定点在日-地(月)系L1点附近的探测器的发射及维持

在限制性三体问题中共线平动点附近的运动虽然是不稳定的,但可以是有条件稳定的,该动力学特征使得一些有特殊目的的探测器只需消耗较少的能量即可定点在这些点附近(如ISEE-3、SOHO).以日-地(月)系的L1点为例,根据其附近的运动特征,探讨定点探测器的发射与轨道控制问题,给出了相应的数值模拟结果,为工程上的实现提供理论依据.     

Global sensitivity to velocity errors at the libration points

The global effects on non-linear stability are investigated at and around the triangular libration points. The model of the circular restricted problem of three bodies is used, considering the Earth and the Moon as the primaries. Areas of the initial conditions in the configuration space leading to stability with zero initial velocity around the equilibrium points are compared to stable areas in the phase space with variable initial velocity and zero initial deviations at the equilibrium points. The behavior of the system concerning errors due to initial conditions in the configuration space is studied for 6 years and the effects of initial velocity errors are considered for 7.73 years.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.     

N-body simulation of two-dimensional stationary stellar distributions: Dissipation of energy and development of the field of velocity

The procedure for the simulation of two-dimensionalN-body configurations described in this paper has been devised to investigate the dissipation of energy and the development of velocity in given sub-regions of stellar systems, especially in the central region of a galaxy. In these simulations massive particles are injected into the given spatial region at a pre-determined constant time rate and at a given distribution of velocity vectors. The mass points are allowed to interact gravitationally and special attention is given to the influence of near-by encounters. After a certain period of time a stationary (equilibrium) situation settles down with a certain distribution of mass points in position and velocity space. Preliminary results obtained so far demonstrate the reliability of this procedure forN-body simulation and for the investigation of the dissipation of energy and of the development of velocity fields. Forthcoming results are hoped to deliver information on the role of three-body encounters in the processes of randomization at work in self-consistent stellar configurations.J. Polcher and W. Wanner also of the Mathematical Physics Group of the IFK took part in many of the discussions concerning the development of this programme.     

卫星与空间碎片碰撞预警的快速算法

提出了一种空间目标与空间碎片碰撞预警的快速计算方法，该算法不仅计算速度快，而且减缓了沿迹误差的影响，延长了预警的有效期，利用该方法，检测一个卫星与5800个空间碎片在一天内是否碰撞，计算时间小于3秒；用2天前的资料，预报计算法国CERISE卫星和空间碎片的碰撞时间误差约为0．02秒，空间位置误差约为500—600米．     

空间目标的圆轨道跟踪法

给出一种空间目标自动跟踪方法：圆轨道跟踪法．该方法在假设目标轨道为圆轨道的前提下计算目标轨道，而后在轨道平面中外推．和位置跟踪法比较表明：该方法不受空间目标视运动不均匀性的影响，有非常高的跟踪精度．即使采用低帧频CCD(1-2HZ)，使用本方法，也能实现对空间目标的高精度跟踪；并能给出目标的多点CCD坐标，实现对空间目标的多点分区采样，提高空间目标的定位精度．     

任意倾角的共轨运动研究

共轨运动天体与摄动天体的半长径相同,处于1:1平运动共振中.太阳系内多个行星的特洛伊天体即为处于蝌蚪形轨道的共轨运动天体,其中一些高轨道倾角特洛伊天体的轨道运动与来源仍未被完全理解.利用一个新发展的适用于处理1:1平运动共振的摄动函数展开方式,对三维空间中的共轨运动进行考察,计算不同初始轨道根数情况下共轨轨道的共振中心、共振宽度,分析轨道类型与初始轨道根数的关系.并将分析方法所得结果与数值方法的结果相互比较验证,得到了广阔初始轨道根数空间内共轨运动的全局图景.     

On the Station-Keeping and Control of the World Space Observatory/Ultraviolet

Collinear libration points play an important role in deep space exploration because of their special positions and dynamical characteristics. Since motion around them is unstable, we need to control the spacecraft if we wish to keep them around such a libration point for a long time. Here we propose a continuous low-thrust control strategy, illustrated with numerical simulations combined with the orbit design and control of the World Space Observatory/UltraViolet (WSO/UV).     

