地球静止轨道卫星碰撞碎片短期演化风险分析
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摘要
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。
In order to solve the collision warning problem without ground observation data in the short term after the collision between the geostationary(GEO) satellite and space debris, all spatial objects distributed in and through the GEO region are selected firstly. The numerical method is compared with the analytical method in terms of the close approach, and the numerical method based on the secant method is given. The orbit is forecasted by the use of the SDP4 model. The NASA standard breakup model is modified by mass conservation and momentum conservation to simulate debris' information. For the short-term evolution risk without the demand for chain collision research, assumptions are made, and the collision-probability's calculation is simplified. In the situations of collisions between GEO satellites with debris in and through the GEO region, the newly generated debris' threat to the GEO region in 3 days is analyzed under the conditions of complete breakup and incomplete breakup. Simulation results show that in the situation of complete breakup, the newly generated space debris will approach original space objects within 20 km for more than 100 times in 3 days, and the nearest distance is reduced to 214.4 m. Under the condition of no ground observation data for newly generated space debris, this study provides a reference for the spacecraft to avoid debris, and provides a theoretical reference for the following long-term evolution analysis.
In order to solve the collision warning problem without ground observation data in the short term after the collision between the geostationary(GEO) satellite and space debris, all spatial objects distributed in and through the GEO region are selected firstly. The numerical method is compared with the analytical method in terms of the close approach, and the numerical method based on the secant method is given. The orbit is forecasted by the use of the SDP4 model. The NASA standard breakup model is modified by mass conservation and momentum conservation to simulate debris' information. For the short-term evolution risk without the demand for chain collision research, assumptions are made, and the collision-probability's calculation is simplified. In the situations of collisions between GEO satellites with debris in and through the GEO region, the newly generated debris' threat to the GEO region in 3 days is analyzed under the conditions of complete breakup and incomplete breakup. Simulation results show that in the situation of complete breakup, the newly generated space debris will approach original space objects within 20 km for more than 100 times in 3 days, and the nearest distance is reduced to 214.4 m. Under the condition of no ground observation data for newly generated space debris, this study provides a reference for the spacecraft to avoid debris, and provides a theoretical reference for the following long-term evolution analysis.
引文
[1] 李怡勇, 李智, 沈怀荣. 地球静止轨道卫星撞击解体的数值模拟[J]. 上海航天, 2011, 28(4): 47-72.
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[3] MARTIN C, WALKER R, KLINKRAD H. The sensitivity of the ESA DELTA model[J]. Space Debris, 2004, 34(5): 969-974.
[4] LIOU J C, HALL D, KRISKO P, et al. Legend:a three-dimensional LEO-to-GEO debris evolutionary model[J]. Space Debris, 2004, 34(5): 981-986.
[5] DOLADO J C, PEREZ R, COSTANZO D, et al. Introducing MEDEE:a new orbital debris evolutionary model[C]// 6th European Conference on Space Debris. 2013: 978-984.
[6] RADTKE J,STOLL E. Comparing long-term projections of the space debris environment to real world data-looking back to 1990[J]. Acta Astronautic, 2016, 127: 482-490
[7] 刘付成, 朱东方, 黄静. 空间飞行器动力学与控制研究综述[J]. 上海航天, 2017, 34(2): 1-29.
[8] 王若璞. 空间碎片环境模型研究[D]. 郑州:信息工程大学, 2010.
[9] KESSLER D J. Collision frequency of artificial satellites: the creation of a debris belt[J]. Journal of Geophysical Research, 1978, 6: 2637-2646.
[10] 王东方. 空间碎片环境预测算法研究[D]. 哈尔滨:哈尔滨工业大学, 2014.
[11] 白显宗, 陈磊, 唐国金. 基于显式表达式的空间目标最大碰撞概率分析[J]. 宇航学报, 2010, 31(3): 880-887.
[12] 白显宗. 空间目标碰撞预警中的碰撞概率问题研究[D]. 长沙:国防科学技术大学, 2008.
[13] 霍俞蓉, 李智, 韩蕾. 基于拉普拉斯变换的空间目标碰撞概率计算方法[J]. 北京航空航天大学学报, 2018, 44(4): 810-819.
[14] WANG D F, PANG B J, XIAO W K, et al. GEO objects spatial density and collision probability in the earth-centered earth-fixed(ECEF) coordinate system[J]. Acta Astronautica, 2016, 118: 218-223.
