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.     

Sailing at the brink – The no-limits of near-/now-term-technology solar sails and SEP spacecraft in (multiple) NEO rendezvous

Near-Earth object (NEO) in-situ exploration can provide invaluable information for science, possible future deflection actions and resource utilisation. This is only possible with space missions which approach the asteroid from its vicinity, i.e. rendezvous. This paper explores the use of solar sailing as means of propulsion for NEO rendezvous missions. Given the current state of sail technology, we search for multiple rendezvous missions of up to ten years and characteristic acceleration of up to 0.10 mm/s². Using a tree-search technique and subsequent trajectory optimisation, we find numerous options of up to three NEO encounters in the launch window 2019–2027. In addition, we explore steerable and throttleable low-thrust (e.g. solar-electric) rendezvous to a particular group of NEOs, the Taurid swarm. We show that an acceleration of 0.23 mm/s² would suffice for a rendezvous in approximately 2000 days, while shorter transfers are available as the acceleration increases. Finally, we show low-thrust options (0.3 mm/s²) to the fictitious asteroid 2019 PDC, as part of an asteroid deflection exercise.     

Rapid design and optimization of low-thrust rendezvous/interception trajectory for asteroid deflection missions

Asteroid deflection techniques are essential in order to protect the Earth from catastrophic impacts by hazardous asteroids. Rapid design and optimization of low-thrust rendezvous/interception trajectories is considered as one of the key technologies to successfully deflect potentially hazardous asteroids. In this paper, we address a general framework for the rapid design and optimization of low-thrust rendezvous/interception trajectories for future asteroid deflection missions. The design and optimization process includes three closely associated steps. Firstly, shape-based approaches and genetic algorithm (GA) are adopted to perform preliminary design, which provides a reasonable initial guess for subsequent accurate optimization. Secondly, Radau pseudospectral method is utilized to transcribe the low-thrust trajectory optimization problem into a discrete nonlinear programming (NLP) problem. Finally, sequential quadratic programming (SQP) is used to efficiently solve the nonlinear programming problem and obtain the optimal low-thrust rendezvous/interception trajectories. The rapid design and optimization algorithms developed in this paper are validated by three simulation cases with different performance indexes and boundary constraints.     

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.     

基于最小轨道交叉距离的小行星顺访探测目标预筛选方法

小行星探测有助于研究太阳系演化等重要科学问题,在深空探测任务转移途中实施小行星顺访探测可增加科学研究回报。直接通过轨道递推筛选小行星探测目标计算量大、效率低,针对该问题提出了基于最小轨道交叉距离的目标预筛选方法。在推导出适用于计算双曲线轨道的最小轨道交叉距离公式后,将此理论应用到小行星顺访探测目标筛选中。首先基于探测器与小行星轨道的形状、空间位置计算二者轨道在空间中的几何最近距离,预筛选出可能满足接近距离标准的小行星目标;然后基于轨道递推模型,筛选出真实最近距离小于可接近标准的目标小行星。仿真结果显示,基于最小轨道交叉距离的预筛选方法可有效减少计算量,降低计算时间,提高小行星顺访目标筛选的效率。      

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.     

精确动力学模型中的行星引力辅助轨道设计

轨道设计分为初步设计和精确模型迭代两步,初步设计基于等效脉冲模型,用圆锥曲线拼接法确定时间窗口和引力辅助产生的速度脉冲。精确模型中引力辅助看作是一个连续的过程,将简化模型得到的引力辅助双曲线轨道化为行星心目标B平面参数,以地心逃逸速度作为设计变量,通过微分修正的方法进行求解。通过算例对比分析了简化模型和精确模型设计结果之间的关系,结果表明,引力辅助脉冲等效模型精度较好。     

从日地系统L2出发借力月球飞越近地小行星

对于停留在日地系统L2的“嫦娥2号”探测器,其后续飞行方案有多个选项,例如主动撞月或重返月球轨道、返回地球轨道或再入大气、飞往地月系统L1/L2或日地系统L1、进入深空飞越近地小行星(最终,“嫦娥2号”于2012年12月13日成功地实现了对Toutatis小行星的近距离飞越)。探讨上述的飞行方案需要对飞行轨道进行初步设计,总的速度脉冲限制在100 m/s以内并且需要考虑探测器同时受到太阳、地球、月球的引力作用。本研究设计了探测器从日地系统L2出发借力月球实现Toutatis小行星飞越的飞行方案,与直接飞越方案相比,借力月球可以进一步节省探测器的燃料消耗,其等效速度脉冲设计值为58.47 m/s。     

