Optimal design of near-Earth asteroid sample-return trajectories in the Sun–Earth–Moon system

In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun,Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-km-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition.In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth–Moon system,and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.     

小行星撞击地球的超高速问题

小行星撞击地球是人类生存面临的潜在威胁之一.在小行星进入地球大气与撞击地球表面过程中,存在烧蚀、解体、空中爆炸、火球、撞击成坑、反溅碎片云、地震以及海啸等一系列复杂的物理化学和力学现象.本文梳理和归纳了与这些现象相关的超高速空气动力学问题和超高速碰撞动力学问题.小行星进入地球大气的超高速空气动力学问题有:极高速($V = 12 ~ 20$km/s)进入条件下的气动力与轨迹,极高速进入条件下的小行星气动加热与烧蚀机理,极高速气动加热条件下的小行星结构传热与热响应,极高速进入条件下的高温气体效应,小行星进入过程的物理特征.小行星撞击地球的超高速碰撞动力学问题有:陆地撞击成坑与反溅碎片云,海洋撞击与海啸,撞击过程的地震效应.由于小行星撞击地球与超高速飞行器的再入过程在速度、材料和结构上存在较大差异,针对这些超高速问题,现有的研究手段在地面试验和数值计算两方面都存在不足.最后,从小行星进入地球大气的弹道方程、质量损失方程、解体判据和解体模型等出发,初步建立了小行星进入与撞击效应分析评估模型,并对Chelyabinsk和Tunguska两次流星事件进行了分析,重构了进入与爆炸解体过程,评估了空爆火球在地面所导致的超压和热辐射损伤.      

碎石堆小行星的散体动力学建模与仿真方法综述

探测小行星将是未来几十年内航天界的研究热点. 现有资料表明小行星多为疏松多孔的碎石堆结构,易受探测活动的影响而破碎瓦解,因此对其探测必须先进行动力学建模,研究探测活动与小行星结构的相互作用,确保探测任务顺利执行. 在中国即将开展小行星探测任务的背景下,调研分析了散体动力学的研究和发展情况;并根据国内外的相关研究,对目前碎石堆小行星动力学模型与数值模拟方法的研究进行了综述;最后,结合小行星探测的应用背景,总结了小行星散体动力学模型中需解决的关键问题.      

基于星历匹配法的载人小行星探测轨迹优化问题求解

对基于星历匹配法的载人小行星探测轨迹优化问题解法进行了研究. 提出星历匹配法的概念,利用其求出最优发射窗口初值与候选最优探测序列,然后利用遗传算法对特定探测序列的时间节点等参数进行优化,最后利用基于庞德里亚金极大值原理的同伦法进行小推力转化以求得最终探测轨道及其推力控制律. 结果显示星历匹配法可以快速准确地求出最优发射窗口初值与候选探测序列,这大大提高了载人小行星探测等多目标交会探测问题的求解效率.     

Near-Earth asteroid flyby trajectories from the Sun-Earth L2 for Chang’e-2’s extended flight

Driven by curiosity about possible flight options for the Chang'e-2 spacecraft after it remains at the Sun-Earth L2 point, effective approaches were developed for designing preliminary fuel-optimal near-Earth asteroid flyby trajectories. The approaches include the use of modified unstable manifolds, grid search of the manifolds' parameters, and a two-impulse maneuver for orbital phase matching and z-axis bias change, and are demonstrated to be effective in asteroid target screening and trajectory optimization. Asteroid flybys are expected to be within a distance of 2×107 km from the Earth owing to the constrained Earth-spacecraft communication range. In this case, the spacecraft's orbital motion is significantly affected by the gravities of both the Sun and the Earth, and therefore, the concept of the "heliocentric oscillating-Kepler orbit" is proposed, because the classical orbital elements of the flyby trajectories referenced in the heliocentric inertial frame oscillate significantly with respect to time. The analysis and results presented in this study show that, among the asteroids whose orbits are the most accurately predicted, "Toutatis", "2005 NZ6", or "2010 CL19" might be encountered by Chang'e-2 in late 2012 or 2013 with total impulses less than 100m/s.     