Earth-Based Support for the Titan Saturn System Mission

The Titan Saturn System Mission (TSSM) concept is composed of a TSSM orbiter provided by NASA that would carry two Titan in situ elements provided by ESA: the montgolfière and the probe/lake lander. One overarching goal of TSSM is to explore in situ the atmosphere and surface of Titan. The mission has been prioritized as the second Outer Planets Flagship Mission, the first one being the Europa Jupiter System Mission (EJSM). TSSM would launch around 2023–2025 arriving at Saturn 9 years later followed by a 4-year science mission in the Saturn system. Following delivery of the in situ elements to Titan, the TSSM orbiter would explore the Saturn system via a 2-year tour that includes Enceladus and Titan flybys before entering into a dedicated orbit around Titan. The Titan montgolfière aerial vehicle under consideration will circumnavigate Titan at a latitude of ~20° and at altitudes of ~10 km for a minimum of 6 months. The probe/lake lander will descend through Titan’s atmosphere and land on the liquid surface of Kraken Mare (~75° north latitude). As for any planetary space science mission, and based on the Cassini–Huygens experience, Earth-based observations will be synergistic and enable scientific optimization of the return of such a mission. Some specific examples of how this can be achieved (through VLBI and Doppler tracking, continuous monitoring of atmospheric and surface features, and Direct-to-Earth transmission) are described in this paper.     

Ellipsoidal Harmonic expansions of the gravitational potential: Theory and application

Small bodies of the solar system are now the targets of space exploration. Many of these bodies have elongated, non-spherical shapes, and the usual spherical harmonic expansions of their gravity fields are not well suited for the modelling of spacecraft orbits around these bodies. An elegant remedy is to use ellipsoidal harmonic expansions instead of the usual spherical ones. In this paper, we present their mathematical theory as well as a real application: the simulation of a landing on the surface of a kilometer-sized comet. We show that with an ellipsoidal harmonic expansion up to degree 5, the error on the landing position is at the meter level, while the corresponding error for the spherical harmonic expansion can reach tens of meters.This revised version was published online in October 2005 with corrections to the Cover Date.     

Distance in the space of energetically bounded Keplerian orbits

In this paper we derive an explicit, analytic formula for the geodesic distance between two points in the space of bounded Keplerian orbits in a particular topology. The specific topology we use is that of a cone passing through the direct product of two spheres. The two spheres constitute the configuration manifold for the space of bounded orbits of constant energy. We scale these spheres by a factor equal to the semi-major axis of the orbit, forming a linear cone. This five-dimensional manifold inherits a Riemannian metric, which is induced from the Euclidean metric on \mathbbR⁶{\mathbb{R}^6}, the space in which it is embedded. We derive an explicit formula for the geodesic distance between any two points in this space, each point representing a physical, gravitationally bound Keplerian orbit. Finally we derive an expression for the Riemannian metric that we used in terms of classical orbital elements, which may be thought of as local coordinates on our configuration manifold.     

Periodic orbits in the generalized photogravitational Chermnykh-like problem with power-law profile

The orbits about Lagrangian equilibrium points are important for scientific investigations. Since, a number of space missions have been completed and some are being proposed by various space agencies. In light of this, we consider a more realistic model in which a disk, with power-law density profile, is rotating around the common center of mass of the system. Then, we analyze the periodic motion in the neighborhood of Lagrangian equilibrium points for the value of mass parameter $0<\mu\leq\frac{1}{2}$ . Periodic orbits of the infinitesimal mass in the vicinity of equilibrium are studied analytically and numerically. In spite of the periodic orbits, we have found some other kind of orbits like hyperbolic, asymptotic etc. The effects of radiation factor as well as oblateness coefficients on the motion of infinitesimal mass in the neighborhood of equilibrium points are also examined. The stability criteria of the orbits is examined with the help of Poincaré surfaces of section (PSS) and found that stability regions depend on the Jacobi constant as well as other parameters.     

Non-linear stability around the triangular libration points

The configuration space around the triangular libration points in the Earth-Moon system is partitioned according to the stability of the motion. The regions aroundL ₄ andL ₅ are established where particles placed with zero initial velocity will librate. The complexity of the partitioning is revealed.     

Effects of triaxiality of primaries on oblate infinitesimal in elliptical restricted three body problem

This paper examines the effects of triaxiality of both the primaries on the position and stability of the oblate infinitesimal mass in the neighborhood of triangular equilibrium points in the framework of Elliptical restricted three body problem. We have found the solutions for the locations of triangular equilibrium points. We have investigated the stability of infinitesimal mass around the triangular equilibrium points.It is observed that the infinitesimal motion around triangular equilibrium points are stable under certain condition with respect to triaxiality of primaries. We have applied the method of averaging used by Grebenivok, throughout the analysis of the stability of the infinitesimal mass around the triangular equilibrium points. We have exploited simulation technique using MATLAB 15 to analyze the stability of the system. The critical mass ratio depends on the triaxiality, oblateness, semi- major axis and eccentricity of the elliptical orbits.     

Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem

In this work, the single-mode motions around the collinear and triangular libration points in the circular restricted three-body problem are studied. To describe these motions, we adopt an invariant manifold approach, which states that a suitable pair of independent variables are taken as modal coordinates and the remaining state variables are expressed as polynomial series of them. Based on the invariant manifold approach, the general procedure on constructing polynomial expansions up to a certain order is outlined. Taking the Earth–Moon system as the example dynamical model, we construct the polynomial expansions up to the tenth order for the single-mode motions around collinear libration points, and up to order eight and six for the planar and vertical-periodic motions around triangular libration point, respectively. The application of the polynomial expansions constructed lies in that they can be used to determine the initial states for the single-mode motions around equilibrium points. To check the validity, the accuracy of initial states determined by the polynomial expansions is evaluated.     