木星系探测及行星穿越任务轨迹初步设计

基于我国未来木星系探测任务需求,初步设计了任务轨迹。以目前的发射能力,要实现木星的环绕探测必将利用行星借力,需设计借力轨迹。首先将脉冲变轨的轨迹设计问题转化为参数优化问题,在满足2029—2032年间发射并且飞行时间不超过7年的约束条件下,使用PSO算法对发射时刻、借力时刻、深空机动时刻、到达时刻等参数进行优化,使得探测器需提供的总速度增量最小。探测器进入木星系后,利用木卫3借力捕获至环木大椭圆轨道,又利用木卫4构造共振借力,最终捕获至木卫4的环绕轨道。在此基础上,还考虑了天王星飞越的拓展任务,天王星探测器在到达木星时与木星系探测器分离,利用木星借力可无消耗飞往天王星,并在2043年完成天王星的飞越探测任务。     

火星探测转移轨道初始设计与分析

根据推进方式和是否采用金星借力,火星转移轨道分为大推力直接转移轨道、大推力金星借力转移轨道、小推力直接转移轨道和小推力金星借力转移轨道4类。传统的轨道设计方法只是针对某一类特定的转移方案进行轨道优化,而并未针对不同的转移方案进行详细对比分析。文章以2020/2022年发射窗口为例,针对4类基本火星转移轨道进行研究。首先,基于不同轨道初始设计方法,对4类轨道进行了初始设计,得到了每类转移方案的能量最优转移轨道。然后,基于设计结果和能耗对4类转移方案进行了横向对比分析,得到了不同策略下的转移轨道的特性。基于小推力的火星探测任务轨道对发射能量要求低;大推力直接转移和借力金星的发射窗口交替分布,可以互为备份;基于小推力推进的探测器采用金星借力转移策略相比直接转移能够减少10%的能耗,优势十分明显。     

主带小行星采样返回任务中的离子电推进应用方案

由于离子电推进的高比冲特性,采用它执行小行星探测器巡航阶段轨道机动任务时,将使探测器在同样的有效载荷下的发射重量大大减轻。针对我国规划中的主带小行星采样返回任务,调研了国外离子电推进在深空探测任务中的应用情况,在借鉴国外成功经验和任务需求分析的基础上,设计了主带小行星探测器离子电推进系统方案和应用策略,计算了在目前离子推力器寿命水平下,既定探测任务对离子电推进推力、比冲、推进剂量以及功耗需求。研究表明,目前研制的离子推力器可以满足规划中的主带小行星探测任务需求。研究成果对探测器的方案设计有参考价值。     

Paths not taken – The Gossamer roadmap’s other options

Highly efficient low-thrust propulsion is increasingly applied beyond commercial use, also in mainstream and flagship science missions, in combination with gravity assist propulsion. Another recent development is the growth of small spacecraft solutions, not in size but in numbers and individual capabilities.Just over ten years ago, the DLR-ESTEC Gossamer Roadmap to Solar Sailing was set up to guide technology developments towards a propellant-less and highly efficient class of spacecraft for solar system exploration and applications missions: small spacecraft solar sails designed for carefree handling and equipped with carried application modules.Soon, in three dedicated Gossamer Roadmap Science Working Groups it initiated studies of missions uniquely feasible with solar sails such as Displaced L₁ (DL1) space weather advance warning and monitoring, Solar Polar Orbiter (SPO) delivery to very high inclination heliocentric orbit, and multiple Near-Earth Asteroid (NEA) rendezvous (MNR). Together, they demonstrate the capability of near-term solar sails to achieve at least in the inner solar system almost any kind of heliocentric orbit within 10 years, from the Earth-co-orbital to the extremely inclined, eccentric and even retrograde. Noted as part of the MNR study, sail-propelled head-on retrograde kinetic impactors (RKI) go to this extreme to achieve the highest possible specific kinetic energy for the deflection of hazardous asteroids.At DLR, the experience gained in the development of deployable membrane structures leading up to the successful ground deployment test of a (20 m)², i.e., 20 m by 20 m square solar sail at DLR Cologne in 1999 was revitalized and directed towards a 3-step small spacecraft development line from as-soon-as-possible sail deployment demonstration (Gossamer-1) via in-flight evaluation of sail attitude control actuators (Gossamer-2) to an envisaged proving-the-principle flight in the Earth-Moon system (Gossamer-3). First, it turned the concept of solar sail deployment on its head by introducing four separable Boom Sail Deployment Units (BSDU) to be discarded after deployment, enabling lightweight 3-axis stabilized sailcraft. By 2015, this effort culminated in the ground-qualified technology of the DLR Gossamer-1 deployment demonstrator Engineering Qualification Model (EQM). For mission types using separable payloads, such as SPO, MNR and RKI, design concepts can be derived from the BSDU characteristic of DLR Gossamer solar sail technology which share elements with the separation systems of asteroid nanolanders like MASCOT. These nano-spacecraft are an ideal match for solar sails in micro-spacecraft format whose launch configurations are compatible with ESPA and ASAP secondary payload platforms.Like any roadmap, this one contained much more than the planned route from departure to destination and the much shorter distance actually travelled. It is full of lanes, narrow and wide, detours and shortcuts, options and decision branches. Some became the path taken on which we previously reported. More were explored along the originally planned path or as new sidings in search of better options when circumstance changed and the project had to take another turn. But none were dead ends, they just faced the inevitable changes when roadmaps face realities and they were no longer part of the road ahead. To us, they were valuable lessons learned or options up our sleeves. But for future sailors they may be on their road ahead.     

