双体小行星系统平衡态与稳定性研究

由于双体小行星独特的运动形式可为行星的演化提供重要线索,因而成为小行星探测中的热点目标。基于双椭球体模型研究了双小行星系统的相对运动、平衡态及稳定性。首先基于双椭球的全二体模型建立了双星系统相对运动的动力学方程;其次利用拉格朗日方程,通过求解系统角动量和能量,建立了双星系统平衡态对应的状态约束;最后给出了通过零速度状态曲面判断双星系统平衡态稳定性的一般性方法,在此基础上分析了小行星物理参数变化对系统平衡态稳定性的影响。研究可为未来双体小行星系统探测任务中的轨道设计与控制提供重要的理论参考。     

双星系统L1点悬停探测控制器设计与仿真

双小行星系统探测具有重要的科学意义,受其复杂动力学环境影响,探测任务极具挑战。利用球谐函数法对双星系统进行引力场建模,求解双星系统平动点,并选取其内部共线平动点L_1点作为双星系统悬停探测目标位置。采用航天探测实际任务中常用的脉冲推力式发动机,设计了一种原理简单、便于工程实现的常值切换bang-bang控制器。以69230Hermes双星系统为例,将Hermes近似为双椭球系统,仿真分析航天器在Hermes双星系统L_1点悬停飞行的控制效果,验证所提控制策略有效性。     

强不规则天体引力场中的动力学研究进展

小行星探测与彗星探测是深空探测的重要方面。一般来说,小行星和彗星因质量都不足以使得万有引力克服应力达到流体静力学平衡,而具有强不规则的外形。研究强不规则天体引力场中的动力学行为及其内在机制,是探测器被不规则天体捕获并对其形成近距离探测轨道的基础。从引力场模型和动力学行为两个方面综述了强不规则天体引力场中动力学的研究进展,在引力场模型的研究方面介绍了强不规则天体引力场建模的球谐函数摄动展开模型、简单特殊体模型及多面体模型的研究现状,在动力学机制的研究方面介绍了强不规则天体引力场中的周期轨道和拟周期轨道、平衡点、流形、分岔与共振以及混沌运动的研究现状,指出了这些方面研究的重点与难点。分析了强不规则体引力场中动力学的研究趋势。     

基于双椭球模型的双星系统稳定性研究

太阳系中存在着数量众多的双星系统。研究双星系统对于认识小行星的起源和演化有着重要意义。本文以双椭球模型,使用Joshua推导的四阶精度相互势,对双互锁双星系统进行研究。并通过KTC定理证明其稳定性。研究结果验证了卫星和主星存在相对滚转角速度是双互锁系统的一种可能的绕转方式。     

Halo轨道间转移的显式制导方法研究

将显式制导方法应用于地月系统L1平动点Halo轨道间的转移问题,用以克服动力学建模误差.通过等时间间隔计算到达目标点的需要速度,得到当前速度与需要速度的矢量差,称为速度增益,其模即为控制冲量.需要速度通过应用Sukhanov-Prado方法求解三体Lambert问题获得.采用圆限制性三体模型(CR3BP)设计标称轨道和进行制导计算,双圆模型(BCM)作为考虑太阳引力的摄动模型进行仿真.结果表明,所提出的方法针对模型误差简单有效、计算速度较快并且所需能耗小.     

基于引力场不对称性的三体系统轨道自主导航

以月球背面的中继通信为背景,提出了基于三体系统引力场不对称特性的星–星测距自主定轨方案。该方案以环月极轨卫星和地–月L2点Halo轨道卫星组成中继通信网,以实现对月球两极和背面的覆盖。通过采集极轨卫星与Halo轨道卫星的测距信息,结合卡尔曼滤波在日–地–月动力学模型下获得两颗卫星的绝对轨道。数值仿真结果表明:本文方法能将导航的位置精度和速度精度分别提高到百米和厘米/秒量级。该自主导航方法还可以扩展到不规则引力场小天体附近星群运动的自主导航。     

三小行星系统216 Kleopatra引力场中的动力学

主带三小行星系统216 Kleopatra是由主星216 Kleopatra及两个小月亮(moonlet)Alexhelios[S/2008(216)1]和Cleoselene[S/2008(216)2]组成。其中主星216Kleopatra是一个具有强不规则形状如哑铃的连接双星,大小为217km×94km×81km,外小月亮Alexhelios大小约为8.9km,内小月亮大小约为6.9km。其动力学行为具有非常丰富的科学内涵。研究了三小行星系统216Kleopatra自身的动力学机制及其引力场中探测器的运动规律,分析了主星质心固连系中探测器的动力学方程,给出了三小行星引力全多体问题的动力学方程及Jacobi积分,方程考虑了三个小行星的不规则外形、轨道与姿态。发现三小行星系统216Kleopatra主星引力场中一种新的周期轨道族的倍周期分岔。考虑主星的不规则精确外形与引力、两个小月亮的相互作用,研究了该三小行星系统的动力学构形。发现Kleopatra的强不规则几何外形及两个小月亮Alexhelios和Cleoselene的相互作用引起两个小月亮的轨道参数的显著变化。     

