一致.     

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.     

热海王星系统HD 106315的近$2:1$ 平运动共振捕获与轨道演化

通过结合理论分析和数值模拟方法,可以对热海王星系统HD 106315轨道迁移中的近2:1平运动共振捕获机制以及潮汐作用下的演化过程进行研究.在轨道迁移阶段,初始轨道半长径、初始偏心率以及行星c的偏心率衰减系数K会对系统轨道构型产生影响.数值模拟结果显示当初始轨道半长径分别为ab～0.4 au、ac～0.8 au,偏心率eb和ec均小于0.03时, HD 106315b和HD 106315c在中央恒星的引力作用以及原行星盘粘滞作用下向内迁移, 65000 yr左右两颗行星均可迁移至当前观测位置附近并形成近2:1平运动共振捕获.此外,中央恒星的潮汐效应也可能会对行星系统共振构型产生影响,理论分析表明当行星潮汐耗散系数Q=100时,潮汐效应造成的轨道半长径衰减使系统轨道周期比发生的变化可能是系统脱离共振构型的原因.数值模拟结果显示, HD 106315系统内两颗行星Q103时,来自中央恒星的潮汐效应并不会使行星系统产生明显的偏心率和轨道半长径衰减,不足以使HD 106315行星系统在剩余寿命内脱离2:1平运动共振轨道构型.     

限制性三体问题中摄动运动方程的坐标系选择

针对限制性三体问题,分别选取以中心天体和摄动体质心为坐标原点的惯性系,及以中心天体为坐标原点的非惯性系,讨论了不同坐标系下天体运动轨道描述的异同。利用运动天体轨道能量E的大小,可以确定受摄运动方程采用椭圆轨道根数还是采用双曲线轨道根数进行描述。为此,推导出一个关于轨道半长径和偏心率满足的临界关系判别式。结果表明,在摄动天体质量较大的情况下,非惯性系中存在大量轨道,这些轨道在原惯性坐标系中是稳定的椭圆轨道,转换到非惯性系中后却无法用椭圆轨道根数进行描述。只能引入双曲线轨道根数来描述轨道,由此将产生非惯性系下摄动运动方程轨道根数类型选择问题。最后,指出选择雅可比坐标系可以避免上述问题,并推导出适用于任意运动区域的具有统一形式的摄动函数展开式。     

近地卫星运动的坐标系附加摄动在拟平均根数法中的处理

在常用的历元地心天球坐标系中研究和处理近地卫星的轨道问题,就必须考虑由于地球赤道面摆动所引起的坐标系附加摄动,正因为如此,给实际工作带来一些麻烦.关于这一问题,曾提出了一种针对瞬根数和平根数之间的转换(仅与坐标系附加摄动的短周期项有关)的解决途径,但并未涉及采用分析法进行轨道外推的有关问题(这与坐标系附加摄动的长期和长周期项有关),这对处理近地卫星的轨道问题而言显然是不完整的.这里结合拟平均根数法进一步改进原提出的方法,较完善地解决这一坐标系附加摄动的计算问题.在此前提下,对于卫星定轨和预报及其相关工作,无论是采用数值法还是分析法,均可采用同一坐标系,即历元(目前是J2000.0)地心天球坐标系.     

两个可能具有2:1平运动共振结构系统的稳定性研究

通过分析现有视向速度资料提供的轨道拟合解,发现HD 155358和24 Sextanis两系统都有可能处于2:1平运动共振状态.主要讨论了两系统共振结构的动力学稳定性问题,计算了两系统最优拟合值1σ置信区间内大量样本的混沌指标?emax.结果表明:HD155358系统长期稳定,不依赖于平运动共振的保护.但是,24 Sextanis系统如果要维持长期稳定,2:1平运动共振保护是必要条件.     

