利用精化误差进行危险交会分析

空间碎片碰撞预警工作主要针对的是可监测的较大空间碎片, 预测航天器与碎片之间的碰撞风险, 并根据一定的预警判据来评估风险的大小, 进而做出合理的轨道规避决策. 碰撞概率是碰撞风险评估的重要依据. 复合体尺寸、交会距离和误差是影响碰撞概率的三个决定性因素. 当复合体尺寸与交会距离差别不大时, 误差因素对碰撞概率结果起着决定性的作用. 在利用整天误差计算碰撞概率的基础上, 提出了利用精化误差计算碰撞概率的方法, 在危险交会分析中取得了良好的效果.      

基于解体事件的空间碎片轨道演化算法研究

针对航天器解体事件所生成的空间碎片的演化过程,进行了数学分析,确定了新生成的空间碎片的速度增量,在该增量作用下碎片轨道会发生变更,本文根据该增量得出了空间碎片在轨道变更后的轨道根数,分析了在大气阻力摄动作用下,空间碎片的数目和轨道分布的演化情况,给出了相关结果,结果表明此算法可行。     

Orbital debris–debris collision avoidance

We focus on preventing collisions between debris and debris, for which there is no current, effective mitigation strategy. We investigate the feasibility of using a medium-powered (5 kW) ground-based laser combined with a ground-based telescope to prevent collisions between debris objects in low-Earth orbit (LEO). The scheme utilizes photon pressure alone as a means to perturb the orbit of a debris object. Applied over multiple engagements, this alters the debris orbit sufficiently to reduce the risk of an upcoming conjunction. We employ standard assumptions for atmospheric conditions and the resulting beam propagation. Using case studies designed to represent the properties (e.g. area and mass) of the current debris population, we show that one could significantly reduce the risk of nearly half of all catastrophic collisions involving debris using only one such laser/telescope facility. We speculate on whether this could mitigate the debris fragmentation rate such that it falls below the natural debris re-entry rate due to atmospheric drag, and thus whether continuous long-term operation could entirely mitigate the Kessler syndrome in LEO, without need for relatively expensive active debris removal.     

空间碎片预警中的碰撞概率方法研究

由于空间碎片对飞行在地球轨道上的航天器危害日益严重,所以必须采取一些有效的防护措施,对于那些直径大于10 cm的碎片,通常是采用主动规避的方法来进行防护.为了避免传统的Box判据造成的过多错误预警,碰撞概率模型开始被应用于空间碎片预警,本文以空间站为例,将碰撞概率方法与传统Box区域判定法进行比较,介绍碰撞概率计算模型的建立方法,基于位置误差矩阵的碰撞概率Pc的算法,并针对实际交会事例进行了计算和分析.      

航天器微流星体及空间碎片环境与风险分析

微流星体及空间碎片的高速撞击威胁着长寿命、大尺寸航天器的安全运行 ,导致其严重的损伤和灾难性的失效。文章对低地球轨道微流星体及空间碎片环境进行了分析 ,给出了微流星体及空间碎片对航天器威胁方向的确定方法 ,得到了空间碎片撞击航天器相对撞击角的概率分布以及地球对微流星体遮挡的影响。编制了风险分析软件 ,以采用单防护屏防护结构的柱状低地球轨道航天器为例进行风险分析。     

基于驻留时间比的近地空间碎片环境建模

为分析近地空间碎片的分布规律,提出了一种以碎片在空间网格内驻留时间为基础的碎片环境统计建模方法.该方法利用多项式拟合和求根方法统计碎片在空间网格内的停留时间,获取模型基础数据,并据此采用多项式预测、插值和时间序列分析等技术,综合分析空间碎片的分布与演化规律.给出了一个基于双行根数(TLE,Two Line Elements)数据的建模实例,该实例通过了ORDEM2000模型的对比验证,并获得了一些更精细的近地空间碎片环境特征.所得建模方法和分析结论可为长期运行的近地航天器轨道设计、碰撞风险评估及防护等提供技术支撑.     

