共振在近地小行星轨道演化中的作用

本文采用了合理的力学模型和可靠的计算方法,研究了近地小行星轨道运动,揭示了共振（轨道共振和长期共振）在其轨道演化中的作用,并初步探讨了近地小行星的起源问题。     

近地小行星轨道演化的研究现状

近地小行星由于与地球的特殊关系为世人所瞩目, 对其研究始于５０ 年代, 近年来已成为太阳系动力学中的一个热门课题。全面地介绍了近年来关于近地小行星（ 小天体） 的研究状况, 包括对近地小行星轨道演化的研究方法和主要结果。阐明了在轨道演化过程中相应力学模型的选取、有关数值方法的引用以及积分步长变化的处理等具体问题, 并介绍了轨道长期共振的作用以及对这种共振的处理方法, 最后给出了根据目前研究所知的与地球轨道距离最近的一些小行星的轨道特征等。     

小行星主带上单个行星的质量上限

介绍了N体模拟的Hermite算法,并利用该算法研究了不同质量行星在小行星主带上轨道的演化情况．采用的演化模型是太阳系N体模型(N=7),即把水星、金星、地球的质量加到太阳上,忽略冥王星,同时在小行星主带附近增加一个假想行星,系统演化时间为1亿年．数值模拟显示能够稳定存在于小行星主带上的单个天体的质量上限其量级为10~(25)kg．模拟同时还显示在某些情况下,假想行星与木星之间的低阶共振可以增强系统的稳定性．     

近地小行星(10302) 1989 ML和(4660) Nereus的轨道特征及演化分析

近地小行星(10302) 1989 ML和(4660) Nereus作为下一代深空探测的候选目标一直备受关注. 在考虑太阳系主要天体的动力学背景下, 通过计算最大Lyapunov指数(MLE)及MEGNO (Mean Exponential Growth factor of Nearby Orbits)指数讨论它们的稳定性. 同时, 对每个小行星, 在其观测误差范围内按多元正态分布各选取1000个克隆粒子, 通过统计分析显示这两个小行星在10万年内可能的运动范围, 给出半长径-偏心率空间中的出现次数分布图, 并统计小行星与地球或其他大行星之间的密近交汇及碰撞的概率. 此外还对这两个小行星的标称轨道进行长期共振、Kozai共振及平运动共振的动力学分析. 综上得出结论, 1989 ML处在平运动共振主导的区域, 发生密近交汇的概率较小, 从而其轨道相对较稳定; 而Nereus处在地球的密近交汇区域, 轨道极不稳定.     

活动小行星311P/PANSTARRS的动力学lk 特性分析

311P/PANSTARRS是一颗活动小行星, 具有小行星和彗星的双重特征, 是中国``天问二号''的探测目标之一. 311P/PANSTARRS直径较小, 约为400 m, 非引力效应可能会对其长期动力学演化产生较大的影响. 通过假定不同表面组分, 研究了Yarkovsky效应对311P/PANSTARRS轨道演化的影响, 讨论了密近交汇、 非破坏性碰撞和YORP (Yarkovsky-O''Keefe-Radzievskii-Paddack)效应等非引力效应, 计算了小行星与大行星密近交汇及碰撞概率, 估计了311P/PANSTARRS达到自转周期分裂极限的时标. 模拟结果显示与纯引力模型相比, Yarkovsky效应可能会加快311P/PANSTARRS离开当前共振区域, 大约在10Myr以后311P/PANSTARRS会离开当前所在共振带, 在表面覆盖风化层的情况下有机会通过v6长期共振成为越火小行星; 在考虑YORP效应的情况下, 311P/PANSTARRS在2 Myr时标内可达到自转周期分裂极限; 在考虑Yarkovsky效应及YORP效应等因素的情况下, 311P/PANSTARRS在10 Myr时标内仍可保持其动力学稳定性, 且YORP效应不会显著影响其半长径偏移量.     

