Continuum Model for Space Debris Evolution with Account of Collisions and Orbital Breakups

The paper discusses the mathematical modeling of long-term orbital debris evolution taking into account mutual collisions of space debris particles of different sizes. Investigations and long-term forecasts of orbital debris environment evolution in low Earth orbits are essential for future space mission hazard evaluation and for adopting rational space policies and mitigation measures. The paper introduces a new approach to space debris evolution mathematical modeling based on continuum mechanics incorporating partial differential equations. This is an alternative to the traditional approaches of celestial mechanics incorporating ordinary differential equations to model fragments evolution. The continuum approach to orbital debris evolution modeling has essential advantages for describing the evolution of a large number of particles, because it replaces the traditional tracking of space objects by modeling the evolution of their density of distribution.     

An International Environmental Agreement for space debris mitigation among asymmetric nations

We investigate how ideas from the International Environmental Agreement (IEA) literature can be applied to the problem of space debris mitigation. Space debris pollution is similar to other international environmental problems in that there is a potential for a “tragedy of the commons” effect: individual nations bear all the cost of their mitigation measures but share only a fraction of the benefit. As a consequence, nations have a tendency to underinvest in mitigation. Coalitions of nations, brought together by IEAs, have the potential to lessen the tragedy of the commons effect by pooling the costs and benefits of mitigation. This work brings together two recent modeling advances: (i) a game theoretic model for studying the potential gains from IEA cooperation between nations with asymmetric costs and benefits, (ii) an orbital debris model that gives the societal cost that specific actions, such as failing to deorbit an inactive spacecraft, have on the environment. We combine these two models with empirical launch-share data for a “proof of concept” of an IEA for a single mitigation measure—deorbiting spacecraft at the end of operational lifetime. Simulations of empirically derived and theoretical launch distributions among nations suggest the possibility that voluntary coalitions can provide significant deorbiting gains relative to nations acting in the absence of an IEA agreement.     

Enhancement and Validation of the IDES Orbital Debris Environment Model

Orbital debris environment models are essential in predicting the characteristics of the entire debris environment, especially for altitude and size regimes where measurement data is sparse. Most models are also used to assess mission collision risk. The IDES (Integrated Debris Evolution Suite) simulation model has recently been upgraded by including a new sodium–potassium liquid coolant droplet source model and a new historical launch database. These and other features of IDES are described in detail. The accuracy of the IDES model is evaluated over a wide range of debris sizes by comparing model predictions to three major types of debris measurement data in low Earth orbit. For the large-size debris population, the model is compared with the spatial density distribution of the United States (US) Space Command Catalog. A radar simulation model is employed to predict the detection rates of mid-size debris in the field of view of the US Haystack radar. Finally, the small-size impact flux relative to a surface of the retrieved Long Duration Exposure Facility (LDEF) spacecraft is predicted. At sub-millimetre sizes, the model currently under-predicts the debris environment encountered at low altitudes by approximately an order of magnitude. This is because other small-size debris sources, such as paint flakes have not yet been characterised. Due to the model enhancements, IDES exhibits good accuracy when predicting the debris environment at decimetre and centimetre sizes. Therefore, the validated initial conditions and the high fidelity future traffic model enables IDES to make long-term debris environment projections with more confidence.     

Local debris congestion in the geosynchronous environment with population augmentation

Forecasting of localized debris congestion in the geostationary (GEO) regime is performed to investigate how frequently near-miss events occur for each of the longitude slots in the GEO ring. The present-day resident space object (RSO) population at GEO is propagated forward in time to determine current debris congestion conditions, and new probability density functions that describe where GEO satellites are inserted into operational orbits are harnessed to assess longitude-dependent congestion in “business-as-usual” launch traffic, with and without re-orbiting at end-of-life. Congestion forecasting for a 50-year period is presented to illustrate the need for appropriately executed mitigation measures in the GEO ring. Results indicate that localized debris congestion will double within 50 years under current 80% re-orbiting success rates.     

