Characterization of the optimal mass problem for aerobraking tethers

In the aerobraking tether concept, a probe, connected to an orbiter by a long, thin tether, passes through the atmosphere of a target planet to provide a desired velocity change, while keeping the orbiter above the sensible atmosphere. In earlier work, simple analytic models have been developed which accurately describe the characteristics of the mass-optimal tether. In this paper these models are generalized so that design of the spacecraft and the aerobraking maneuver can be completely characterized by four independent parameters. By comparing the tether mass (e.g. for aerocapture) with the propellant mass required to capture the orbiter, we show that aerobraking tethers have a clear advantage for a wide range of maneuvers.     

序列凸优化的小天体附着轨迹优化

针对小天体附着多约束轨迹优化问题,提出一种基于序列凸优化的轨迹优化方法。首先采用内球谐引力场模型对目标小天体附近的不规则引力场进行精确建模,内球谐引力场模型是对经典球谐系数法的改进,形式简单,计算量小,并且克服了经典球谐系数模型在形状不规则的小天体附近不收敛的问题。对于小天体附着多约束轨迹优化问题,通过约束松弛、线性化、离散化过程,转化为一个可以迭代求解的二阶锥规划问题（SOCP）,进而采用内点法进行解算。数学仿真结果显示,优化结果符合各项约束条件,以零速度到达了目标着陆点,且符合燃耗最优的优化目标。利用序列凸优化算法进行小天体附着燃耗最优轨迹设计,推导简便,计算速度快,精度高,具有应用价值。     

Human spaceflight and an asteroid redirect mission: Why?

The planning of human spaceflight programmes is an exercise in careful rationing of a scarce and expensive resource. Current NASA plans are to develop the new capability for human-rated launch into space to replace the Space Transportation System (STS), more commonly known as the Space Shuttle, combined with a heavy lift capability, and followed by an eventual Mars mission. As an intermediate step towards Mars, NASA proposes to venture beyond Low Earth Orbit to cis-lunar space to visit a small asteroid which will be captured and moved to lunar orbit by a separate robotic mission. The rationale for this and how to garner support from the scientific community for such an asteroid mission are discussed. Key points that emerge are that a programme usually has greater legitimacy when it emerges from public debate, mostly via a Presidential Commission, a report by the National Research Council or a Decadal Review of science goals etc. Also, human spaceflight missions need to have support from a wide range of interested communities. Accordingly, an outline scientific case for a human visit to an asteroid is made. Further, it is argued here that the scientific interest in an asteroid mission needs to be included early in the planning stages, so that the appropriate capabilities (here the need for drilling cores and carrying equipment to, and returning samples from, the asteroid) can be included.     

一种提升近地小行星防御中拦截效率的方法

利用核爆直接炸毁小行星或改变小行星的轨道以避免其与地球相撞,是近地小行星防御最主要的手段之一。文章基于美国爱荷华州立大学的超高速小行星拦截器(HAIV)概念,提出一种将原撞击引导器改为长杆撞击器的方案,采用自主研发的欧拉型冲击动力学仿真软件NTS模拟长杆撞击器对小行星连续开坑的过程,并在仿真中加入能量源以模拟核爆装置在不同深度爆炸对小行星产生的偏转与破坏效应。研究结果表明,采用长杆撞击器并合理控制撞击速度,能够引导核爆装置进入更深的地下爆炸,从而更加高效地耦合核爆能量,提升偏转小行星或直接摧毁小行星的能力。     

Tether satellite system collision study

A study was performed to determine the probability of collision with resident space objects and untrackable debris for the tether component of the Tethered Satellite System (TSS) after it broke away from the space shuttle orbiter (mission STS-75) in February 1996. Both an analytical and a numerical approach were used in this study, and the results obtained with these two methods were found to be in good agreement. These results show that the deployed tether is expected to have been impacted by several particles 0.1 mm or larger in size. The probability of collision with objects 10 cm in size or larger was on the order of 10⁻³ per month. Since the severed tether reentered within one month after deployment, the collision hazard to other objects while in orbit was small. The analytical methods used in this study are general and can be applied to future tether collision evaluations.     

Analysis of the orbital motion of the asteroid Apophis’ satellite

We have analyzed the orbital disturbed spacecraft motion near an asteroid. The equations of the asteroidocentric spacecraft motion have been used with regard to three perturbations from celestial bodies, the asteroid’s nonsphericity, and solar radiation pressure. It has been shown that the orbital parameters of the main spacecraft and a small satellite with a radio beacon can be selected such that the orbits are rather stable for a fairly long period of time, i.e., a few weeks for the main spacecraft with an orbit initial radius of ~0.5 km and a few years before approaching Apophis with the Earth in 2029, for a small satellite at an orbit initial radius of ~1.5 km. The initial orientation of the spacecraft orbital plane perpendicular to the sunward direction is optimal from the point of view of the stability of the spacecraft flight near an asteroid.     