小行星(360)Carlova自转参数的测定

小行星自转参数的资料不仅可以为小行星碰撞演化提供数据,还可以为太阳系的演化研究提供依据．利用云南天文台1米望远镜对主带碳类小行星(360)Carlova进行了新的CCD测光观测,结合前人的测光资料,利用Epoch-方法对(360)的自转参数进行了反演计算,得到该小行星自转的恒星周期为0．25780417±0．00000003天,自转轴的黄道坐标为(95°±3,°40°±1°)．新的结果与前人的结果相比较为一致,其精度稍高于以前的估算结果．     

近地小行星轨道演化的数值研究与辛算法有效性的探讨

本文采用改进的显式辛算法（symplecticalgorithm）和嵌套的RKF7（8）积分器对43颗已命名（或编号）的近地小行星的轨道演化进行数值研究．在力学模型上,除考虑各大行星的引力振动外,还增加了后牛顿效应,而在算法上则着重探索辛算法在近地小行星轨道演化研究中的应用前景,特别是当小行星与某一大行星靠近时辛算法的有效性．本文的结果可为了解近地小行星的轨道演化状况和对它们进行监测提供可靠的信息．     

皖小行星轨道演化的研究现状

近地小行星由于地球的特殊关系为世人所瞩目,对其研究始于５０年代,近年来已成为太阳系动力学中的一个热门课题。全面地介绍了近年来关于近地小行星的研究状况,包括对近地小行星轨道演化的研究的方法和主要结果。     

使用体积离散方法计算不规则小天体表面重力场

在小行星探测任务中,航天器轨道设计需要充分考虑到小行星的非球形引力场的影响.太阳系中大部分小行星具有形状不规则、密度不均匀的特点,因此,在没有绕飞轨道数据的情况下,精确计算其引力场非常困难.利用不规则小行星的多面体模型,采用体积离散方法通过直接积分计算小行星引力场球谐系数和表面重力场分布情况.将该方法与多面体方法进行了比较,并以(433)Eros为例,通过该方法计算得到的结果与NEAR(Near-Earth Asteroid Rendezvous)探测器的轨道数据反演结果比较,C20项误差不超过2%,使用该方法对我国小行星探测任务拟探测的(1996)FG3小行星的重力场进行了计算.以嫦娥二号探测器飞越的(4179)Toutatis小行星为例,结合相应的雷达观测数据提供的小行星形状模型,计算其表面引力势情况,为通过飞越任务获取的光学图像分析其表壤的分布、流向等提供了相应的理论依据.该方法适用于密度不均匀天体,可为小行星探测任务轨道设计和着陆提供可靠的小行星引力场数据.     

近地小行星轨道演化的研究

主要阐述近年来在近地小行星轨道演化研究工作中所获得的一些基本结果，即合理的力学模型和相应的有效算法，并以实际预报算例（近地小行星与地球的交会状态）与有关权威性的结果作了比较，证实这些研究结果确实是可信的。在给出的力学模型中，考虑了所有可能影响近地小行星运动的力学因素，包括各大天体和较大的主带小行星的引力作用、有关天体的扁率影响以及源于太阳引力的后牛顿效应。而在计算方法中，合理地处理了变步长问题和月球位置量这种相对而言的快变化问题，使得数值求解一个高维方程组时，对各天体而言，可采用同一步长进行 积分，避免了求解过程中的复杂性。     

The evolution of bodies orbiting in the trans-Neptunian region on to intermediate-type orbits

We investigate the dynamical evolution of 210 hypothetical massless bodies initially situated between 10 and 30 au from the Sun in order to determine the general characteristics of the evolved system. This is of particular relevance to the understanding of the origin of Edgeworth–Kuiper belt objects on scattered intermediate orbits, such as 1996 TL ₆₆, which have high eccentricity and semimajor axis but nevertheless have perihelion in the region between 30 and 50 au from the Sun.     

