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。     

地球静止轨道卫星碰撞碎片短期演化风险分析

地球静止轨道(GEO)卫星与空间碎片发生碰撞后短期内会出现无地面观测数据的情况。为解决该问题,筛选了所有运行或穿越GEO区域的空间目标,分析了数值法和解析法在进行接近分析时的优劣势,给出了基于弦截法的接近分析数值求解方法,运用SDP4模型进行轨道预报。运用质量守恒和动量守恒对NASA标准解体模型进行修正,生成空间碎片信息。针对短期演化风险,在无连锁碰撞研究需求时进行假设,进而简化碰撞概率计算方法。对GEO区域内碎片的碰撞和穿越GEO区域碎片的碰撞2类事件进行分析,在碰撞完全解体和非完全解体2种条件下,分析3 d内碰撞产生的碎片对GEO区域的威胁程度。仿真实验结果表明:在完全解体的情形下,新产生的空间碎片3 d内与原有空间目标会发生100多次小于20 km的接近,最近距离降低到214.4 m。在无地面对新生成空间碎片观测数据的条件下,该研究为航天器规避机动提供参考,为下一步的长期演化分析提供理论借鉴。     

航天器撞击解体碎片的短期危害评估

讨论了航天器与短期碎片云碰撞概率的计算流程。基于碎片云中碎片的数量、航天器的横截面积和碰撞概率风险阈值,提出了“风险区域判据”的方法,用于快速判断筛选航天器是否存在与碎片云碰撞的风险。推导了基于NASA标准解体模型的碎片分离速度概率密度函数,建立了计算航天器与单颗碎片碰撞概率的时间积分算法。针对在计算航天器与整个碎片云碰撞概率时的数据量无限制增长问题,提出了近似简化的“准平均概率”方法,有效地解决了计算速度的瓶颈问题。分析讨论了航天器与碎片云的轨道误差对计算碰撞概率的影响。最后,采用仿真算例进行计算分析与验证。     

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。     

美俄卫星碰撞事件验证及其对我国卫星的影响分析

北京时间2009年2月11日0时55分,美国铱星-33和俄罗斯宇宙-2251两颗卫星在太空相撞,在所在的高度产生了大量新增空间碎片,使得空间碎片环境更加严峻,低轨航天器运行遭受空间碎片撞击的风险大幅增加。文章通过碰撞前后轨道数据分析,确认并验证了此次碰撞事件;利用事前轨道数据进行碰撞预警分析,得出碰撞的相关的参数;通过分析此次事件产生的新增碎片的轨道数据,进一步验证确认碰撞事件;从空间碎片密度和通量角度分析其时当前空间碎片环境产生的影响;通过新增碎片寿命计算分析其对空间碎片环境的长期的影响;从碰撞概率出发分析对航天器运行安全的威胁。分析结果表明：我国低轨卫星在一定程度上增大了空间碎片碰撞风险,需要进行在轨空间碎片碰撞预警,以确保我国卫星的安全运行。     

StarLink星座对空间安全态势的影响

针对StarLink星座部署后带来的空间安全问题，对StarLink星座构型仿真，利用碰撞概率的算法，从碰撞风险的角度分析了StarLink星座部署后对其他卫星在轨安全的影响。结果表明:StarLink星座部署对低轨航天器将带来较大的碰撞风险，碰撞风险比部署前提升一个量级，对535~555 km空间区域的航天器影响尤为突出，一旦产生碰撞碎片将带来更大的碰撞风险。通过分析提出了警示，并针对大型卫星星座带来的碰撞危险提供了应对建议。     

地球同步轨道卫星结构爆炸解体碎片的轨道仿真

为快速确定与预报卫星在轨爆炸解体产生的大量空间碎片的轨道,提出了一种基于ANSYS/AUTODYN、MATLAB、STK等多软件平台联合仿真分析卫星结构爆炸解体碎片运行轨道的方法。利用ANSYS/AUTODYN对典型薄壁圆柱模拟地球同步轨道卫星结构进行爆炸数值分析,得到碎片的数量、质量分布和速度特性信息。再利用MATLAB软件对卫星爆炸仿真得到的碎片参数进行处理,将处理后的数据导入到STK软件的通用摄动SGP4模型中,得出卫星爆炸碎片的早期轨道数据。最后对爆炸碎片的轨道分布、速度增量、轨道演化等进行分析。结果表明:该方法能满足大量爆炸碎片的轨道仿真要求,能有效提高碎片轨道信息转换效率,对目前难以跟踪的cm级以下碎片,也能提供相应的初始轨道数据,使用方便,通用性好。研究结果可为快速捕获卫星爆炸碎片,及时规避航天器碰撞风险提供参考。     