地月DRO星载光学测量近地小行星轨道确定

针对地基光学监测系统对近地小行星在近太阳方向的监测存在盲区的问题,提出了远距离逆行轨道(Distant Retrograde Orbit,DRO)天基光学平台对近地小行星进行跟踪定轨的方法.通过可视性分析,筛选仿真观测数据,利用美国宇航局喷气推进实验室(Jet Propulsion Laboratory,JPL)公布的小行星初始轨道信息对不同轨道类型的目标天体进行轨道确定,将计算结果与参考轨道对比分析.仿真结果表明:在测量精度2角秒,定轨弧长3年的情况下,DRO平台对仿真算例中所选择的近地小行星的定轨精度可以达到几十公里量级,其中Atira型轨道精度可达10公里以内.由此可见,DRO天基平台对近地小行星具有较好的监测能力,定轨精度能实现对目标小行星的精确跟踪,并对其进行轨道预报.     

在电离中电感应阻力对带电卫星轨道根数的摄动影响

研究了在高空电离层中运动的带电荷的卫星受电感应阻力后对轨道根数产生的摄动影响。研究结果表明 ,电感应阻力对带电卫星的轨道半长轴、轨道偏心率、近地点赤经、历元平赤经均有周期摄动影响 ,但除对半长轴有长期摄动效应外对其它轨道根数均无长期摄动。轨道倾角和升交点赤经不受摄动影响。文中以飞行在高度 1 50 0km的电离层中的导体卫星作为算例。计算结果显示 :带电导体卫星在高空电离层中带有一定电量时电感应阻力对轨道半长轴的缩短产生显著效应     

分点和赤道改正的分离摄动项求解法

本文所提出的分离摄动项求解法,是利用小行星在整个轨道上分布的不少于9次的位置测定值,与用该小行星的轨道根数初值计算出的列表位置进行比较,将由太阳系其它天体摄动力对小行星位置、速度的影响进行分离,求解出分点及赤道改正,小行星轨道根数改正,地球轨道根数改正和由摄动力引起的小行星位置和速度改正。这种方法的优点在于:(1)列表位置仅需根据小行星的轨道根数初值计算出,不考虑摄动力的作用,这样可避免小行星运动理论不完善对确定分点和赤道改正的影响;(2)在解算中,可以单独地求出摄动力对小行星运动速度和位置的影响,通过对摄动函数的数值积分,可求得任一时刻的小行星的真位置。     

Neptune Trojans: a Revisit and a New Membertwo

Up to now, 17 Neptune Trojan asteroids have been detected with their orbits being well determined by continuous observations. This paper analyzes systematically their orbital dynamics. Our results show that except for two temporary members with relatively short lifespans on Trojan orbits, the vast majority of Neptune Trojans located within their orbital uncertainties may survive in the solar system age. The escaping probability of Neptune Trojans, through slow diffusion in the orbital element space in 4.5 billion years, is estimated to be ～50%. The asteroid 2012 UW177 classified as a Centaur asteroid by the IAU Minor Planet Center currently is in fact a Neptune Trojan. Numerical simulations indicate that it is librating on the tadpole-shaped orbit around the Neptune's L₄ point. It was captured into the current orbit approximately 0.23 million years ago, and will stay there for at least another 1.3 million years in the future. Its high inclination of i ≈ 54^° not only makes it the most inclined Neptune Trojan, but also makes it exhibit the complicated and interesting co-orbital transitions between the leading and trailing Trojans via the quasi-satellite orbit phase.     

A survey of orbits of co-orbitals of Mars

Many asteroids with a semimajor axis close to that of Mars have been discovered in the last several years. Potentially some of these could be in 1:1 resonance with Mars, much as are the classic Trojan asteroids with Jupiter, and its lesser-known horseshoe companions with Earth. In the 1990s, two Trojan companions of Mars, 5261 Eureka and 1998 VF₃₁, were discovered, librating about the L₅ Lagrange point, 60° behind Mars in its orbit. Although several other potential Mars Trojans have been identified, our orbital calculations show only one other known asteroid, 1999 UJ₇, to be a Trojan, associated with the L₄ Lagrange point, 60° ahead of Mars in its orbit. We further find that asteroid 36017 (1999 ND₄₃) is a horseshoe librator, alternating with periods of Trojan motion. This asteroid makes repeated close approaches to Earth and has a chaotic orbit whose behavior can be confidently predicted for less than 3000 years. We identify two objects, 2001 HW₁₅ and 2000 TG₂, within the resonant region capable of undergoing what we designate “circulation transition”, in which objects can pass between circulation outside the orbit of Mars and circulation inside it, or vice versa. The eccentricity of the orbit of Mars appears to play an important role in circulation transition and in horseshoe motion. Based on the orbits and on spectroscopic data, the Trojan asteroids of Mars may be primordial bodies, while some co-orbital bodies may be in a temporary state of motion.     

