一种不规则小行星附近周期轨道全局搜索策略

研究不规则小行星附近的自然周期轨道,有助于更好地认识小行星附近的动力学特性。周期轨道的搜索过程需要频繁地进行轨道递推,其中绝大多数的计算时间消耗在不规则小行星附近的引力加速度计算中。为提高加速度计算效率,提出一种不规则小行星引力加速度快速估计方法;在此基础上,通过参数空间内随机化粗略搜索获得周期轨道的初值猜想;利用遗传算法在初值猜想附近区间进行精细搜索,找到周期轨道的初值。通过对不规则小行星433 Eros附近周期轨道的搜索,对其附近不同形状的周期轨道进行了分类,分析周期轨道在小行星附近的分布规律。     

载人小行星探测目标选择与轨道优化设计

针对2020-2040年载人小行星探测任务,研究了探测目标选择与轨道优化设计问题。首先,针对已编目的近地小行星,综合考虑绝对星等、燃料消耗等多方面因素与约束,给出了适合载人探测任务的候选小行星序列;然后,构建了载人小行星探测任务轨道的设计模型,采用参数优化算法对探测轨道进行了设计;进一步,为了获得最优探测轨道,利用主矢量原理对探测轨道进行了优化。该研究可为载人小行星探测任务设计提供有价值的参考。     

空间非合作目标双行轨道根数快速生成算法

针对空间目标TLE拟合过程中可能出现的奇点问题,提出了基于无奇异变换的空间目标双行轨道根数（TLE）生成算法. 为提高观测平台对空间目标状态估计效率,提出带有自适应遗忘因子的非线性最小二乘递推算法,利用最速下降法在线修正遗忘因子,使得估计值有较快的跟踪速度和较小的稳态误差. 仿真结果表明,该TLE生成算法的数据处理速度和轨道预报误差满足要求,可用于低轨目标的天基监视.      

载人小行星探测轨道设计

文章应用Lambert理论对载人小行星探测的轨道进行设计。结合轨道设计的基本条件与假设,建立了基于Lambert问题的轨道模型,并进行了仿真验证,结果证明模型正确有效。采用该模型,以发射窗口在2045年编号为89136的载人探测小行星A为例,给出了轨道设计的结果,同时对不同的故障情况下任务中止轨道及其特性进行了分析,对探测器应急返回能力进行了探讨。     

对空间多目标多次接近的轨道设计

基于单航天器对空间多目标单次接近轨道设计的研究结果, 讨论了单航天器对空间 多目标多次接近的轨道设计问题. 提出了接近指标用于设计能多次接近多个空间目标的航天器轨道;以二体接近轨道为基础, 给出了接近轨道解空间的求取方法; 利用三种轨道调整方法构造了三种复杂度不同的新解并产生算子, 分析了它们的解空间和最优解分布, 采用改进的模拟退火算法求解出最优接近轨道. 仿真实验验证了轨道设计算法的正确性.      

遗传算法在星座多星接近轨道优化中的应用

以三颗非共轨的Walker星座卫星为研究对象, 对航天器无需变轨与其接近的可能性进行研究. 将Lambert方法得到的航天器轨道作为初始轨道, 利用遗传算法对初始轨道进行优化. 对初始轨道在参考时刻位置和速度的改变量进行编码,形成对应的种群. 以航天器与星座卫星之间的最近距离为适应度函数, 通过种群的繁殖得到优化结果. 结合仿真算例, 分析了最小二乘算法和遗传算法在轨道优化中的优劣以及接近过程中轨道摄动的影响. 结果表明, 遗传算法适用于所提出的轨道改进问题. 研究结果可为单航天器无需变轨对星座多星接近问题提供理论依据.      