小行星进入与撞击效应评估模型敏感性研究

近地小行星对地球的撞击是人类生存和发展面临的潜在威胁之一.当前小行星进入与撞击效应评估模型输入参数不确定度大, 给模型的使用带来困扰,也较大地影响了危害评估结果. 本文分析了输入参数的取值范围,以范围中概率最大或文献的推荐值作为敏感性研究的基准值,利用所发展的小行星进入与撞击效应分析评估软件AICA, 通过改变一个或多个输入参数, 研究能量沉积、空爆高度、4 psi (1 psi = 6.89 kPa)超压损伤半径和3级烧伤半径等模型输出参数对输入参数的敏感性.对于直径60~300 m、进入速度12~40 km/s的石质小行星, 本文的计算分析指出:随着尺寸的增大、进入速度的减小、烧蚀系数的减小、初次解体强度的增大或者碎片云质量分数的增大,小行星的空爆高度总体上减小; 小行星及碎片阻力系数、强度指数对空爆高度和地面损伤范围影响较小;超压损伤半径和热辐射损伤半径总体上随着小行星尺寸和进入速度的增大而增大;碎片云质量分数小于50%时, 能量沉积及地面损伤半径评估结果会出现波动,较大的碎片云质量分数基准值(如80%)能够代表大多数进入情况;流明效率仅影响热辐射损伤范围; 3级烧伤半径小于4 psi超压损伤半径.      

THE MYSTERIES OF RETROGRADE ASTEROIDS

首颗与木星成逆行$1:1$共振的小行星——2015 BZ509的发现,点燃了公众对于逆行小行星的好奇心。本文简要介绍太阳系内鲜为人知的逆行小行星及其起源问题,并对与2015 BZ509相关的逆行共振问题提供通俗易懂的讲解。     

Low-thrust trajectory optimization for multiple target bodies tour mission

Spacecraft science missions to planets or asteroids have historically visited only one or several celestial bodies per mission. The research goal of this paper is to create a trajectory design algorithm that generates trajectory allowing a spacecraft to visit a significant number of asteroids during a single mission. For the problem of global trajectory optimization, even with recent advances in low-thrust trajectory optimization, a full enumeration of this problem is not possible. This work presents an algorithm to traverse the searching space in a practical fashion and generate solutions. The flight sequence is determined in ballistic scenario, and a differential evolution method is used with constructing a three-impulse transfer problem, then the local optimization is implemented with low-thrust propulsion on the basis of the solutions of impulsive trajectories. The proposed method enables trajectory design for multiple asteroids tour by using available low thrust propulsion technology within fuel and time duration constraints.     

不规则小行星引力场内的飞行动力学

小行星探测是当前深空探测的主要方向之一,具有重要的科学意义.绝大多数小行星引力场极不规则,探测器在小行星附近运动形态复杂多样.由于同时受到中心引力、快速自旋的不规则形状摄动力、以及光压摄动等作用,探测器容易与小行星发生碰撞或逃逸.概述小行星研究现状和不规则引力场建模方法.重点介绍不规则引力场内动力学特性,包括引力平衡点、局部流形、自然周期轨道和悬停探测轨道等,尝试提出新的研究方向.     

Asteroid debris: Temporary capture and escape orbits

We investigate the dynamical behaviour of debris ejected from the surface of an asteroid, due to a generic – natural or artificial – surface process. We make an extensive statistical study of the dynamics of particles flowing from the asteroid. We observe different behaviours: particles which fall again on the asteroid surface, or rather escape from its gravitational field or are temporary trapped in orbit around the asteroid. The tests are made by varying different parameters, like the size of the asteroid, its eccentricity, the angular velocity of the asteroid, the area-to-mass ratio of the debris.We also extend the study to the case of a sample of binary asteroids with a mass ratio equal to 10⁻³; we vary the distance of the moonlet from the asteroid, to see its effect on the debris dynamics.Our simulations aim to identify regions where the debris can temporarily orbit around the asteroid or rather escape from it or fall back on the surface. These results give an important information on where a spacecraft could be safely stay after the end of the process which has produced the debris.     