空间碎片环境的长期演化建模方法

针对空间碎片环境的长期演化问题，从宏观和微观两个方面，分别构建了碎片环境的整体演化模型和数值演化计算模型，并在此基础上研究了不同条件下碎片环境的长期演化分布特点，分析了碎片环境的稳定性和主要影响因素。低地球轨道碎片环境在未来200年内的演化结果表明，空间目标的相互碰撞解体，是空间碎片不断增加的主要因素；即使停止一切航天发射活动，空间碎片的数量仍在不断增加，表明低地球轨道空间碎片规模已经超越稳定临界点；进一步的发射活动会增强空间碎片环境演化的不稳定性，加剧“碰撞-目标解体-碰撞”反馈连锁碰撞效应。     

空间碎片环境现状与主动移除技术

概述了空间碎片环境现状和对航天活动的影响,讨论了空间碎片主动移除对保持空间碎片环境稳定的必要性。空间碎片研究重心先从防护转向减缓,再转到主动移除,最终是清洁空间。评述了空间碎片主动移除技术现状,指出天基激光主动移除空间碎片技术具有很好的工程应用潜力。     

空间碎片数据形式及轨道演化算法

根据建立空间碎片工程模型的需要,定义了一种描述单个空间碎片运行位置及其物理特性的数据形式。基于空间碎片运动规律给出了一种用于计算单个空间碎片运行时＂平均位置＂的演化算法。计算的演化结果与STK软件计算的标称轨道比较表明：该演化算法正确。     

基于计算机的低地球轨道航天器设计与观测的轨道碎片环境模型

文章介绍了一个半经验的基于计算机的轨道碎片模型。该模型将轨道环境简化为6个不同的倾角带,每个倾角带都有各自的半长轴和近地点分布及根据不同的碎片来源有其各自的尺寸分布。用碰撞概率方程将轨道碎片分布与航天器上的碎片通量或通过地面探测器视角的通量联系起来。经比较,碎片的半长轴、近地点和倾角分布与美国空间司令部大于10cm的碎片目录是一致的。对于较小的碎片,这些分布与地面望远镜、“干草堆”雷达的测量结果一致,同时也与LDEF卫星和航天飞机的测量结果一致。     

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.     

Biobjective planning of an active debris removal mission

The growth of the orbital debris population has been a concern to the international space community for several years. Recent studies have shown that the debris environment in Low Earth Orbit (LEO, defined as the region up to 2000 km altitude) has reached a point where the debris population will continue to increase even if all future launches are suspended. As the orbits of these objects often overlap the trajectories of satellites, debris create a potential collision risk. However, several studies show that about 5 objects per year should be removed in order to keep the future LEO environment stable. In this article, we propose a biobjective time dependent traveling salesman problem (BiTDTSP) model for the problem of optimally removing debris and use a branch and bound approach to deal with it.     

A model for the evolution of the on-orbit man-made debris environment

A model for the evolution of the low Earth orbit man-made debris population is presented and the results of several test cases discussed. Debris sources include normal operations in space, explosions occurring on spacecraft in orbit, and collisions between objects in orbit; the stochastic occurrence of these deposition events is modeled using Monte Carlo techniques. A technique for discriminating between objects populating long-life vs rapid-decay orbits is discussed and applied to the analysis of debris contributions from collisions of comparable sized objects. In varying degrees, each of the cases presented indicate there is cause for concern for spacecraft and space operations from the 1990s onward-man-made debris will play a role which may vary from presenting a considerable hazard to certain operations or certain spacecraft to effectively prohibiting the use of certain spaceccraft or space operations.     