A Perturbative Treatment of The Co-Orbital Motion

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.     

Trojans in Stable Chaotic Motion

The orbits of 13 Trojan asteroids have been calculated numerically in the model of the outer solar system for a time interval of 100 million years. For these asteroids Milani et al. (1997) determined Lyapunov times less than 100 000 years and introduced the notion "asteroids in stable chaotic motion". We studied the dynamical behavior of these Trojan asteroids (except the asteroid Thersites which escaped after 26 million years) within 11 time intervals - i.e. subintervals of the whole time - by means of: (1) a numerical frequency analysis (2) the root mean square (r.m.s.) of the orbital elements and (3) the proper elements. For each time interval we compared the root mean squares of the orbital elements (a, e and i) with the corresponding proper element. It turned out that the variations of the proper elements e_p in the different time intervals are correlated with the corresponding r.m.s.(e); this is not the case for sin I_p with r.m.s.(i). This revised version was published online in July 2006 with corrections to the Cover Date.     

Orbital correlation of space objects based on orbital elements

Orbital correlation of space objects is one of the most important elements in space object identification. Using the orbital elements, we provide correlation criteria to determine if objects are coplanar,co-orbital or the same. We analyze the prediction error of the correlation parameters for different orbital types and propose an orbital correlation method for space objects. The method is validated using two line elements and multisatellite launching data. The experimental results show that the proposed method is effective, especially for space objects in near-circular orbits.     

Collective resonant phenomena on small bodies in the solar system

For both asteroids and meteor streams, and also for comets, resonances play a major role for their orbital evolutions but on different time scales. For asteroids both mean motion resonances and secular resonances not only structure the phase space of regular orbits but are mainly at the origin for the inherent chaos of planet crosser objects.For comets and their chaotic routes temporary trapping into orbital resonances is a well known phenomenon. In addition for slow diffusion through the Kuiper belt resonances are the only candidates for originating a slow chaos.Like for asteroids, resonances with Jupiter play a major role for the orbital evolution of meteor streams. Crossing of separatrix like zones appears to be crucial for the formation of arcs and for the dissolution of streams. In particular the orbital inclination of a meteor stream appears to be a critical parameter for arc formation. Numerical results obtained in an other context show that the competition between the Poynting-Robertson drag and the gravitational interaction of grains near the 2/1 resonance might be very important in the long run for the structure of meteor streams.     

On quasi-satellite periodic motion in asteroid and planetary dynamics

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.     

The perturbations of the orbital elements of Trojan asteriods

An asymptotic solution for the cylindrical coordinates of Trojan asteroids is derived by using a three-variable expansion method in the elliptic restricted three-body problem. The perturbations of the orbital elements are obtained from this solution by applying the formulas of the two-body problem. The main perturbations of the mean motion are studied in detail.     

Numerical Simulation of the Orbital Evolution of Near-Earth Asteroids Close to Mean Motion Resonances

The dynamics of near-Earth asteroids near mean motion resonances with the Earth or other planets is considered. The probability domains of the motion of some near-Earth asteroids close to low-order resonances are presented. The investigations have been carried out by means of a numerical integration of differential equations, taking into account the perturbations from the major planets and the Moon. For each investigated object an ensemble of 100 test particles with orbital elements nearby those of the nominal orbit has been constructed and its evolution has been retraced over the time interval (–3000, +3000 years). The initial set of orbits has been generated on the basis of probable variations of the initial orbital elements obtained from the least square analysis of observations.This revised version was published online in October 2005 with corrections to the Cover Date.     

Long periodic perturbations of Trojan asteroids

The motion of the Trojan asteroids is studied in the elliptic restricted three-body problem of the Sun-Jupiter-asteroid system. Long periodic perturbations of the orbital elements are discussed. Relations between dynamical parameters are considered and comparisons are made with Bien's and Schubart's results.