Assessment on the feasibility of future shepherding of asteroid resources

Most plausible futures for space exploration and exploitation require a large mass in Earth orbit. Delivering this mass requires overcoming the Earth's natural gravity well, which imposes a distinct obstacle to any future space venture. An alternative solution is to search for more accessible resources elsewhere. In particular, this paper examines the possibility of future utilisation of near Earth asteroid resources. The accessibility of asteroid material can be estimated by analysing the volume of Keplerian orbital element space from which Earth can be reached under a certain energy threshold and then by mapping this analysis onto an existing statistical near Earth objects (NEO) model. Earth is reached through orbital transfers defined by a series of impulsive manoeuvres and computed using the patched-conic approximation. The NEO model allows an estimation of the probability of finding an object that could be transferred with a given Δv budget. For the first time, a resource map provides a realistic assessment of the mass of material resources in near Earth space as a function of energy investment. The results show that there is a considerable mass of resources that can be accessed and exploited at relatively low levels of energy. More importantly, asteroid resources can be accessed with an entire spectrum of levels of energy, unlike other more massive bodies such as the Earth or Moon, which require a minimum energy threshold implicit in their gravity well. With this resource map, the total change of velocity required to capture an asteroid, or transfer its resources to Earth, can be estimated as a function of object size. Thus, realistic examples of asteroid resource utilisation can be provided.     

Control of the deployment of an orbital tether system that consists of two small spacecraft

Control of an orbital tether system that consists of two small spacecraft has been considered. The proposed control laws are based on the modification of well-known programs for the deployment of tether system systems under the assumption that the masses of spacecraft and the tether are comparable in magnitude. To construct nominal deployment programs, we have developed a mathematical model of the motion of the given system in an orbital moving coordinate system taking into account the specific features of this problem. The performance of the proposed deployment programs is assessed by a mathematical model of the orbital tether system with distributed parameters written in the geocentric coordinate system. The test calculations involve a linear regulator that implements feedback on the tether length and velocity.     

Tethers and debris mitigation

In recent years, the use of tethers has been proposed for reduction of space debris either through momentum transfer or use of electrodynamic effects. Tethers have been shown to at least theoretically allow for quick, elegant and cost-effective deorbit of defunct satellites or spent stages. On the other hand, the large risk that tethers themselves may pose to other satellites in orbit has been recognized as well. The large collision area of tethers, combined with operational hazards and meteoroid risk may result in a large orbital exposure. For example, in 1997, the ESA/Dutch 35-km tether deployment of YES from TEAMSAT was inhibited after an analysis of the collision risk for the case the tether operation would fail. The question rises how these two points of view compare to eachother. This paper intends to highlight a representative selection of the proposed tether applications while taking into account the added risks caused by the tethers themselves.Typical applications from recent literature will be briefly described, such as an Ariane 502 spent stage re-entry from GTO and the concept of deboost of defunct satellites by interaction of a conductive tether with the Earth magnetic field.Mass savings of the tethered sytems versus conventional equivalents will be evaluated.Based on a crude risk analysis, involving elements such as mission complexity, dynamic stability, meteoroid risk and orbital life time, a general outline of limiting factors can be given for the various applications. Special attention is reserved for implementation of mechanisms that help reduce this tether risk, such as the DUtether (Tether Degradable by Ultraviolet), utilization of airdrag and solar pressure, the effect of residual current in bare tethers, tether retrieval etc.It is proposed how a net tether-induced mitigation can be compared to that of conventional alternatives, i.e. deboost by rocket engine or a completely passive approach.This comparison is put in the perspective of an ever-increasing occupation of the space environment.It is concluded that tethers can in fact help mitigate the debris risk and that for each application a useful niche can be defined. It is argued that eliminating pollution directly after use of the precious resource of space is not only good custom, but also an important way to make the risk of debris controllable and independent of future trends. Although tethers may have large exposure in terms of area-time product, they deliver a quick cleaning service that may be appreciated by the future users of space.     