The origins of the “Long-term Sustainability of Outer Space Activities” initiative at UN COPUOS

The success of space-based systems worldwide, providing services to society and satisfying defence and security needs, has led to a situation where outer space is increasingly crowded. In addition, the rapid proliferation of space debris threatens the safe utilization of outer space on the most commonly used orbits. Beyond the mitigation of the orbital debris threat, additional measures will be needed to ensure the safety and security of activities in outer space for the long-term. This article describes the initiative to introduce a new agenda item in the United Nations Committee on the Peaceful Uses of Outer Space (COPUOS), first presented to COPUOS delegations in 2007, which led to a formal decision in 2009. This in turn led to the establishment of a dedicated Working Group of the Scientific and Technical Sub-Committee in 2010, with a work plan leading to a report and associated recommendations in 2014. Some references are made to other initiatives affecting space security, such as the Russia–China draft treaty (PPWT) tabled at the Conference on Disarmament and the EU-proposed Code of Conduct.     

USA-193 decay predictions using public domain trajectory data and assessment of the post-intercept orbital debris cloud

In early 2008, the need arose to predict the orbital decay of the American spacecraft USA-193, whose characteristics, function and orbit were classified information. With no orbit data and independent Italian tracking capability available, we turned our attention on the orbits determined by a worldwide network of about 20 visual satellite observers. The orbits of USA-193 obtained from their visual observations were therefore used as the sole source of orbit information. Contrary to our expectations, this exercise was extremely successful and we learned a lot in the process. The orbits provided by the visual observers were very accurate for such a low satellite (although the minimum and very stable level of solar activity helped considerably); however, data gaps of a few days were sometimes possible, due to unfavorable pass geometry or weather and light conditions. In any case, the orbital period and the semimajor axis were so accurate that it was possible for us to obtain very good decay fits using special perturbation software, including various atmospheric density models together with all the other relevant perturbing accelerations. We were therefore able to estimate accurate values of the ballistic parameter and the resulting decay and reentry predictions were extremely stable. Amateur optical observations and images of USA-193 had also led to a rough estimation of the shape and sizes of the satellite, revealing that the solar arrays had never been deployed. With this information, and taking into account our estimates of the ballistic parameter, we obtained reasonable and consistent values of the spacecraft mass. Based on previous reentry fragmentation analyses, we were then able to guess the expected USA-193 casualty area, casualty expectancy, debris ground footprint and probability of impact in Italy. Lastly, after the decision by the US Government to destroy the satellite, we independently predicted the interception time windows and the post-event ground tracks. Following the successful spacecraft breakup, we analyzed the evolution of the resulting debris cloud and assessed its (very limited) adverse impact on the circumterrestrial environment.     

空间目标轨道信息软件平台的建设

空间目标轨道信息是空间态势感知的重要要素,是空间碰撞预警、空间碎片环境模型和许多空间应用的基础。因而,空间目标轨道确定成为空间态势感知的主要任务之一。文章介绍武汉大学测绘学院正在开发建设的空间目标轨道信息服务软件平台,该平台拥有的主要功能有:利用多源数据的卫星/空间碎片轨道确定(包括初轨确定)与预报、大气质量密度模型精化、空间碰撞预警和半解析法快速精密轨道传播等。文章还针对软件平台功能的研究进展进行了综述,介绍了软件平台发展规划。     

Compliance of disposal orbits with the French Space Operations Act: The Good Practices and the STELA tool

Space debris mitigation is one objective of the French Space Operations Act (FSOA), in line with Inter-Agency Space Debris Coordination Committee (IADC) recommendations, through the removal of non-operational objects from populated regions. At the end of their mission, space objects are to be placed on orbits that will minimize future hazards to space objects orbiting in the same region. The FSOA, which came into force in 2010, ensures that technical risks associated with space activities are properly mitigated. The Act confers CNES a central support role in providing technical expertise to government on regulations dealing with space operations. In order to address the compliance of disposal orbits with the law technical requirements, CNES draws up Good Practices as well as a dedicated tool, Semi-analytic Tool for End of Life Analysis (STELA).     

