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 0.1mm or larger in size. The probability of collision with objects 10cm 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 useful for tether collision evaluations in general.     

空间目标碰撞概率的等效矩形域快速算法

针对线性相对运动假设下的碰撞概率计算问题，提出了等效矩形域方法。利用该方法将概率积分计算进行近似处理，推导出概率密度积分的解析表达式。针对空间目标误差椭球形状固定的情况，给出了最大碰撞概率的计算方法。对目标在交会时刻相距较远和接近碰撞的情况进行了碰撞概率以及最大碰撞概率计算。通过将计算结果与空间压缩无穷级数法的对比，验证了等效矩形域方法近似计算碰撞概率积分的可靠性，同时对于不同的碰撞概率计算情况，等效矩形域方法显示出更高精确度和更好的估计偏差稳定性。     

对欧空局轨道碎片模型的评价

文章评价了颗粒大于1cm的碎片模型,它包含大于10cm的一组粒子和介于1～10cm之间的粒子,它们是由空间暴露模拟得到的。接着讨论了尺寸范围介于0.1～10mm之间的小粒子束流。假定这些粒子主要是由小粒子与卫星碰撞产生的。这种碰撞主要发生在450～500kin的高度范围内(空间站高度),碰撞与否还取决于轨道高度和离心率。     

The Investigation of Possible Approaches of Cataloged Space Objects to Manned Spacecraft

Initial orbital parameter errors are used to examine the miss distance between a spacecraft and an ensemble of tracked objects by a Monte Carlo-type analysis. The radial separation between orbits is evaluated and a keep-out zone is determined, which reduces the risk of collision to an acceptable level.An operational prediction methodology is suggested based on a catalog database, which identifies potentially hazardous approaches and computes the probability of collision for selected spacecraft. An example for the Mir Space Station is presented, which estimates the collision probability and the cross-sectional flux of cataloged objects for the time frame of interest. The results appear to be in good agreement with those of other space debris models.     

碰撞风险评估中的空间环境激励图方法

因航天器物理特征、空间环境扰动变化、预报技术和大气模型性能等既有不确定因素的存在，空间目标碰撞概率等与轨道预报相关的评估工作存在模糊度问题，无法准确描述碰撞风险水平。文章基于碰撞概率极值，简化气动力误差模型，量化计算轨道预报相关事务的边界；提出空间环境激励图和3σ区的概念，并给出具体实施方法以及空间碎片碰撞预警、空间物体陨落预报的计算示例。计算结果表明，该方法能较好应对轨道预报相关事务中的模糊度问题，可为相关航天工程实践和决策提供参考。     

Assessing the Impact Risk of Orbital Debris on Space Tethers

Tethers are being proposed for a growing number of space applications. However, they may be particularly vulnerable to orbital debris and meteoroid impacts. In order to provide useful reference data for tether systems design, detailed analytical and numerical computations were carried out to assess the average impact rate of artificial debris and meteoroids. The specific geometric properties of tethers as debris targets, when compared to typical satellites, are discussed, and the results obtained are presented in tabular form, as a function of debris size and tether diameter.The computations were carried out for six circular orbits, spanning three altitudes (600, 800 and 1000km) and two inclinations (30° and 50°). Tether diameters in between 1mm and 2cm and debris larger than 0.1mm were considered in the analysis. The collision risk of tethers with spacecraft and upper stages in orbit was estimated as well.In the debris interval and orbital regimes considered, artificial debris represent the dominant contributor to the impact rate. At 600km and in the 0.1–10mm size range, the meteoroid and orbital debris impact rates are still comparable; however, at higher altitudes and in the 1–10cm size range, meteoroids contribute 20–30 times less to the collision probability.The results obtained confirm that for single-strand tethers in low Earth orbit the probability to be severed by orbital debris and meteoroid impacts is quite significant, making necessary the adoption of innovative designs for long duration missions.     