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。     

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。     

超高速碰撞数值模拟的工程算法模型

提出了双层板防护结构的超高速碰撞数值模拟的工程算法模型，采取理论分析、经验公式和数值模拟相结合的研究方法来模拟碎片云的产生，以及碎片云对结构的破毁过程。本模型中，碎片云的产生采用理论分析和经验公式得到，结构响应采用有限元动力学软件Dyna3D进行计算。数值模拟结果与文献中给出的破坏效果基本一致，说明提出的工程算法是可行的，模拟得到的结果能定性的描述相应的超高速碰撞的现象，得到基本正确的结果。     

Estimation of debris dispersion due to a space vehicle breakup during reentry

This paper studies the problem of the estimation of the extent of the airspace containing falling debris due to a space vehicle breakup. A precise propagation of debris to the ground is not practical for many reasons. There is insufficient knowledge of the initial state vector, ambient wind conditions, and the key parameters including the ballistic coefficients. In addition, propagation of all debris pieces to the ground would require extensive computer time. In this paper, a covariance propagation method is introduced for the estimation of debris dispersion due to a space vehicle breakup. The falling debris is simulated, and the data are analyzed to derive the probability of debris evolution in different altitude layers over time. The concept of positional probability ellipsoids is employed for the visualization of the results. Through a case study, it is shown that while the results of the covariance propagation method are in close agreement with those of the Monte Carlo method, the covariance propagation method is much more computationally efficient than the Monte Carlo method.     

地球静止轨道卫星撞击解体的数值模拟

分析了地球静止轨道（GE0）环内的物体现状,引入美国家航空航天局（NASA）的标准解体模型,给出了卫星撞击解体算法,编写了数值仿真软件,仿真研究了GEO卫星撞击解体形成碎片的特征及其轨道分布。结果表明：撞击会产生大量碎片,对空间环境造成长期的严重危害。研究结果对分析卫星撞击解体特性、保护空间环境有一定的参考价值。     

对美国宇航公司使用的轨道碎片模型的评价

文章介绍了碰撞程序和碎片程序,并进行了评价。前一个程序说明了碎片撞击的破裂特性;后一个程序给出了当一个空间物体进入碎片云时的撞击概率。     

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.     

空间碎片现状与清理

分析了空间碎片的严峻现状和空间碎片的10个来源,指出轨道碰撞是产生碎片最多的因素;介绍了空间碎片的观测方法、原理和观测系统的概况,包括正在兴建的观测系统——“空间篱笆”。最后,根据不同轨道高度和空间碎片的数量与大小,提出空间碎片清理原则、要求和9种清理方法。     

Evaluation of a satellite constellation for active debris removal

This paper analyzes an example of a three-dimensional constellation of debris removal satellites and proposes an effective constellation using a delta-V analysis that discusses the advisability of rendezvousing satellites with space debris. Lambert?s Equation was used to establish a means of analysis to construct a constellation of debris removal satellites, which has a limit of delta-V injection by evaluating the amount of space debris that can be rendezvoused by a certain number of removal satellite. Consequently, we determine a constellation of up to 38 removal satellites for debris removal, where the number of space debris rendezvoused by a single removal satellite is not more than 25, removing up to 584 pieces of debris total. Even if we prepare 38 removal satellites in their respective orbits, it is impossible to remove all of the space debris. Although many removal satellites, over 100 for example, can remove most of the space debris, this method is economically disproportionate. However, we can also see the removal satellites are distributed nearly evenly. Accordingly, we propose a practical two-stage strategy. The first stage is to implement emergent debris removal with the 38 removal satellites. When we find a very high probability of collision between a working satellite and space debris, one of the removal satellites in the constellation previously constructed in orbit initiates a maneuver of emergent debris removal. The second stage is a long-term space debris removal strategy to suppress the increase of space debris derived from collisions among the pieces of space debris. The constellation analyzed in this paper, which consists of the first 38 removal satellites, can remove half of the over 1000 dangerous space debris among others, and then the constellation increases the number of the following removal satellites in steps. At any rate, an adequate orbital configuration and constellation form is very important for both space debris removal and economic efficiency. Though the size of constellation of debris removal satellites would be small originally, such a constellation of satellites should be one of the initial constellations of removal satellites to ensure the safety of the future orbital environment.     

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.     

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.