空间碎片减缓策略效果仿真

根据机构间空间碎片协调委员会(IADC)和欧空局(ESA)的空间碎片减缓要求,在建立航天发射、爆炸和碰撞模型,以及碎片演化机制的基础上,对常规发射(BAU)、禁止在轨爆炸(NO-EX)和全面减缓(MIT)三种空间碎片减缓策略条件下,对2000~2100年空间碎片环境进行了仿真计算。结果表明,禁止航天器在轨爆炸、对失效的卫星和火箭上面级实施离轨操作,以及在航天器的发射和运行中不产生或抛弃分离物等减缓措施是限制空间碎片数量增长的有效方法。     

空间超高速撞击碎片云前端速度的预测模型

文章利用一组二级轻气炮发射2017-T4 铝质球形弹丸撞击6061-T6单层铝板的地面试验数据,通过选择适当的函数模型,采用多元函数拟合的方法,得到了碎片云前端速度与靶板厚度、弹丸直径和弹丸速度关系的三元二阶多项式模型。再用另外一组数据对该模型进行检验,验证了其对碎片云前端速度具有较好的预测效果。将以上两组数据同样用于建立“无量纲化”模型进行碎片云前端速度预测,并与前述多项式模型的预测结果进行比较发现,该多项式模型预测的方均根误差及平均相对误差均明显优于“无量纲化”模型。该多项式模型可用于预测空间碎片撞击航天器产生的碎片云的前端速度,有助于航天器的空间碎片防护设计。     

Additional historical solid rocket motor burns

The use of orbital solid rocket motors (SRM) is responsible for the release of a high number of slag and Al₂O₃ dust particles which contribute to the space debris environment. This contribution has been modeled for the ESA space debris model MASTER (Meteoroid and Space Debris Terrestrial Environment Reference). The current model version, MASTER-2005, is based on the simulation of 1076 orbital SRM firings which mainly contributed to the long-term debris environment. SRM firings on very low earth orbits which produce only short living particles are not considered. A comparison of the modeled flux with impact data from returned surfaces shows that the shape and quantity of the modeled SRM dust distribution matches that of recent Hubble Space Telescope (HST) solar array measurements very well. However, the absolute flux level for dust is under-predicted for some of the analyzed Long Duration Exposure Facility (LDEF) surfaces. This indicates that some past SRM firings are not included in the current event database. Thus it is necessary to investigate, if additional historical SRM burns, like the retro-burn of low orbiting re-entry capsules, may be responsible for these dust impacts. The most suitable candidates for these firings are the large number of SRM retro-burns of return capsules. This paper focuses on the SRM retro-burns of Russian photoreconnaissance satellites, which were used in high numbers during the time of the LDEF mission. It is discussed which types of satellites and motors may have been responsible for this historical contribution. Altogether, 870 additional SRM retro-burns have been identified. An important task is the identification of such missions to complete the current event data base. Different types of motors have been used to de-orbit both large satellites and small film return capsules. The results of simulation runs are presented.     

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.     

Solution of the flyby problem for large space debris at sun-synchronous orbits

the paper considers the flyby problem related to large space debris (LSD) objects at low earth orbits. The data on the overall dimensions of known last and upper stages of launch vehicles makes it possible to single out five compact groups of such objects from the NORAD catalog in the 500–2000 km altitude interval. The orbits of objects of each group have approximately the same inclinations. The features of the mutual distribution of the orbital planes of LSD objects in the group are shown in a portrait of the evolution of deviations of the right ascension of ascending nodes (RAAN). In the case of the first three groups (inclinations of 71°, 74°, and 81°), the straight lines of relative RAAN deviations of object orbits barely intersect each other. The fourth (83°) and fifth (97°–100°) LSD groups include a considerable number of objects whose orbits are described by straight lines (diagonals), which intersect other lines many times. The use of diagonals makes it possible to significantly reduce the temporal and total characteristic velocity expenditures required for object flybys, but it complicates determination of the flyby sequence. Diagonal solutions can be obtained using elements of graph theory. A solution to the flyby problem is presented for the case of group 5, formed of LSD objects at sun-synchronous orbits.