Analytical and numerical re-entry analysis of simple-shaped objects

The application of SCARAB (spacecraft atmospheric re-entry and aerothermal break-up) to several re-entry objects within the last years has shown the need of fast methods and easy-to use guidelines for a first assessment of the survival probability for these objects or parts of them. Such methods and guidelines will be also very helpful during the design process of a satellite in order to decide, whether a controlled re-entry had to be foreseen at the end of the lifetime, or an uncontrolled re-entry would be acceptable.Within current studies HTG has developed analytical and numerical methods to analyze the demise of simple-shaped objects like spheres, boxes, and cylinders. In addition, the SCARAB software system has been used to evaluate the shielding effects of concentric shells.This paper presents the analytical and numerical models used within the study and the results which have been achieved, including demise ranges for several object/material combinations. The SCARAB results for shielding effects are presented as well.     

航天器碰撞分析方法研究

作为航天器碰撞与规避控制方法研究课题的一部分,为此分别建立了航天器及其它空间目标的轨道确定方法;并在此基础上,提出了可能与航天器碰撞的其它空间编目目标的初选准则和碰撞预报算法。实测数据计算表明,该方法对于航天器轨道设计以及飞行安全性分析等均是实用可行的。     

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.     

Ground assisted rendezvous with geosynchronous satellites for the disposal of space debris by means of Earth-oriented tethers

Previous studies have shown that extended length Earth-oriented tethers in the geosynchronous (GEO) region can be used to re-orbit satellites to disposal orbits. One such approach involves the extension of a GEO based tether, collection of a debris object, and retraction of the tether, which transfers the retracted configuration to a higher energy orbit for debris disposal. The re-extension of the tether after debris disposal returns the configuration to the near-GEO altitude. The practical feasibility of such a system depends on the ability to collect GEO debris objects, attach them to a deployed tether system, and retract the tethers for transfer to the disposal orbits.This study addresses the collection and delivery of debris objects to the deployed tether system in GEO. The investigation considers the number, type and the characteristics of the debris objects as well as the collection tug that can be ground controlled to detect, rendezvous and dock with the debris objects for their delivery to the tethers system.A total of more than 400 objects are in drift orbits crossing all longitudes either below or above the geostationary radius. More than 130 objects are also known to librate around the stable points in GEO with periods of libration up to five or more years. A characterization of the position and velocity of the debris objects relative to the collection tug is investigated. Typical rendezvous performance requirements for uncooperative GEO satellites are examined, and the similarities with other approaches such as the ESA's CX-OLEV commercial mission proposal to extend the life of geostationary telecommunication satellites are noted.     

Benefits and risks of using electrodynamic tethers to de-orbit spacecraft

By using electrodynamic drag to greatly increase the orbital decay rate, an electrodynamic space tether can remove spent or dysfunctional spacecraft from low Earth orbit (LEO) rapidly and safely. Moreover, the low mass requirements of such tether devices make them highly advantageous compared to conventional rocket-based de-orbit systems. However, a tether system is much more vulnerable to space debris impacts than a typical spacecraft and its design must be proved to be safe up to a certain confidence level before being adopted for potential applications. To assess space debris related concerns, in March 2001 a new task (Action Item 19.1) on the “Potential Benefits and Risks of Using Electrodynamic Tethers for End-of-life De-orbit of LEO Spacecraft” was defined by the Inter-Agency Space Debris Coordination Committee (IADC). Two tests were proposed to compute the fatal impact rate of meteoroids and orbital debris on space tethers in circular orbits, at different altitudes and inclinations, as a function of the tether diameter to assess the survival probability of an electrodynamic tether system during typical de-orbiting missions. IADC members from three agencies, the Italian Space Agency (ASI), the Japan Aerospace Exploration Agency (JAXA) and the US National Aeronautics and Space Administration (NASA), participated in the study and different computational approaches were specifically developed within the framework of the IADC task. This paper summarizes the content of the IADC AI 19.1 Final Report. In particular, it introduces the potential benefits and risks of using tethers in space, it describes the assumptions made in the study plan, it compares and discusses the results obtained by ASI, JAXA and NASA for the two tests proposed. Some general conclusions and recommendations are finally extrapolated from this massive and intensive piece of research.     