Optimal thrust program for deviating an Earth-pointing asteroid

The purpose of this study is to investigate the optimal thrust program for deviating an asteroid when it is flying directly toward or crossing the Earth. Under some assumptions, the problem can be considered as a two-body problem of Earth-asteroid system. The initial relative speed and distance are specified to be 10 km/s and 150 times of Earth's radius, respectively. We have about 1 day (or, 93681 seconds exactly) to take action. If a single impulse is applied to the asteroid at the specified initial point, the required impulse to obtain a miss distance of 2 times of Earth's radius is 169.5 m/s per kg mass. For an asteroid of 10 m in diameter, the total impulse required is 3.02 × 10⁸ m/s. It needs a typical large launching rocket to provide the total impulse. When the asteroid is larger or the initial distance is shorter, the number of launching rockets required increases rapidly. For further analysis with physical and engineering constraints imposed, we shall have to use the variational formulation method.     

Experiments and numerical simulations of an electrodynamic tether deployment from a spool-type reel using thrusters

The amount of space debris is ever increasing, and pollution of the space environment has become a serious problem that can no longer be ignored. Consequently, the active removal of large space debris from crowded economically useful orbits should begin as soon as possible. The Japan Aerospace Exploration Agency has been investigating an active debris removal system that employs highly efficient electrodynamic tether (EDT) technology for orbital transfer. This study investigates the tether deployment from a spool-type reel using thrusters by means of numerical simulations of an EDT system. The thrusters are used in order to ensure the deployment of a tether with the length of several kilometers. In the simulations using a multiple mass tether model, the key parameters are estimated from various on-ground experiments. By means of the numerical simulations, the dynamics of tether deployment is studied and requirements of thruster needed for the deployment, such as the thrust forces and the periods of thruster activation, are clarified.     

载人小行星探测的任务特点与实施途径探讨

介绍了载人小行星探测的发展现状,对目前美国基于"猎户座"飞船的载人小行星探测的概要方案进行了描述,包括探测器系统组成、运载火箭和飞行方案等内容。从速度增量、目标星引力等方面,分析了载人小行星探测的任务特点,并与载人火星探测、载人月球探测以及无人小行星探测的任务特点进行了比较。给出了载人小行星探测的实施途径建议,包括目标星选择、载人飞船系统设计等。讨论了其所涉及的推进、星际飞行安全保障、小行星表面行走等关键技术。研究结果可为我国开展载人深空探测提供参考。     

Optimal flights to near-Earth asteroid

The spacecraft flights to the Near-Earth asteroid in order to give an impact influence on the asteroid, correct its orbit and prevent the asteroid’s collision with the Earth are analyzed.In the first part, the impulse flights are analyzed in the Lambert approach. There are determined the optimal trajectories maximizing the asteroid deviation from the Earth.In the second part, the flights with the chemical and electric-jet engines are analyzed. The high thrust is used to launch the spacecraft from the geocentric orbit, and the low thrust is applied for the heliocentric motion. On the base of optimal impulse transfer, the optimal low thrust trajectories are determined using Pontryagin maximum principle.The numerical results are given for the flight to the asteroid Toutatis. Parameters of the spacecraft impact on the asteroid are determined. The asteroid deviation from the Earth caused by the spacecraft influence is presented.     

Equilibrium attitude and stability of a spacecraft on a stationary orbit around an asteroid

The stationary orbits around an asteroid, if exist, can be used for communication and navigation purposes just as around the Earth. The equilibrium attitude and stability of a rigid spacecraft on a stationary orbit around a uniformly-rotating asteroid are studied. The linearized equations of attitude motion are obtained under the small motion assumption. Then, the equilibrium attitude is determined in both cases of a general and a symmetrical spacecraft. Due to the higher-order inertia integrals of the spacecraft, the equilibrium attitude is slightly away from zero Euler angles. Then necessary conditions of stability of this conservative system are analyzed based on the linearized equations of motion. The effects of different parameters, including the harmonic coefficients C₂₀ and C₂₂ of the asteroid and higher-order inertia integrals of the spacecraft, on the stability are assessed and compared. Due to the significantly non-spherical shape and rapid rotation of the asteroid, the effects of the harmonic coefficients C₂₀ and C₂₂ are very significant, while effects of the third- and fourth-order inertia integrals of the spacecraft can be neglected. Considering a spacecraft on a stationary orbit around an example asteroid, we show that the classical stability domain predicted by the Beletskii–DeBra–Delp method on a circular orbit in a central gravity field is modified due to the non-spherical mass distribution of the asteroid. Our results are confirmed by a numerical simulation.     