月地转移轨道快速设计方法

月地转移轨道设计一般分为初步轨道设计和精确轨道设计.其中,初步轨道设计的准确性是确保后续精确轨道设计收敛的关键.提出了一种基于Lambert算法的月地转移轨道快速设计方法.以出月球影响球的时刻、位置和速度为中间变量,将轨道分为地心段和月心段分别进行计算.将探测器飞出月球影响球至指定再入点的地心段轨道简化为一个Lambert问题进行求解,提出了通过牛顿迭代法求解月地转移轨道Lambert问题的方法,避免了Lambert问题求解时大量的超几何函数和级数计算,提高了计算效率.在月心段轨道的快速计算中,提出了根据探测器出影响球速度矢量、月球停泊轨道倾角和近月点高度计算月心双曲线轨道根数的新方法.通过迭代计算,使得两段轨道在月球影响球处的位置和速度连续,从而获得一条完整的满足两端约束的双二体月地转移轨道.该方法计算速度快,精度相对较高.计算结果可以作为后续精确轨道设计的初值.      

接收模式下加罩天线系统特性的快速电磁仿真

针对接收模式下电大尺寸的天线-天线罩系统电磁特性分析问题,提出了一种全波法和高频法结合的混合算法:积分方程/修正型表面积分+多层快速多极子(IE/MSI+MLFMA)方法.该方法将由高频方法MSI得到的天线罩内场分布作为天线阵列的激励场,再利用基于体-面混合积分方程(VSIE)和MLFMA的快速全波分析方法精确计算天线阵;同时应用球谐函数展开、预处理技术、混合并行等技术进一步改进算法的计算效率.同传统的全波数值法相比,该方法在保证计算精度、满足工程需要的前提下,解决了求解计算时间长、计算效率低的问题,实现了对电大尺寸天线-天线罩系统的快速、高效仿真.      

三维引力辅助机理分析

针对星际探测中的引力辅助技术,通过引入两个参数,将平面椭圆型限制性三体模型拓展到三维椭圆型限制性三体模型.通过逆向与正向积分,得到引力辅助前后飞行器的能量和角动量,据此将引力辅助轨道划分为16种类型.深入讨论了这两个参数对轨道类型、轨道能量和轨道倾角的影响,总结出了相应的变化规律.以地月系统为例,针对不同任务要求,给出了通过月球引力辅助,实现地月系统俘获与逃逸的引力辅助参数的选择区域,并对引力辅助参数进行了优化.     

Orbital stability close to asteroid 624 Hektor using the polyhedral model

We investigate the orbital stability close to the unique L4-point Jupiter binary Trojan asteroid 624 Hektor. The gravitational potential of 624 Hektor is calculated using the polyhedron model with observational data of 2038 faces and 1021 vertexes. Previous studies have presented three different density values for 624 Hektor. The equilibrium points in the gravitational potential of 624 Hektor with different density values have been studied in detail. There are five equilibrium points in the gravitational potential of 624 Hektor no matter the density value. The positions, Jacobian, eigenvalues, topological cases, stability, as well as the Hessian matrix of the equilibrium points are investigated. For the three different density values the number, topological cases, and the stability of the equilibrium points with different density values are the same. However, the positions of the equilibrium points vary with the density value of the asteroid 624 Hektor. The outer equilibrium points move away from the asteroid’s mass center when the density increases, and the inner equilibrium point moves close to the asteroid’s mass center when the density increases. There exist unstable periodic orbits near the surface of 624 Hektor. We calculated an orbit near the primary’s equatorial plane of this binary Trojan asteroid; the results indicate that the orbit remains stable after 28.8375?d.     