Behavior of tethered debris with flexible appendages

Active exploration of the space leads to growth of a near-Earth space pollution. The frequency of the registered collisions of space debris with functional satellites highly increased during last 10 years. As a rule a large space debris can be observed from the Earth and catalogued, then it is possible to avoid collision with the active spacecraft. However every large debris is a potential source of a numerous small debris particles. To reduce debris population in the near Earth space the large debris should be removed from working orbits. The active debris removal technique is considered that intend to use a tethered orbital transfer vehicle, or a space tug attached by a tether to the space debris. This paper focuses on the dynamics of the space debris with flexible appendages. Mathematical model of the system is derived using the Lagrange formalism. Several numerical examples are presented to illustrate the mutual influence of the oscillations of flexible appendages and the oscillations of a tether. It is shown that flexible appendages can have a significant influence on the attitude motion of the space debris and the safety of the transportation process.     

基于显式表达式的空间目标最大碰撞概率分析

最大碰撞概率的计算在空间目标碰撞风险评估中具有重要意义。基于碰撞概率的显式 表达式,利用一元函数和二元函数求极值的方法分别讨论了目标误差椭球形状固定和不定两 种情况下最大碰撞概率的计算方法,得到了两种情况下最大碰撞概率的表达式。对于误差椭 球形状固定的情况得到了碰撞概率最大时两目标位置协方差的取值,对于误差椭球不定情况 得到了碰撞概率最大时径向联合方差的取值和水平面内联合方差所满足的关系。分析了最大 碰撞概率的影响因素,讨论了水平面内误差方差的耦合特性。对今年二月发生的美俄卫星碰 撞事件进行了分析,得到误差椭球任意形状时最大碰撞概率为1.864E-3。
     

非线性相对运动的飞行器碰撞概率研究

发展了一种非线性相对运动情况下的飞行器碰撞概率描述和计算方法。采用拟最大瞬时碰撞概率和总碰撞概率两个主要指标来定量描述飞行器碰撞的危险性，并针对这两个指标发展了相应的计算方法。对于拟最大瞬时碰撞概率的计算，首先需要在相对轨迹上寻找最小相对距离或最大概率密度的点，然后在这个点上计算拟最大瞬时碰撞概率。对于总碰撞概率的计算，由于总碰撞概率的增量可以表示成一个时间的函数，因此总碰撞概率的计算就是一个在时间域上的积分。所建立的这种描述和计算方法适用于相对速度和误差协方差矩阵随时间任意变化的情况。数值算例表明所提出的指标比单纯采用总碰撞概率能够更好的描述飞行器的碰撞危险性，并且碰撞概率的计算方法和线性相对运动情况下的计算方法是兼容的。     

A sensitivity study of the effectiveness of active debris removal in LEO

The near-Earth orbital debris population will continue to increase in the future due to ongoing space activities, on-orbit explosions, and accidental collisions among resident space objects. Commonly adopted mitigation measures, such as limiting postmission orbital lifetimes of satellites to less than 25 years, will slow down the population growth, but will be insufficient to stabilize the environment. To better limit the growth of the future debris population, the remediation option, i.e., removing existing large and massive objects from orbit, needs to be considered. This paper does not intend to address the technical or economical issues for active debris removal. Rather, the objective is to provide a sensitivity study to illustrate and quantify the effectiveness of various remediation options. An effective removal criterion based upon mass and collision probability is developed. This study includes simulations with removal rates ranging from 5 to 20 objects per year, starting in the year 2020. The outcome of each simulation is analyzed and compared with others. The summary of the study serves as a general guideline for future debris removal consideration.     