Chebyshev不等式在空间碎片碰撞概率置信度中的应用

空间碎片的碰撞预警与规避能有效避免碰撞事件的发生.碰撞概率是碰撞预警的主要判据,也是航天器规避机动决策的主要依据.由于计算碰撞概率的各相关参数带有误差,导致计算得到的碰撞概率值并不准确,难以做出规避机动决策,因此评估碰撞概率值的可信程度是亟需解决的问题.本文给出了一种碰撞概率置信度的计算方法,利用各影响参数的标准差,通过误差传递的方法计算碰撞概率的标准差,结合单边Chebyshev不等式,给出碰撞概率值大于10-4阈值时的置信度,并结合实际案例进行了分析.      

基于雷诺数的大气阻力模型在飞行器再入预报中的应用

随着对空间技术服务需求的增加和空间碎片主动移除技术的实现,未来空间碎片将以数量多、质量大、难分解等特点频繁再入大气层,给地面人员和财产安全造成更多威胁.因此,亟需对火箭体等大型航天器的大气再入进行预警,然而因缺乏合适的大气阻力系数模型难以实现高精度的大气再入预报.为此,在简化航天器模型的基础上引入基于雷诺数的大气动力模...     

Analysis of the orbit lifetime of CubeSats in low Earth orbits including periodic variation in drag due to attitude motion

It is estimated that more than 22,300 human-made objects are in orbit around the Earth, with a total mass above 8,400,000 kg. Around 89% of these objects are non-operational and without control, which makes them to be considered orbital debris. These numbers consider only objects with dimensions larger than 10 cm. Besides those numbers, there are also about 2000 operational satellites in orbit nowadays. The space debris represents a hazard to operational satellites and to the space operations. A major concern is that this number is growing, due to new launches and particles generated by collisions. Another important point is that the development of CubeSats has increased exponentially in the last years, increasing the number of objects in space, mainly in the Low Earth Orbits (LEO). Due to the short operational time, CubeSats boost the debris population. One of the requirements for space debris mitigation in LEO is the limitation of the orbital lifetime of the satellites, which needs to be lower than 25 years. However, there are space debris with longer estimated decay time. In LEÓs, the influence of the atmospheric drag is the main orbital perturbation, and is used in maneuvers to increment the losses in the satellite orbital energy, to locate satellites in constellations and to accelerate the decay.The goal of the present research is to study the influence of aerodynamic rotational maneuver in the CubeSat?s orbital lifetime. The rotational axis is orthogonal to the orbital plane of the CubeSat, which generates variations in the ballistic coefficient along the trajectory. The maneuver is proposed to accelerate the decay and to mitigate orbital debris generated by non-operational CubeSats. The panel method is selected to determine the drag coefficient as a function of the flow incident angle and the spinning rate. The pressure distribution is integrated from the satellite faces at hypersonic rarefied flow to calculate the drag coefficient. The mathematical model considers the gravitational potential of the Earth and the deceleration due to drag. To analyze the effects of the rotation during the decay, multiple trajectories were propagated, comparing the results obtained assuming a constant drag coefficient with trajectories where the drag coefficient changes periodically. The initial perigees selected were lower than 400 km of altitude with eccentricities ranging from 0.00 to 0.02. Six values for the angular velocity were applied in the maneuver. The technique of rotating the spacecraft is an interesting solution to increase the orbit decay of a CubeSat without implementing additional de-orbit devices. Significant changes in the decay time are presented due to the increase of the mean drag coefficient calculated by the panel method, when the maneuver is applied, reducing the orbital lifetime, however the results are independent of the angular velocity of the satellite.     

卫星发射对空间碎片环境影响分析

未来航天发射情况直接影响空间碎片环境，必须对其进行合理规划，以维护外空长期可持续发展.利用中国自主建立的空间碎片长期演化模型（SOLEM），结合蒙特卡洛方法，量化分析了空间物体发射数量、发射质量、发射面积等因子对未来空间碎片环境的影响，进一步研究了大型星座造成的未来空间物体碰撞次数和碎片数量的增加.仿真结果可为合理规划未来的航天发射规模提供理论依据.      