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.     

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。     

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.     

The dynamical environments analysis of surface particles for different shaped asteroids

Asteroids are coming to be a popular topic in the areas of astrophysical studies and deep space exploration recently. However, surface dynamics of asteroids is still a difficult problem. This paper aims at the motion analysis of surface particles for different asteroids. The dynamical analysis method of particles’ movement is given for three parts: global motion trend, local motion trend and static analysis. A dimensionless parameter ζ is defined to distinguish the predominant term to determine the distribution of effective potential. Three kinds of common asteroids: spheroidal asteroid, spindle-shaped asteroid and dumbbell-shaped asteroid are all discussed for those three parts with different parameter ζ. The motion trend of particles on the surface of each kind of asteroid is given. The static analysis of surface particles for different asteroids is also illustrated. Based on them, some common rules for different shaped asteroids are revealed. This paper could not only provide a reference for asteroid exploration missions but also be meaningful for the research of morphologic evolution of asteroids.     

Spacecraft fuel-optimal and balancing maneuvers for a class of formation reconfiguration problems

This paper presents fuel optimal and balancing methodologies for reconfiguring multiple spacecraft in formation subject to a Newtonian gravity field. For a kind of continuous-thrust propulsion system, a fuel-optimal control problem is formulated to minimize the integral squared control subject to the linearized Hill or Clohessy–Wiltshire dynamics of relative motion with respect to a circular reference orbit. Palmer’s analytical solution for general reconfiguration is adapted to maneuvers between projected circular orbits, resulting in the optimal fuel consumption index as a function of configuration parameters such as orbit radius, phase angle, and transfer time. Parametric analyses reveal unique characteristics of individual fuel optimality and gross fuel consumption: for an arbitrary selection of initial/terminal orbit radii, (i) there exist special transfer times such that individual fuel consumption is optimally uniform for all phase angles, and (ii) the total fuel expenditure for a group of three or more spacecraft is invariant for the relatively same configuration with respect to the departure phase. These results serve to effectively design fuel balancing strategies for formation reconfiguration of multiple spacecraft.     

小推力转移燃料消耗估计的机器学习方法

深空探测任务设计初段往往需要求解复杂的全局优化问题。小推力轨迹的设计与优化问题精确求解较为复杂,求解速度较慢。由于计算能力与时间要求,不可能在全局优化的过程中对每一个方案都进行精确的小推力数值求解,所以在全局优化阶段需要对小推力转移进行快速准确地估计。采用机器学习的方法,对燃料最优小推力转移的燃料消耗进行了估计,其结果明显优于目前最为常用的Lambert估计方法。根据轨道描述方法的不同以及是否带有Lambert估计特征,采用不同的特征组合进行机器学习,分析结果发现带有Lambert估计特征的春分点轨道根数的特征组合为较好的机器学习特征组合。可为未来深空探测任务轨道设计提供参考。     

连续小推力非开普勒悬浮轨道研究综述

连续小推力非开普勒悬浮轨道在深空探测与地球极地观测任务中有着重要的应用前景。归纳了电推进、太阳帆推进等连续小推力技术的发展历程与现状;阐述了日心、行星悬浮轨道的动力学特性、稳定性、轨道保持策略;分析了三体问题下人工拉格朗日点的优势及其在深空探测方面的应用;讨论了悬浮轨道编队飞行的研究方法与控制策略。最后针对小推力悬浮轨道研究发展面临的难题,提出了研究新思路和应用新方向。     

小行星探测电推进系统方案研究

小行星探测以及资源开发与利用对国家抢占深空探测主动权和制高点有着不可估量的战略意义。电推进具有高比冲、长寿命和高度自主巡航等特点,小行星探测器采用电推进执行巡航阶段轨道机动任务,将大幅减少推进剂重量和提高载重比。调研了国外小行星探测的电推进系统方案,针对我国小行星探测对电推进系统的任务需求及现有电推力器的技术基础,提出了5种电推进系统方案,并进行多维度对比,对最优方案进行了设计和关键技术梳理。