再论空间系绳在回收容器返回中的应用

在已有的研究结果的基础上，对空间系绳在回收容器回中的应用，作了进一步分析，包括从回收容器离开空间站至回收容器从系绳上脱落的系绳伸展运动，（２）从系绳脱落的回收容器的返回运动，（３）释放容器后的系绳的收回运动。对回收容器的动态释放，除了两阶段指数型伸展程序外，还提出了另外两种导致系绳后摆的方式。对静态释放与动态释放，不仅对系绳长度，而且对系绳张力作了计算与分析。为了系绳收回过程的稳定，不仅要施加张力     

空间目标态势行为与事件本体设计与构建

针对空间目标态势威胁响应和预警研究不完善的问题，为实现空间目标行为和事件的智能推理、实时响应和主动预警，保障航天活动和空间利益，提出面向行为与事件的空间目标态势本体模型(BEO-SO2)。基于基本形式本体(BFO)，构建空间目标态势行为与事件本体模型。在统一时空框架下建立空间目标关系模型，实现空间目标行为执行和事件发生过程的动态推演。以空间目标碰撞威胁为背景，设计对象实体等级体系和碰撞威胁行为与事件要素，建立碰撞威胁推理规则，基于空间目标态势行为与事件本体进行实现、验证与展示。结果表明,空间目标态势行为与事件本体能够实现空间目标碰撞威胁的等级推理与预警，并指导进一步的空间活动，为航天任务与空间活动提供有效保障。     

编队卫星碰撞规避方法研究

对编队卫星碰撞规避方法进行了研究。通过递推编队卫星的初始状态协方差阵,将碰撞概率密度函数在危险区域积分获得编队卫星的碰撞概率。当碰撞概率大于安全阈值时,向卫星施加最小脉冲速度修正量Δv,在垂直于终止时刻相对速度的平面机动一定距离以降低碰撞概率。仿真结果表明:用计算的碰撞概率能较好地预测编队卫星的潜在碰撞危险,所选机动策略有效。     

New insights on the orbital debris collision hazard at GEO

An analysis is performed of the orbital debris collision hazard to operational spacecraft at geosynchronous orbit (GEO). As part of the examination, the contribution of individual components of the population are considered and presented to provide a clearer linkage between object characteristic and resulting risk. Our examination of GEO collision risk reveals several critical new insights: (1) the current probability of collision in GEO is relatively low, yet the future is difficult to predict due to our limited ability to observe objects in GEO and the uncertainty in past and future debris-generating events in GEO; (2) the probability of collision in GEO is not uniform by longitude — it is seven times greater in regions centered about the geopotential wells; (3) the probability of a mission-terminating collision is greatly dependent upon the approximately 2200 objects in the 10 cm–1 m range observed in GEO but not yet cataloged; (4) hardware relocated to GEO “graveyard” disposal orbits pose a potential additional, but not fully understood, collision hazard to operational GEO satellites; and (5) the collision hazard throughout the course of a day or year is highly episodic (i.e. non-uniform).     

空间非合作目标物柔性捕获技术进展

分类探讨了近年来出现的多种空间柔性捕获技术的原理及性能特点，给出了一些具有代表性的案例，结果表明：空间绳系捕获技术在理论及试验研究方面都相对成熟，是未来行之有效、可工程实现的柔性捕获方式之一。重点针对空间非合作目标物捕获中容易出现的翻滚问题，对比分析现有的几种常用的接触式消旋方法，分析表明能同时实现捕获+消旋的一步式消旋法更具有应用前景。以空间绳系捕获技术作为空间柔性捕获的代表，对其捕获后的空间绳系组合体动力学模型建立过程中的系绳模型进行了综述，指出了各种系绳模型的优缺点及适用条件。对系绳控制机构进行了分类综述，给出了设计系绳控制机构需重点关注的问题。最后对空间绳系捕获技术的发展方向做了展望。