Magnetobraking for Mars return vehicles

It is proposed that magnetobraking may be used to dissipate hyperbolic excess velocity from a spacecraft returning from Mars to Earth orbit. In magnetobraking, an electrodynamic tether is deployed from the spacecraft. The Earth's magnetic field produces a force on electrical current in the tether, which can be used to either brake or accelerate the spacecraft without expenditure of reaction mass. The peak acceleration on the Mars return is 0.007 m/s², and the amount of braking possible is dependent on the density and current-carrying capacity of the tether, but is independent of length. Since energy is produced as the spacecraft velocity decreases, no on-board power source is required. As the spacecraft approaches the Earth, the magnetic field increases and the power produced by the tether increases, reaching a maximum of about 800 W per kg of spacecraft mass at closest approach.     

Working and walking on small asteroids with circumferential ropes

The low gravity of a small asteroid would present a challenge for an astronaut attempting to work on its surface. Extravehicular activities (EVAs) of the sophistication of the Apollo Moon missions are not likely to be possible if astronauts attempt to walk freely on the asteroid, hover above its surface, or anchor locally into the regolith. Manipulating large rocks, drilling, and excavating at multiple locations is a high priority science objective, but would be difficult without a hold-down mechanism. If the asteroid has even a small rotation rate, maneuvering precisely over its surface could be cumbersome. A plausible means of conducting complex EVAs is to tie ropes entirely around the asteroid, under which the astronaut is pushed downward onto the asteroid surface by the tension in the rope. The downward force provides an artificial gravity that permits the astronaut to drill, excavate, hammer, and carefully document materials on the surface without the worry of being thrown from the asteroid. An astronaut could also use the ropes as handholds or guides to maneuver freely over the surface.     

Working and walking on small asteroids with circumferential ropes

The low gravity of a small asteroid would present a challenge for an astronaut attempting to work on its surface. Extravehicular activities (EVAs) of the sophistication of the Apollo Moon missions are not likely to be possible if astronauts attempt to walk freely on the asteroid, hover above its surface, or anchor locally into the regolith. Manipulating large rocks, drilling, and excavating at multiple locations is a high priority science objective, but would be difficult without a hold-down mechanism. If the asteroid has even a small rotation rate, maneuvering precisely over its surface could be cumbersome. A plausible means of conducting complex EVAs is to tie ropes entirely around the asteroid, under which the astronaut is pushed downward onto the asteroid surface by the tension in the rope. The downward force provides an artificial gravity that permits the astronaut to drill, excavate, hammer, and carefully document materials on the surface without the worry of being thrown from the asteroid. An astronaut could also use the ropes as handholds or guides to maneuver freely over the surface.     

System design of the Hayabusa 2—Asteroid sample return mission to 1999 JU3

The Japan Aerospace Exploration Agency is currently developing the second asteroid sample return mission, designated as Hayabusa 2. Following the successful return of Hayabusa from the asteroid “Itokawa”, Hayabusa 2 is designed as a round-trip mission to the asteroid “1999 JU3”. The 1999 JU3 is a C-type asteroid, which is believed to contain organic matter and hydrated minerals. Thus, it is expected that successful sample collection will provide additional knowledge on the origin and evolution of the planets and, in particular, the origin of water and organic matter. The current mission scenario will enable the spacecraft to reach 1999 JU3 in the middle of 2018 and perform an asteroid proximity operation for 1.5 years. Three touch downs for sampling and one 2-m-class crater generation by means of a high-speed impact operation are planned during the asteroid proximity operation. The samples are to be brought back to the Earth by a re-entry capsule. The present paper describes the system design of Hayabusa 2, some key technical challenges of the mission, and the development status.     

Stability of a ring of connected satellites

The motion of a large number of artificial satellites connected in a ring one after another by tethers of variable length is considered. Every satellite is supposed to have a control system programmed according to some tether tension law as a function of the distance between tethered satellites. The effect of the tension control law on the stability of stationary rotation of this ring is investigated. The final stability condition includes two requirements: 1) the nominal tether tension should be less than a definite limit equal, up to numerical coefficient, to one satellite weight divided by the number of satellites; 2) tether tension should decrease (or remain constant) with the increase of the distance between tethered satellites. In dynamics the artificial rings of this kind are much like their natural prototype—meteor rings. On the other hand, the investigation of the artificial rings contributes to developing an unexpected view upon meteor rings, suggesting a model of an imaginary equivalent string.     

绳系卫星系统的运动与控制

绳系卫星系统的运动与控制分析,是绳系卫星应用的基础。本文的数学模型考虑了作用在子星、主星及系绳上的空气阻力以及在伸展与收回阶段主星与系绳之间的质量传递,给出了相应的具体的计算式。应用该数学模型,本文对现有的几种主要控制法,进行了模拟计算,作出评审意见。