倾角函数的一个递推公式

在分析计算地球引力场球谐调和项引起的轨道摄动时,需用到倾角函数Ftmp(i)。如果直接应用其分析表达式,则计算量非常大。文中导出一组递推公式,利用这些递推公式可以大大简化计算,极大地减少计算时间。     

小行星附近制导与控制研究综述

由于小行星具有引力场不规则、物理参数不确定性大、表面逃逸速度小等因素,使得小行星附近制导和控制极具挑战性。回顾了小行星探测任务的历史、现状和意义;针对小行星附近制导与控制研究的基础即小行星附近动力学,分析了研究现状;针对悬停、绕飞、转移、着陆等任务形式,详细介绍了轨道制导和控制方法方面的热点问题和研究现状;基于研究现状,列举了部分未来可进一步研究的方向和问题。     

“嫦娥二号”小行星探测试验定轨计算与分析

嫦娥二号于2012-04-15开展对图塔蒂斯小行星的探测试验,至2012-12-13与图塔蒂斯交会,共飞行243 d,这是我国对小行星的首次探测.因为未安装星载导航设备,CE-2 在小行星探测试验的全过程均基于地基USB（Unified S-Band）与甚长基线干涉测量技术（VLBI,Very Long Baseline Interferometry）测量实现导航.对小行星探测期间的定轨计算及精度分析进行了讨论,对我国新建深空站的测量数据进行了分析.针对交会前最后一次轨道机动后,仅有13 d控后数据的现状,提出了快速轨道重建策略.计算结果表明该策略不仅可以有效改进定轨计算精度,还可以实现轨控速度增量的标定.基于重叠弧段的轨道分析比较表明,单独使用USB长弧数据计算可以获得10 km的定轨精度,综合USB与VLBI数据联合定轨,定轨精度可以提高1倍.     

地气光辐射对空间目标成像特性影响分析

为分析地气光辐射对空间目标成像特性的影响，以地球同步轨道(GEO)卫星搭载的可见光成像器为探测平台，利用卫星工具包(STK)设计高椭圆轨道(HEO)及近地轨道(LEO)目标运动场景，根据空间目标、地球、太阳、探测平台之间的位置关系，采用微元法建立空间目标与地气光背景等效星等模型，推导出空间目标信噪比(SNR)计算公式。分析了距离、角度参数变化对不同轨道空间目标、地气光背景等效星等及空间目标信噪比的影响。仿真结果表明:当探测平台距离空间目标较远时，地气光背景等效星等低于空间目标等效星等，地气光辐射比空间目标信号强。当地气光辐射进入和离开空间目标探测视场时，空间目标信噪比最大，该时间段是进行空间目标探测的最佳“观测窗口”。仿真得出的空间目标信噪比值为空间目标探测识别提供了理论计算依据。      

Trajectory optimization of multiple asteroids exploration with asteroid 2010TK7 as main target

In this study, the Earth’s Trojan asteroid 2010 TK₇ is selected as the rendezvous target. The multiple flyby sequence of asteroid exploration was proposed by optimizing the probe’s orbit. Impulsive maneuvers and low-thrust propulsion were used respectively to design the trajectories of the multiple asteroids exploration mission. Under impulsive maneuvers, gravity assist technique was adopted to reduce fuel consumption. First a reference orbit with only 2010 TK₇ as the rendezvous target was designed. Then five asteroids near the reference orbit were selected as candidates. Finally, we obtained a multiple asteroids exploration sequence of three asteroids based on gravity assist technique and genetic algorithm, and an additional velocity impulse of 0.4?km/s was required. In the subsequent section, a sixth-degree inverse polynomial shape-based method is applied to the low-thrust trajectory design of 2010 TK₇, and the exploration sequence under the action of low-thrust propulsion was provided.     