柱状弹丸撞击防护屏形成碎片云材料状态特性研究

微流星体及空间碎片的高速撞击威胁着长寿命、大尺寸航天器的安全运行，导致其严重的损伤和灾难性的失效。为精确估计微流星体及空间碎片高速撞击防护屏所产生碎片云对舱壁的损伤，必须确定碎片云中三种状态材料的特性，建立了碎片云特性分析模型，分别计算了柱状弹丸撞击防护屏所产生碎片云以及碎片云中弹丸和防护屏材料三种状态物质的质量分布。通过计算分析可见，弹丸以不同速度撞击防护屏所产生碎片云三种状态物质的质量分布是不同的，速度增大，液化和气化增强，对靶件的损伤小。而在速度小于7km/s时，碎片云以固体碎片的形式存在，对靶件的损伤大。     

Progress in Space Debris Research

During recent years, A de-orbit disposal of SinoSat 2 satellite and the depletion of the residual propellant after SC/LV separation for all LM-4 series launch vehicles were carried out. Stuffed Whipple Shields based on hypervelocity impact particles were developed. Routine observation and collision avoidance were performed. The main progress in space debris research will be introduced from three aspects: mitigation, spacecraft protection, observation and collision avoidance.      

Atmospheric drag modelling for orbital micro-debris at LEO altitudes

Data from satellite impact experiments and the scanning of recovered spacecraft offers an extended timebase to examine, using a consistent methodology, the microparticle fluxes. New penetration data from the TiCCE experiment on Eureca /1, 2/ adds to this database and shows that - despite an expected growth in the micro-debris flux - the observed flux is not greater than either LDEF or SMM. The question arises: “is this consistent with the micro particle flux being dominated by space debris or by meteoroids”.

To assist this assessment, numerical modelling using the Gear method /3/ of explicit time integration of the atmospheric drag lifetime of micron dimensioned orbital debris in both circular (LEO) and eccentric (GTO) orbits has been performed for the relevant space exposures. Results are applied to the data to examine whether the recent variations in flux can be attributed to varying levels of, orbital micro-debris caused by atmospheric drag and its changes during the solar cycle.     

弹丸撞击防护屏形成碎片云速度特性研究

微流星及空间碎片的高速撞击威胁着长寿命，大尺寸航天器的安全运行，导致其严重的损伤和灾难性的失效，为精确估计微流星及空间碎片主速撞击防护屏产生的碎片对舱壁的损伤，必须确定碎片云速度特性。文章在冲量和能量守恒的基础上，建立了碎片速度性分析模型，研究了碎片云的速度特性，得到了碎片云材料传播及碎片云喷射角随弹丸撞击速度的变化规律。     

Micro-meteoroids and space debris impact risk assessment for the ConeXpress satellite using ESABASE2/Debris

Micro-meteoroid and space debris impact risk assessments are performed to investigate the risk from hypervelocity impacts to sensitive spacecraft sub-systems. For these analyses, ESA’s impact risk assessment tool ESABASE2/Debris is used. This software tool combines micro-particle environment models, damage equations for different shielding designs and satellite geometry models to perform a detailed 3D micro-particle impact risk assessment. This paper concentrates on the impact risk for exposed pressurized tanks. Pressure vessels are especially susceptible to hypervelocity impacts when no protection is available from the satellite itself. Even small particles in the mm size range can lead to a fatal burst or rupture of a tank when impacting with a typical collision velocity of 10–20 km/s. For any space mission it has to be assured that the impact risk is properly considered and kept within acceptable limits. The ConeXpress satellite mission is analysed as example. ConeXpress is a planned service spacecraft, intended to extend the lifetime of telecommunication spacecraft in the geostationary orbit. The unprotected tanks of ConeXpress are identified as having a high failure risk from hypervelocity impacts, mainly caused by micro-meteoroids. Options are studied to enhance the impact protection. It is demonstrated that even a thin additional protective layer spaced several cm from the tank would act as part of a double wall (Whipple) shield and greatly reduce the impact risk. In case of ConeXpress with 12 years mission duration the risk of impact related failure of a tank can be reduced from almost 39% for an unprotected tank facing in flight direction to below 0.1% for a tank protected by a properly designed Whipple shield.     

