﻿ 基于驻留时间比的近地空间碎片环境建模
 文章快速检索 高级检索

1. 北京航空航天大学 宇航学院, 北京 100191;
2. 北京航天飞行控制中心 航天飞行动力学技术重点实验室, 北京 100094;
3. 北京航空航天大学 宇航学院, 北京 100191

Space debris environment modeling in low earth orbit based on resident time ratio
Shen Jingsong1, Liu Ye2 , Hu Songjie2, Han Chao3
1. School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. Science and Technology on Aerospace Flight Dynamics Laboratory, Beijing Aerospace Control Centre, Beijing 100094, China;
3. School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:For the distribution analysis of space debris in the low earth orbit, a new statistical modeling method for space debris was proposed based on the debris resident time in the space grid. Polynomial fitting and extraction techniques for debris resident time statistic were introduced to obtain the basic modeling datum. Then, the distribution and evolution regularity of debris in low earth orbit was studied by virtue of the polynomial prediction, polynomial interpretation, time serials analyses and so on according to the modeling datum storage. Finally, a modeling case utilizing the two line elements (TLEs) was given. The modeling results were validated by the ORDEM2000 model. Some subtle distribution regularities were deduced. The modeling method and analysis results are helpful for researches on orbit designing, collision risk evaluation and collision defense for spacecraft long-term flying in the low earth orbit.
Key words: space debris     modeling     low earth orbit     grid     polynomial

1 碎片环境建模流程 1.1 碎片初选

1.2 建模流程

 图 1 空间碎片环境建模流程Fig. 1 Modeling diagram for space debris environment

1) 根据数据更新频率和精度进行轨道预报,并计算与该段轨道交会的网格及交会起止时间;

2) 在基本时间单元内(季度),统计碎片在各网格内的驻留(飞行)时间和通量,获得工程模式所需的基础数据源;

3) 根据应用需求,内嵌一系列数据插值和时间序列分析等方法,输出应用模型所需的结果. 2 碎片环境建模方法 2.1 碎片分布

1) ti1,sti2,s均在区间内,此时轨道按高度可划分单调区间[ti,s,ti1,s],[ti1,s,ti2,s]与[ti2,s,ti+1,s];

2) ti+1,s不在区间内,此时轨道按高度可划分单调区间[ti,s,ti2,s]与[ti2,s,ti+1,s];

3) ti2,s不在区间内,此时轨道按高度可划分单调区间[ti,s,ti1,s]与[ti1,s,ti+1,s];

4) ti1,sti2,s均不在区间内,此时轨道按高度为一个单调区间[ti,j,ti+1,j].

2.2 模型数据

2.3 模型分析

ORDEM2000模型可以按年度和尺度给出碎片的空间密度分布,其中大于10 cm的碎片与TLE有类似的测量数据来源,因此,将RTS与其进行对比验证.

 图 2 本文模型(RTS)与ORDEM2000模型的 空间密度对比Fig. 2 Space debris density according to RTS and ORDEM2000

 图 3 驻留时间比的经纬度分布情况 空间密度对比Fig. 3 Geodetic distribution of the residual time ration

 图 4 驻留时间比的纬度分布情况 空间密度对比Fig. 4 Latitude distribution of the residual time ration

 图 5 碎片空间密度随时间的变化情况 空间密度对比Fig. 5 Space debris density changes with time
4 结 论

 [1] 王海福,冯顺山,刘有英.空间碎片导论[M].北京:科学出版社,2010 Wang Haifu,Feng Shunshan,Liu Youying.Introduction of space debris[M].Beijing:Science Press,2010(in Chinese) [2] Johnson N L.History of on-orbit satellite fragmentations[R].NASA/TM-2008-214779,2008 [3] 彭科科.空间碎片环境探测数据处理方法及工程模型建模方法研究[D].哈尔滨:哈尔滨工业大学,2010 Peng Keke.Research on sapce debris environment exploration data processing measure and engineering modeling method[D].Harbin:Harbin Institute of Technology,2010(in Chinese) Cited By in Cnki [4] 张平平.近地轨道空间碎片轨道参数分布规律研究[D].哈尔滨:哈尔滨工业大学,2006 Zhang Pingping.Research on space debris orbital parameter distribution uule in LEO[D].Harbin:Harbin Institute of Technology,2006(in Chinese) Cited By in Cnki (8) [5] 唐颀,庞宝君,张伟.空间碎片环境工程模式参数分析[J].中国空间科学技术,2004,24(5):22-27 Tang Qi,Pang Baojun,Zhang Wei.Analysis of the parameters in space debris environment engineering model[J].Chinese Space Science and Technology,2004,24(5):22-27(in Chinese) Cited By in Cnki (5) [6] Fukushige S,Akahoshi Y,Kitazawa Y.Comparison of debris environment models:ORDEM2000,MASTER2001 and MASTER2005[J].IHI Engineering Review,2007,40(1):31-41 Click to display the text [7] Liou J C.The new NASA orbital debris engineering model [R].ORDEM2000,NASA/TP-2002-210780,2002 Click to display the text [8] Liou J C.NASA's ORDEM2010 status[C]//28th Inter-agency Debris Coordination Committee Meeting(IADC).Trivandrum,India:NASA,2010:1-20 Click to display the text [9] 王海福,余庆波,刘有英.空间碎片碰撞风险评估系统[J].北京理工大学学报,2008,28(12):1039-1042 Wang Haifu,Yu Qingbo,Liu Youying.Orbital debris risk assessment system[J].Transactions of Beijing Institute of Technology,2008,28(12):1039-1042(in Chinese) Cited By in Cnki (4) | Click to display the text [10] Xu X L,Xiong Y Q.A research on the collision probability calculation of space debris for nonlinear relative motions[J].Chinese Astronomy and Astrophysics,2011(35):304-317 Click to display the text [11] 《数学手册》编写组.数学手册[M].北京:高等教育出版社,2010:87-89 "Handbook of Mathematics" Writing Group.Handbook of mathematics [M].Beijing:Higher Education Press,2010:87-89(in Chinese) [12] Klinkrad H.Space debris-models and risk analysis[M].New York:Springer & Praxis,2006 [13] 王正明,易东云.测量数据建模与参数估计[M].长沙:国防科技大学出版社,1996 Wang Zhengming,Yi Dongyun.Instrumental data modeling and parameter estimation[M].Changsha:University of National Defence Technology Press,1996(in Chinese) [14] Felix R,Ronald L.Space track report No.3:models for propagation of NORAD element sets[R].Peterson:Aerospace Defense Command,United States Air Force,1980 [15] Levit C,Marshall W.Improved orbit predictions using two-line elements[J].Advances in Space Research,2011,47(7):1107-1115 Click to display the text

#### 文章信息

Shen Jingsong, Liu Ye, Hu Songjie, Han Chao

Space debris environment modeling in low earth orbit based on resident time ratio

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(11): 1512-1517.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0716