Mapping orbits around the asteroid 2001SN263

The present paper has the goal of mapping orbits, with respect to the perturbations, for a spacecraft traveling around the asteroid 2001SN₂₆₃. This asteroid is a triple system, which center of mass is in an elliptic orbit around the Sun. The perturbations considered in the present model are the ones due to the oblateness of the central body, the gravity field of the two satellite bodies (Beta and Gamma), the Sun, the Moon, the asteroids Vesta, Pallas and Ceres and all the planets of the Solar System. This mapping is important, because it shows the relative importance of each force for a given orbit for the spacecraft, helping to make a decision about which forces need to be included in the model for a given accuracy and nominal orbit. Another important application of this type of mapping is to find orbits that are less perturbed, since it is expected that those orbits have good potential to require a smaller number of station-keeping maneuvers. Simulations under different conditions are made to find those orbits. The main reason to study those trajectories is that, currently, there are several institutions in Brazil studying the possibility to make a mission to send a spacecraft to this asteroid (the so-called ASTER mission), because there are many important scientific studies that can be performed in that system. The results showed that Gamma is the main perturbing body, followed by Beta (10 times smaller) and the group Sun–Mars-oblateness of Alpha, with perturbations 1000 times weaker than the effects of Gamma. The other bodies have perturbations 10⁷ times smaller. The results also showed that circular and polar orbits are less perturbed, when compared to elliptical and equatorial orbits. Regarding the semi-major axis, an internal orbit is the best choice, followed by a larger external orbit. The inclination of the orbit plays an important role, and there are values for the inclination where the perturbations show minimum and maximum values, so it is important to make a good decision on those values.     

On two kinds of intermediate orbits for asteroid explorations

In the paper, two kinds of intermediate orbits for asteroid explorations are proposed. One is around the collinear libration points of the Sun-asteroid restricted three-body problem. The other is around the asteroid itself. The first kind of intermediate orbit is applicable to asteroids with known masses, while the second is suitable for asteroids with unknown or negligible masses. Analytical solutions of these two intermediate orbits in the simplified models are introduced first, and then numerical algorithms are used to refine them to obtain the true orbits in the real force model. At last, the problem of station-keeping is addressed. The linear optimal feedback control law is used, and numerical simulations are made to both kinds of intermediate orbits. The results show that both kinds of orbits are feasible. The cost is reasonable and mainly depends on the initial insertion error.     

Economic assessment of high-thrust and solar-sail propulsion for near-earth asteroid mining

Asteroid mining has the potential to greatly reduce the cost of in-space manufacturing, production of propellant for space transportation and consumables for crewed spacecraft, compared to launching the required resources from the Earth’s deep gravity well. This paper discusses the top-level mission architecture and trajectory design for these resource-return missions, comparing high-thrust trajectories with continuous low-thrust solar-sail trajectories. The paper focuses on maximizing the economic Net Present Value, which takes the time-cost of finance into account and therefore balances the returned resource mass and mission duration. The different propulsion methods are compared in terms of maximum economic return and sets of attainable target asteroids. Results for transporting resources to geostationary orbit show that the orbital parameter hyperspace of suitable target asteroids is considerably larger for solar sails, allowing for more flexibility in selecting potential target asteroids. Also, results show that the Net Present Value that can be realized is larger when employing solar sailing instead of chemical propulsion. In addition, it is demonstrated that a higher Net Present Value can be realized when transporting volatiles to the Lunar Gateway instead of geostationary orbit. The paper provides one more step towards making commercial asteroid mining an economically viable reality by integrating trajectory design, propulsion technology and economic modelling.     

Solar sails for perturbation relief: Application to asteroids

A major cause of spacecraft orbital variation comes from natural perturbations, which, in close proximity of a body, are dominated by its non-spherical nature. For small bodies, such as asteroids, these effects can be considerable, given their uneven (and uncertain) mass distribution. Solar sail technology is proposed to reduce or eliminate the net secular effects of the irregular gravity field on the orbit. Initially, a sensitivity analysis will be carried out on the system which will show high sensitivity to changes in initial conditions. This presents a challenge for optimisation methods which require an initial guess of the solution. As such, the Genetic Algorithm (GA) is proposed as the preferred optimisation method as this requires no initial guess from the user. A multi-objective optimisation is performed which aims to achieve a periodic orbit whilst also minimising the effort required by the sail to do so. Given the system sensitivity, the control law for one orbit is not necessarily applicable for any subsequent orbit. Therefore, a new method of updating the control law for subsequent orbits is presented, based on linearisation and use of a Control Transition Matrix (CTM). The techniques will later find application in a multiple asteroid rendezvous mission with a solar sail as the primary propulsion system.     