Cylindrical isomorphic mapping applied to invariant manifold dynamics for Earth–Moon Missions

Several families of periodic orbits exist in the context of the circular restricted three-body problem. This work studies orbital motion of a spacecraft among these periodic orbits in the Earth–Moon system, using the planar circular restricted three-body problem model. A new cylindrical representation of the spacecraft phase space (i.e., position and velocity) is described, and allows representing periodic orbits and the related invariant manifolds. In the proximity of the libration points, the manifolds form a four-fold surface, if the cylindrical coordinates are employed. Orbits departing from the Earth and transiting toward the Moon correspond to the trajectories located inside this four-fold surface. The isomorphic mapping under consideration is also useful for describing the topology of the invariant manifolds, which exhibit a complex geometrical stretch-and-folding behavior as the associated trajectories reach increasing distances from the libration orbit. Moreover, the cylindrical representation reveals extremely useful for detecting periodic orbits around the primaries and the libration points, as well as the possible existence of heteroclinic connections. These are asymptotic trajectories that are ideally traveled at zero-propellant cost. This circumstance implies the possibility of performing concretely a variety of complex Earth–Moon missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible application of manifold dynamics to defining a suitable, convenient end-of-life strategy for spacecraft placed in any of the unstable orbits. The final disposal orbit is an externally confined trajectory, never approaching the Earth or the Moon, and can be entered by means of a single velocity impulse (of modest magnitude) along the right unstable manifold that emanates from the Lyapunov orbit at \(L_2\) .     

Perturbation of an electrostatic probe by a spacecraft at small speed ratios

The disturbance of an electrostatic probe, by the spacecraft carrying it, in the intermediate altitude regime from about 3000 km to the plasmapause, is discussed. Three kinds of disturbance are studied: loss of symmetry of the probe sheath due to the presence of the spacecraft; creation of potential barriers around the probe; and particle removal, or shadowing, by the spacecraft. The first of these effects is shown to be nonexistent for a spherical probe if it is operated under orbit-limited conditions. Methods are given for estimating the magnitudes of the other two effects in any given situation. The electrostatic probe experiment on the Explorer 31 spacecraft is discussed as an example.     

利用双视角消除太阳矢量磁场观测中的180◦不确定性

随着"环日轨道器"(Solar Orbiter, SO)的在轨运行,太阳磁场观测进入了双视角遥测的时代.对利用太阳磁场的双视角观测改正矢量磁图中存在的横场(垂直于视线方向的磁场分量) 180°不确定性进行了模拟,首先模拟了对解析解得到磁图的双视角观测,然后利用"日震学和磁学成像仪"(Helioseismic and Magnetic Imager, HMI)在不同时间观测到的一个老化黑子的磁图模拟了双视角观测.发现要改正一个磁图中横场方向的180°不确定性,在观测上只需要另外一个平行于视线方向的磁场即纵向磁场观测的协助.利用HMI的磁场观测模拟,估算显示30°的张角能够改正50 Gs磁场中的180°不确定性.更大的张角虽然更有利于更弱磁场的改正,但是考虑到投影效应的不利影响, 30°左右的张角应该是未来空间设备进行多视角观测太阳磁场的最佳张角.     

星载氢钟VLBI观测实验及分析

中国计划于2025年左右建立月球轨道VLBI (Very Long Baseline Interferometer)测站,将会搭载被动型星载氢钟作为时间频率标准.由于是首次在VLBI观测中使用星载氢钟,需要研究和验证其可行性.因此,利用星载氢钟作为频率基准开展了VLBI观测.实验时,分别使用主动型地面氢钟和被动型星载氢钟作为频率基准,利用上海天文台佘山25 m射电望远镜和其他测站对我国火星探测器天问一号进行了交替VLBI观测.数据处理分析结果表明,基于地面氢钟与星载氢钟的VLBI残余群时延标准差均在0.5 ns以内,表明星载氢钟可满足深空探测VLBI测定轨的精度要求,验证了其作为月球VLBI测站频率基准的可行性.     

Periodic orbits in the Chermnykh-like restricted problem of oblate bodies with radiation

In this paper, the periodic orbits around triangular points in the range of linear stability of the restricted three body problem, when the smaller primary and the test particle have the shape of an oblate spheroid and the larger primary is a radiation emitter with the allowance for the gravitational potential from the belt, is studied. It is observed that the orbits around these points are elliptical and have long and short periodic orbits. The period, orientation, eccentricities, the semi-major and semi-minor axis of the elliptic orbits are found. The study includes some numerical examples in the case of the Sun-Earth and Sun-Jupiter systems.