地磁场模型简化计算方法

为了实现地磁导航在近地轨道卫星上的应用,需要解决传统的高斯球谐函数递推法在计算地磁场强度时存在方法复杂、计算量大、实时性难以保证等问题.针对上述问题,提出一种用地球磁场估计函数代替球谐函数的地磁场强度计算方法.该方法利用伪地心下的磁偶极子模型代替主磁场模型,通过多项式拟合离线得到高度范围内固定经纬度网格点的伪中心距系数,进而利用插值法和偶极子模型得到任意点的地磁场强度.仿真结果表明,轨道高度为300～500km,经纬度网格间隔为0.5°时,地球磁场估计函数法的导航精度与地球主磁场模型WMM精度一致的同时,降低了计算负担,提高了算法计算效率.      

Modeling irregular small bodies gravity field via extreme learning machines and Bayesian optimization

Close proximity operations around small bodies are extremely challenging due to their uncertain dynamical environment. Autonomous guidance and navigation around small bodies require fast and accurate modeling of the gravitational field for potential on-board computation. In this paper, we investigate a model-based, data-driven approach to compute and predict the gravitational acceleration around irregular small bodies. More specifically, we employ Extreme Learning Machine (ELM) theories to design, train and validate Single-Layer Feedforward Networks (SLFN) capable of learning the relationship between the spacecraft position and the gravitational acceleration. ELM-base neural networks are trained without iterative tuning therefore dramatically reducing the training time. Analysis of performance in constant density models for asteroid 25143 Itokawa and comet 67/P Churyumov-Gerasimenko show that ELM-based SLFN are able learn the desired functional relationship both globally and in selected localized areas near the surface. The latter results in a robust neural algorithm for on-board, real-time calculation of the gravity field needed for guidance and control in close-proximity operations near the asteroid surface.     

On tethered sample and mooring systems near irregular asteroids

A tethered asteroid sample and mooring system is investigated in this paper. In this system the spacecraft is moored to the surface of an irregular asteroid such as 216 Kleopatra by using a rocket-propelled anchor with a cable. The rocket-propelled anchor is a kind of space penetrator, which can inject into asteroids at high speeds generated by its own rocket engine. It can be used to explore the interior structure of asteroids, and it can also be used as a sample collector. When the sampling mission is done, the sample can be pulled back to the spacecraft with the anchor. Using this method, the spacecraft can be kept in a safe region in which it cannot be trapped by the gravitational field of the asteroid. This work is concerned with the dynamics of the tethered system near irregular asteroids. First, a shape model and gravitational field model of irregular asteroids are built. Then, the configuration and the stability of the tethered system are investigated, and the quasi-periodic motion near the equilibrium point of the tethered system is analyzed. Finally, the non-uniform density distribution of the asteroids is considered. The deployment process and the oscillation of the tethered system in the uncertain asteroid gravity field are simulated using the Monte Carlo method. The feasibility of the tethered asteroid sample and mooring system is proved.     

Solar-photon sail hovering orbits about single and binary asteroids

Solar-photon sails can be useful for missions towards and about asteroids. Indeed, for the interplanetary transfer phase, missions to asteroids often require a large variation in inclination and solar-photon sails perform very well for such high energy missions. In the same way, solar-photon sails are also expected to perform well in the phase about the asteroid. This paper studies single and binary asteroids’ hovering regions by using a sailcraft. In order to consider a sailcraft with its own mass and shape, the mutual polyhedral method (usually used to study asteroid dynamics) is used; therefore, the sailcraft is designed by means of tetrahedra. The procedure to obtain the hovering regions about a single asteroid is presented and an accurate analysis of the control variables is carried out. Moreover, control torques required to maintain hovering orbits are obtained by considering the gravitational torques acting on the sailcraft due to the asteroid. In the end, the theory for hovering orbits is extended to binary-asteroid systems and applied to the binary system 1999 KW4.     

An alternative computation of a gravity field model from GOCE

GOCE is the first satellite with a gravitational gradiometer (SGG). This allows to determine a gravity field model with high spatial resolution and high accuracy. Four of the six independent components of the gravitational gradient tensors (GGT) are measured with high accuracy in the so-called measurement band (MB) from 5 to 100 mHz by the GOCE gradiometer. Based on more than 1 year of GOCE measurements, two gravity field models have been derived. Here, we introduce a strategy for spherical harmonic analysis (SHA) from GOCE measurements, with a bandpass filter applied to the SGG data, combined with orbit analysis based on the integral equation approach, and additional constraints (or stabilization) in the polar areas where no observation is available due to the orbit geometry. In addition, we combined the GOCE SGG part with a set of GRACE normal equations. This improves the accuracy of the gravity field in the long-wavelength parts, due to the complementarity of GOCE and GRACE. Comparison with other models and with external data shows that our results are rather close to the GPS-levelling data in well-selected test regions, with an uncertainty of 4–7 cm, for truncation at degree 200.