Accumulation and migration of the bodies from the zones of giant planets

Within the model of solid-body accumulation of planets (or their nuclei) the accumulation and migration of bodies from the feeding zones of the giant planets are investigated. The investigation is based on results of computer simulation of evolving disks which initially consisted of hundreds of particles moving about the Sun and coagulating under collisions. In some models the disks initially consisted of identical bodies. In other models they included also almost-formed planets. The computer simulation results as well as analytical investigations of the disk evolution depending on the number of particles in the disk allowed some estimates and conclusions on the accumulation process when the number of initial bodies was great (~ 10⁶–10¹²). In this paper the characteristics of an initial protoplanetary circumsolar cloud, the body migration in the forming solar system, the planet orbit evolution, the formation of the beyond-Neptune belt and asteroid belts between the giant planet orbits are considered. The results obtained confirm many analytical estimates earlier made by V. S. Safronov and his colleagues.     

On the capture of the Moon

This paper studies the possibility of lunar capture depending on variations of the solar mass under certain well specified conditions and assumptions regarding the behaviour of the three-body dynamical system formed by the Sun, Earth and Moon. It is found that a large amount of decrease in the solar mass (approximately 37%) would be required to allow capture if the model of the planar restricted problem of three bodies is assumed, if the masses of the Earth and Moon did not change and if the angular momentum of the Sun-Earth system did not change. Such large mass-changes of the Sun can not be associated with radiation mass losses only with catastrophic events, such as stellar close approaches.     

The dynamics of velocity fluctuations in the solar wind – I. Coronal mass ejections

In this paper we present a simple, analytic model for the dynamical evolution of supersonic velocity fluctuations at the base of the ambient solar wind. These fluctuations result in the formation of dense working surfaces that travel down the wind. It is shown how the initial parameters of the fluctuations (velocity, density and duration) are related to the characteristics of the working surfaces far from the Sun (for instance at the Earth). We apply the model to the evolution of the coronal mass ejections in the IP medium, finding that the model is in good agreement with satellite observations of these phenomena, thus providing physical insight into their dynamical evolution. Our model may contribute to future 'space weather forecasting' on the Earth, based on detailed satellite monitoring of the solar corona.     

Orbital dispersion of comet Encke's meteoroids

The orbital evolution of model meteoroids ejected from the comet Encke has been investigated. The particles abandon the mother body with velocities 20 and 40 ms^-1 perihelion within the interval of the past 10,000 years. Their 10,000 years old osculating orbits were numerically integrated forward, using a dynamical model of the solar system consisting of all planets. Forces from solar electromagnetic and corpuscular radiation effecting the particles are considered, too. Orbital dispersions of the model meteoroids are presented. The importance of nongravitational forces for a long-term orbital evolution of meteoroid streams is shown.     

Dynamical behaviour of the primitive asteroid belt

In this paper we consider the dynamical evolution and orbital stability of objects in the asteroid belt. A simple physical model, including full gravitational perturbations from both giant planets, is used to compute the dynamical evolution of 1000 test particles simulating the primitive asteroids. The criterion of planet crossing (or close approach in the case of resonant objects) is used to reject particles from the simulation. 44 per cent of the particles survived for the whole time-span covered by the numerical integration (∼10⁹ yr).
The 4:1, 3:1 and to a lesser extent the 2:1 Kirkwood gaps are formed in ∼10⁷ yr of evolution, representing direct numerical evidence about their gravitational origin.
We found that the rms eccentricity and inclination of the sample experience a fast increase during the first 10⁶ yr. The final rms eccentricity is 0.11, ∼60 per cent smaller than the present rms eccentricity (0.17). Nevertheless, the gravitational action of the giant planets suffices to prevent the formation of large objects, allowing catastrophic collisions and the subsequent depletion of material from this zone of the Solar system. The excited eccentricity by Jupiter and Saturn may favour mutual encounters and the further increase of the relative velocities up to their present values.     