载人月球极地探测定点返回轨道设计

针对载人月球极地探测任务，对定点返回轨道优化设计问题进行了研究。根据月球极地轨道的特性，介绍了三种返回轨道机动方案。结合三脉冲变轨方案，采用了从初步计算到精确计算的串行求解策略，对定点返回轨道进行优化设计。初步计算阶段，建立了基于近月点伪参数的三段二体拼接模型，将三脉冲机动段与月球逃逸段解耦，求解轨道初值；精确计算阶段，提出了两段拼接方法，分别进行逆向和正向高精度数值积分。经过仿真测试，验证了该策略求解的有效性和准确性。最后，通过大量的仿真计算，分析了定点返回轨道的特性。研究结论对未来载人月球极地探测定点返回轨道方案的设计具有重要的参考价值。     

A fast Chebyshev polynomial method for calculating asteroid gravitational fields using space partitioning and cosine sampling

This paper presents a computationally fast method for solving gravitational accelerations near irregularly-shaped asteroids. This method is based on analytical three-dimensional Chebyshev polynomial approximation of the polyhedral gravity. For the purpose of improving the approximation accuracy, space partitioning schemes based on practical flight zones is used to avoid interpolation the whole space around the target asteroid. Specifically, a minimum ellipsoid close to the asteroid surface is defined to select the space for surrounding trajectories with safe distance and a cone connected to the surface is defined to select the space for descent trajectories. Moreover, interpolation points are sampled in a cosine sampling fashion according to the Chebyshev-Gauss-Lobatto nodes and a radial adaption technique. The performance of different space partitioning schemes is analyzed. The effectiveness of the proposed method is validated through simulations of solving gravitational accelerations at the test points near different shaped asteroids 1996 HW1, 433 Eros, 25143 Itokawa and 101955 Bennu.     

Synergistic approach of asteroid exploitation and planetary protection

The asteroid and cometary impact hazard has long been recognised as an important issue requiring risk assessment and contingency planning. At the same time asteroids have also been acknowledged as possible sources of raw materials for future large-scale space engineering ventures. This paper explores possible synergies between these two apparently opposed views; planetary protection and space resource exploitation. In particular, the paper assumes a 5 tonne low-thrust spacecraft as a baseline for asteroid deflection and capture (or resource transport) missions. The system is assumed to land on the asteroid and provide a continuous thrust able to modify the orbit of the asteroid according to the mission objective. The paper analyses the capability of such a near-term system to provide both planetary protection and asteroid resources to Earth. Results show that a 5 tonne spacecraft could provide a high level of protection for modest impact hazards: airburst and local damage events (caused by 15–170 m diameter objects). At the same time, the same spacecraft could also be used to transport to bound Earth orbits significant quantities of material through judicious use of orbital dynamics and passively safe aero-capture manoeuvres or low energy ballistic capture. As will be shown, a 5 tonne low-thrust spacecraft could potentially transport between 12 and 350 times its own mass of asteroid resources by means of ballistic capture or aero-capture trajectories that pose very low dynamical pressures on the object.     

Contingency target assessment,trajectory design,and analysis for NASA’s NEA scout solar sail mission

The presented study examines contingency target selection and trajectory design for NASA’s Near-Earth Asteroid Scout mission under the assumption of a missed lunar gravity assist. Two previously considered asteroids are selected as potential targets for the given scenario based on favorable orbital characteristics for launch dates ranging from June 27, 2020 through July 26, 2020. Initially, a simplified circular restricted 3-body problem + ideal solar sail model is utilized to survey trajectory options for a month-long launch window. Selected solutions from this data set are then converged in an N-body ephemeris + non-ideal sail model. Results suggest that NEA Scout can still perform asteroid rendezvous mission under the missed lunar gravity assist scenario with new targets, 2019 GF1, 2018 PK21, and 2007 UN12, based on the target launch dates. Further target assessment is carried out for 165 days beyond the current June 27, 2020 launch date.