A method for classifying orbits near asteroids

A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near aster- oids are very complex. According to the variation in orbit characteristics after being affected by gravitational perturbation during the periapsis passage, orbits near an as- teroid can be classified into 9 categories： （1） surrounding- to-surrounding, （2） surrounding-to-surface, （3） surrounding- to-infinity, （4） infinity-to-infinity, （5） infinity-to-surface, （6） infinity-to-surrounding, （7） surface-to-surface, （8） surface- to-surrounding, and （9） surface-to- infinity. Assume that the orbital elements are constant near the periapsis, the gravitation potential is expanded into a harmonic series. Then, the influence of the gravitational perturbation on the orbit is studied analytically. The styles of orbits are dependent on the argument of periapsis, the periapsis radius, and the periapsis velocity. Given the argument of periapsis, the orbital energy before and after perturbation can be derived according to the periapsis radius and the periapsis velocity. Simulations have been performed for orbits in the gravitational field of 216 Kleopatra. The numerical results are well consistent with analytic predictions.     

双小行星探测轨道动力学研究进展

双小行星系统由在万有引力作用下彼此环绕的两颗小行星组成, 对研究太阳系起源、行星系统演化和行星防御都具有重要的价值, 近年来成为行星科学和航天动力学研究的热门对象, 对双小行星系统的原位探测也即将迎来热潮. 双小行星系统的独特构型和附近的复杂动力学环境为探测器轨道动力学和任务设计带来了全新的挑战, 为应对这些挑战所进行的研究也推动了轨道动力学基础理论的发展. 本文对双小行星探测轨道动力学的研究进展进行综述, 首先介绍了双小行星研究和探测的背景及意义, 简要阐述了双小行星系统形成理论及其附近轨道动力学的研究概况. 其次, 介绍了双小行星系统不规则引力场和相互引力势的建模方法, 进而展示了双星的姿态轨道耦合动力学, 即完全二体问题, 包括双星相对运动的平衡构型和稳定性. 接着, 介绍了描述双星附近探测器轨道运动的限制性完全三体问题的动力学模型, 以及该模型下的平动点、平动点周期轨道、大范围周期轨道、转移轨道和轨道维持等方面的研究进展. 第四部分综述了环绕双小行星系统单颗星的受摄二体问题, 以轨道摄动理论和行星系统中受摄二体问题的研究现状为背景, 介绍了环绕双小行星系统主星的半解析轨道动力学建模与轨道稳定性分析. 之后, 介绍了目前面向探测任务需求和考虑实际约束的轨道动力学研究和轨道设计. 最后, 基于目前研究进展, 分析了面临的若干问题, 对未来双小行星探测轨道动力学及相关技术的发展进行了讨论和展望.      

Design of low-energy transfer from lunar orbit to asteroid in the Sun-Earth-Moon system

Asteroid exploration trajectories which start from a lunar orbit are investigated in this work.It is assumed that the probe departs from lunar orbit and returns to the vicinity of Earth,then escapes from the Earth by performing a perigee maneuver.A low-energy transfer in Sun-EarthMoon system is adopted.First,the feasible region of lowenergy transfer from lunar orbit to perigee within 5 000 km height above the Earth surface in Sun-Earth-Moon system is calculated and analyzed.Three transfer types are found,i.e.,large maneuver and fast transfers,small maneuver and fast transfers,and disordered and slow transfers.Most of feasibility trajectories belong to the first two types.Then,the lowenergy trajectory leg from lunar orbit to perigee and a heliocentric trajectory leg from perigee to asteroid are patched by a perigee maneuver.The optimal full-transfer trajectory is obtained by exploiting the differential evolution algorithm.Finally,taking 4179 Toutatis asteroid as the target,some low-energy transfer trajectories are obtained and analyzed.     