Change in the orbital period of a binary system due to dynamical tides for main-sequence stars

We investigate the change in the orbital period of a binary system due to dynamical tides by taking into account the evolution of a main-sequence star. Three stars with masses of one, one and a half, and two solar masses are considered. A star of one solar mass at lifetimes t = 4.57 × 10⁹ yr closely corresponds to our Sun. We show that a planet of one Jupiter mass revolving around a star of one solar mass will fall onto the star in the main-sequence lifetime of the star due to dynamical tides if the initial orbital period of the planet is less than P _orb ≈ 2.8 days. Planets of one Jupiter mass with an orbital period P _orb ≈ 2 days or shorter will fall onto a star of one and a half and two solar masses in the mainsequence lifetime of the star.     

Orbital Evolution of Dust Particles in the Sublimation Zone near the Sun

We have performed the calculations of the orbital evolution of dust particles from volcanic glass (p-obsidian), basalt, astrosilicate, olivine, and pyroxene in the sublimation zone near the Sun. The sublimation (evaporation) rate is determined by the temperature of dust particles depending on their radius, material, and distance to the Sun. All practically important parameters that characterize the interaction of spherical dust particles with the radiation are calculated using the Mie theory. The influence of radiation and solar wind pressure, as well as the Poynting–Robertson drag force effects on the dust dynamics, are also taken into account. According to the observations (Shestakova and Demchenko, 2016), the boundary of the dust-free zone is 7.0–7.6 solar radii for standard particles of the zodiacal cloud and 9.1–9.2 solar radii for cometary particles. The closest agreement is obtained for basalt particles and certain kinds of olivine, pyroxene, and volcanic glass.     

Galactic kinematics derived from classical cepheids

On the basis of radial velocity and Hipparcos proper motion data, we have analyzed the galactic kinematics of classical Cepheids. Using the 3-D Ogorodnikov-Milne model we have determined the rotational velocity of the Galaxy to be V₀ = 240.5 ± 10.2 km/s, on assuming a glactocentric distance of the Sun of R₀ = 8.5 kpc. The results clearly indicate a contracting motion in the solar neighbourhood of (∂V_θ∂θ)/R = −2.60 ± 1.07 km s⁻¹ kpc⁻¹, along the direction of galactic rotation. Possible reason for this motion is discussed. The solar motion found here is S = 18.78 ± 0.86 km/s in the direction l = 54.4° ± 2.9° and b = +26.6° ± 2.6°.     

Radiation Pressure and the Poynting-Robertson Effect for Fluffy Dust Particles

A correct understanding of the dynamical effect of solar radiation exerted on fluffy dust particles can be achieved with assistance of a light scattering theory as well as the equation of motion. We reformulate the equation of motion so that the radiation pressure and the Poynting-Robertson effect on fluffy grains are given in both radial and nonradial directions from the center of the Sun. This allows numerical estimates of these radiation forces on fluffy dust aggregates in the framework of the discrete dipole approximation, in which the first term of the scattering coefficients in Mie theory determines the polarizability of homogeneous spheres forming the aggregates.The nonsphericity in shape turns out to play a key role in the dynamical evolution of dust particles, while its consequence depends on the rotation rate and axis of the grains. Unless a fluffy dust particle rapidly revolves on its randomly oriented axis, the nonradial radiation forces may prevent, apart from the orbital eccentricity and semimajor axis, the orbital inclination of the particle from being preserved in orbit around the Sun. However, a change in the inclination is most probably controlled by the Lorentz force as a consequence of the interaction between electric charges on the grains and the solar magnetic field. Although rapidly and randomly rotating grains spiral into the Sun under the Poynting-Robertson effect in spite of their shapes and structures, fluffy grains drift inward on time scales longer at submicrometer sizes and shorter at much larger sizes than spherical grains of the same sizes. Numerical calculations reveal that the dynamical lifetimes of fluffy particles are determined by the material composition of the grains rather than by their morphological structures and sizes. The Poynting-Robertson effect alone is nevertheless insufficient for giving a satisfactory estimate of lifetimes for fluffy dust grains since their large ratios of cross section to mass would reduce the lifetimes by enhancing the collisional probabilities. We also show that the radiation pressure on a dust particle varies with the orbital velocity of the particle but that this effect is negligibly small for dust grains in the Solar System.