Predicting the vulnerability of spacecraft components: Modelling debris impact effects through vulnerable-zones

The space environment around the Earth is populated by more than 130 million objects of 1 mm in size and larger, and future predictions shows that this amount is destined to increase, even if mitigation measures are implemented at a far better rate than today. These objects can hit and damage a spacecraft or its components. It is thus necessary to assess the risk level for a satellite during its mission lifetime. Few software packages perform this analysis, and most of them employ time-consuming ray-tracing methodology, where particles are randomly sampled from relevant distributions. In addition, they tend not to consider the risk associated with the secondary debris clouds. The paper presents the development of a vulnerability assessment model, which relies on a fully statistical procedure: the debris fluxes are directly used combining them with the concept of vulnerable zone, avoiding the random sampling the debris fluxes. A novel methodology is presented to predict damage on internal components. It models the interaction between the components and the secondary debris cloud through basic geometrical operations, considering mutual shielding and shadowing between internal components. The methodologies are tested against state-of-the-art software for relevant test cases, comparing results on external structures and internal components.     

空间物体解体碎片云的长期演化建模与分析

空间碎片云由空间物体解体产生的大量空间碎片组成,由于其相对集中地分布在有限的空间内,将会对临近航天器产生较大的碰撞威胁。为了分析解体碎片云长期分布特点,文章首先利用数值积分方法对空间碎片云短期分布规律进行了研究;在此基础上,针对处于环状分布的碎片云,根据碎片所在的轨道高度和具有的面质比值,将碎片划分到不同分组,以每个组作为研究对象,建立了描述碎片云在大气阻力作用下的解析演化模型。模型避免了对单个解体碎片的运动状态进行积分,可大大降低对计算资源和计算时间的需求。考虑在高度为1422km 圆轨道上运行的物体,解体产生了1780个碎片,利用解析演化模型得到碎片云未来50年内的演化分布状态。数值结果表明,碎片云的峰值密度在解体物体轨道高度附近,并在大气阻力作用下向更大高度区间内扩散;较低高度区间内碎片密度具有先增加,然后在大气阻力作用下不断减少的特点。     

Modeling spatial density in low earth orbits using wavelets and random search

The events that occurred after 2007 such as Chinese anti-satellite test, explosion of Briz-M upper stage, break up of cosmos-2421 and collision of cosmos-2251 with Iridium-33 satellites have completely changed the spatial density patterns in low earth orbits. This has increased the risk of collision between active satellites and debris created by them. Aftermath, the risk assessment of possible collisions called as conjunction analysis of working satellites from day to day has become more crucial. Spatial density models are useful in understanding the long-term likelihood of a collision in a particular region of space and helpful in pre-launch orbit planning. In this paper we present an algorithmic procedure for automatically estimating exact model parameters corresponding to the peak location and number of peaks using wavelets that will speed up the parameter estimation process for the models with peaks.     

The ratio of hazardous meteoroids to orbital debris in near-Earth space

Orbital debris is known to pose a substantial threat to Earth-orbiting spacecraft at certain altitudes. For instance, the orbital debris flux near Sun-synchronous altitudes of 600–800 km is particularly high due in part to the 2007 Fengyun-1C anti-satellite test and the 2009 Iridium-Kosmos collision. At other altitudes, however, the orbital debris population is minimal and the primary impactor population is not man-made debris particles but naturally occurring meteoroids. While the spacecraft community has some awareness of the risk posed by debris, there is a common misconception that orbital debris impacts dominate the risk at all locations. In this paper, we present a damage-limited comparison between meteoroids and orbital debris near the Earth for a range of orbital altitude and inclination, using NASA’s latest models for each environment. Overall, orbital debris dominates the impact risk between altitudes of 600 and 1300 km, while meteoroids dominate below 270 km and above 4800 km.     

Physical properties and long-term evolution of the debris clouds produced by two catastrophic collisions in Earth orbit

The population of cataloged orbital debris increased by approximately 40% in just a couple of years, from January 2007 to February 2009. This was due to two collisions in space, which involved the catastrophic destruction of three intact satellites (Fengyun 1C, Cosmos 2251 and Iridium 33) in high inclination orbits. Both events occurred in the altitude range already most affected by previous launch activity and breakup events, thus boosting the cataloged population in low Earth orbit by more than 60%.