Forced resonance orbit analysis of binary asteroid system with consideration of solar radiation pressure

The solar radiation pressure is one of the major perturbations to orbits in the study of binary asteroid system, since asteroids have relatively weak gravity fields. In this paper, based on the idea of treating the solar radiation pressure as periodic external excitation, one novel family of orbits due to primary resonance and another novel family of orbits due to both primary resonance and internal resonance have been found by the classical perturbation method. The two types of steady-state orbits due to external resonance with different area-to-mass ratios have been determined and discussed by the frequency–response equations analytically. Four binary asteroid systems, 283 Emma-S/2003 (283) 1, 22 Kalliope-Linus, 2006 Polonskaya-S/2005 (2006) 1 and 4029 Bridges have been taken as examples to show the validity of the proposed mechanism in the explanation of orbits formation due to resonance. The multiple shooting method is applied to obtain the resonance orbits after numerical iterations.

     

HOVERING ORBITS DESIGN FOR PERTURBED ASTEROIDS WITH PARAMETRIC EXCITATION RESONANCE 1)

本文将太阳引力摄动视为受摄不规则小行星系统的组成部分,借鉴非线性振动理论中参数激励共振的概念,创新性地设计了不规则小行星平衡点附近稳定的悬停观测轨道.为了同时考虑不规则小行星引力和太阳引力, 本文采用受摄粒杆模型描述系统.通过对未扰系统平衡点以及固有频率的分析, 给出系统存在参激共振轨道的条件.再以第二类参激主共振和1:3内共振为例,采用多尺度方法求得参数激励共振轨道的稳态解, 并对稳态解的稳定性进行判断.通过受摄小行星系统的幅频响应曲线以及力频响应曲线分析了系统的非线性特性以及参数激励效应.此外, 对内共振引起的长短周期能量转移现象进行了分析.本文的研究成果可以拓展现有小行星系统周期轨道族设计方法.     

On the nonlinear stability of relative equilibria of the full spacecraft dynamics around an asteroid

The full dynamics of a spacecraft around an asteroid, in which the gravitational orbit–attitude coupling is considered, has been shown to be of great value and interest. Nonlinear stability of the relative equilibria of the full dynamics of a rigid spacecraft around a uniformly rotating asteroid is studied with the method of geometric mechanics. The non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are given in the differential geometric method. A classical kind of relative equilibria of the spacecraft is determined from a global point of view, at which the mass center of the spacecraft is on a stationary orbit, and the attitude is constant with respect to the asteroid. The conditions of nonlinear stability of the relative equilibria are obtained with the energy-Casimir method through the semi-positive definiteness of the projected Hessian matrix of the variational Lagrangian. Finally, example asteroids with a wide range of parameters are considered, and the nonlinear stability criterion is calculated. However, it is found that the nonlinear stability condition cannot be satisfied by spacecraft with any mass distribution parameters. The nonlinear stability condition by us is only the sufficient condition, but not the necessary condition, for the nonlinear stability. It means that the energy-Casimir method cannot provide any information about nonlinear stability of the relative equilibria, and more powerful tools, which are the analogues of the Arnold’s theorem in the canonical Hamiltonian system with two degrees of freedom, are needed for a further investigation.     

基于参激共振的受摄小行星悬停轨道设计方法

本文将太阳引力摄动视为受摄不规则小行星系统的组成部分,借鉴非线性振动理论中参数激励共振的概念,创新性地设计了不规则小行星平衡点附近稳定的悬停观测轨道.为了同时考虑不规则小行星引力和太阳引力, 本文采用受摄粒杆模型描述系统.通过对未扰系统平衡点以及固有频率的分析, 给出系统存在参激共振轨道的条件.再以第二类参激主共振和1:3内共振为例,采用多尺度方法求得参数激励共振轨道的稳态解, 并对稳态解的稳定性进行判断.通过受摄小行星系统的幅频响应曲线以及力频响应曲线分析了系统的非线性特性以及参数激励效应.此外, 对内共振引起的长短周期能量转移现象进行了分析.本文的研究成果可以拓展现有小行星系统周期轨道族设计方法.      

Routing the asteroid surface vehicle with detailed mechanics

The motion of a surface vehicle on/above an irregular object is inv.estigated for a potential interest in the insitu explorations to asteroids of the solar system. A global valid numeric method, including detailed gravity and geo- morphology, is developed to mimic the behaviors of the test particles governed by the orbital equations and surface cou- pling effects. A general discussion on the surface mechanical environment of a specified asteroid, 1620 Geographos, is presented to make a global evaluation of the surface vehicle＇s working conditions. We show the connections between the natural trajectories near the ground and differential features of the asteroid surface, which describes both the good and bad of typical terrains from the viewpoint of vehicles＇ dynamic performances. Monte Carlo simulations are performed to take a further look at the trajectories of particles initializing near the surface. The simulations reveal consistent conclusions with the analysis, i.e., the open- field flat ground and slightly concave basins/valleys are the best choices for the vehicles＇ dynamical security. The dependence of decending trajectories on the releasing height is studied as an application; the results show that the pole direction （where the centrifugal force is zero） is the most stable direction in which the shift of a natural trajectory will be well limited after landing. We present this work as an example for pre-analysis that provides guidance to engineering design of the exploration site and routing the surface vehicles.     

ARCJET ABLATION EXPERIMENT TO SIMULATE THE CHELYABINSK ASTEROID ENTRY 1)

烧蚀是小行星极高速进入地球大气层后最重要的现象之一,在很大程度上决定了小行星的质量/尺寸变化、飞行轨迹、甚至光辐射特性. 为观测小行星材料在超高速高温流场中的烧蚀现象,在电弧加热器上开展了模拟Chelyabinsk小行星事件典型弹道状态(速度约5.6 km/s,高度17 km,流星体直径1 m)的烧蚀实验. 试件为钝头外形,头部半径20 mm,半锥角18$^\circ$. 作为对比,试件分别采用玄武岩和碳钢材料. 成功记录了清晰的烧蚀动态过程,观察到两种材料试件表面的熔融损失流动、以及玄武岩试件的蒸发喷射和崩裂剥落等现象,全程测得烧蚀气体发射光谱、试件实时外形变化、表面热图变化等数据. 分析结果显示了两种材料明显不同的烧蚀现象和质量损失机制：碳钢在高温气流冲击作用下溅射成大量微小液滴,跟随气流高速流失;玄武岩质量损失以熔融物剪切流动为主,并伴随少量块状剥落及蒸发喷射. 烧蚀时间为4 s,玄武岩和碳钢的质量损失及驻点后退量分别为37.9 g,72.7 g以及7.3 mm,13.1 mm,估算玄武岩材料的有效烧蚀焓约为2.6 MJ/kg,两种材料的烧蚀光谱测量组分与电镜能谱扫描结果吻合.     

First-round design of the flight scenario for Chang’e-2’s extended mission:take off from lunar orbit

Chang'e-2, Chinese second lunar probe, was inserted into a 100 km altitude low lunar orbit on October 9th, 2010, its purpose is to continuously photograph the lunar surface and possibly chosen landing sites for future lunar missions. The probe will still carry considerable amount of propellant after completing all prescribed tasks in about six months. After the successful launch of Chang'e-2, we began designing the probe's subsequent flight scenario, considering a total impulse of 1 100 m/s for takeoff from low lunar orbit and a maximum 3×10 6 km distance for Earth-probe telecommunication. Our first-round effort proposed a preliminary flight scenario that involves consecutive arrivals at the halo orbits around the Earth-Moon L1/L2 and Sun-Earth L1/L2 points, near-Earth asteroid flyby, Earth return, and lunar im- pact. The designed solution of Chang'e-2's subsequent flight scenario is a multi-segment flight trajectory that serves as a reference for making the final decision on Chang'e-2's extended mission, which is a flight to the Sun-Earth L2 point, and a possible scheme of lunar impact via Earth flyby after remaining at the Sun-Earth L2 point was also presented. The proposed flight trajectory, which possesses acceptable solution accuracy for mission analysis, is a novel design that effectively exploits the invariant manifolds in the circular restricted three-body problem and the patched-manifold-conic method.