[15] 黄铎, 陈兰平, 王风. 数值分析[M]. 北京:科学出版社, 2000: 200-222.
[16] 封建湖, 车刚明, 聂玉峰. 数值分析原理[M]. 北京:科学出版社, 2001: 209-213.
[17] 陈磊, 白显宗, 梁彦刚. 空间目标轨道数据应用:碰撞预警与态势分析[M]. 北京:国防工业出版社, 2015: 99-100.
[18] 周新耀, 陶勇鹏, 曾亮,等. 空间轨道交会非线性优化方法研究[J]. 上海航天, 2018, 35(1): 54-58.
[19] DAVID A. Fundamentals of astrodynamics and application[M]. 2nd ed. EI Segundo: Microcosm Press, 2004: 20-25.
[20] HOST F R, ROEHRICH R L. Space track report No.3: models for propagation of norad element sets[R]. Peterson: Aerospace Defense Command, United States Air Force, 1980: 1-79.
[21] 李彬. 空间碎片快速精密轨道确定与预报若干关键问题研究[D]. 武汉:武汉大学, 2017.
[22] 贺波勇, 顾绍景, 黄海兵,等. 中秋节载人登月任务窗口与转移轨道设计研究[J]. 上海航天, 2017, 34(5): 9-15.
[23] CHAN K. Collision probability analysis for earth orbiting satellites[J]. Space Cooperation into the 21st Century, 1997, 14(6): 1033-1048.
[24] CHAN F K. Spacecraft collision probability[M]. El Segundo, CA: Aerospace Press, 2008: 34-56.
[25] 齐跃, 李怡勇, 来嘉哲. 航天器碰撞解体模型分析比较[J]. 兵工自动化, 2018, 37(2): 74-77.
[2] LEWIS H G, SWINERD G, WILLIAMS N, et al. Damage: a dedicated geo debris model framework[C]// Proceedings of the 3rd European Conference on Space Debris. 2001: 373-378.
[3] MARTIN C, WALKER R, KLINKRAD H. The sensitivity of the ESA DELTA model[J]. Space Debris, 2004, 34(5): 969-974.
[4] LIOU J C, HALL D, KRISKO P, et al. Legend:a three-dimensional LEO-to-GEO debris evolutionary model[J]. Space Debris, 2004, 34(5): 981-986.
[5] DOLADO J C, PEREZ R, COSTANZO D, et al. Introducing MEDEE:a new orbital debris evolutionary model[C]// 6th European Conference on Space Debris. 2013: 978-984.
[6] RADTKE J,STOLL E. Comparing long-term projections of the space debris environment to real world data-looking back to 1990[J]. Acta Astronautic, 2016, 127: 482-490
[7] 刘付成, 朱东方, 黄静. 空间飞行器动力学与控制研究综述[J]. 上海航天, 2017, 34(2): 1-29.
[8] 王若璞. 空间碎片环境模型研究[D]. 郑州:信息工程大学, 2010.
[9] KESSLER D J. Collision frequency of artificial satellites: the creation of a debris belt[J]. Journal of Geophysical Research, 1978, 6: 2637-2646.
[10] 王东方. 空间碎片环境预测算法研究[D]. 哈尔滨:哈尔滨工业大学, 2014.
[11] 白显宗, 陈磊, 唐国金. 基于显式表达式的空间目标最大碰撞概率分析[J]. 宇航学报, 2010, 31(3): 880-887.
[12] 白显宗. 空间目标碰撞预警中的碰撞概率问题研究[D]. 长沙:国防科学技术大学, 2008.
[13] 霍俞蓉, 李智, 韩蕾. 基于拉普拉斯变换的空间目标碰撞概率计算方法[J]. 北京航空航天大学学报, 2018, 44(4): 810-819.
[14] WANG D F, PANG B J, XIAO W K, et al. GEO objects spatial density and collision probability in the earth-centered earth-fixed(ECEF) coordinate system[J]. Acta Astronautica, 2016, 118: 218-223.
[15] 黄铎, 陈兰平, 王风. 数值分析[M]. 北京:科学出版社, 2000: 200-222.
[16] 封建湖, 车刚明, 聂玉峰. 数值分析原理[M]. 北京:科学出版社, 2001: 209-213.
[17] 陈磊, 白显宗, 梁彦刚. 空间目标轨道数据应用:碰撞预警与态势分析[M]. 北京:国防工业出版社, 2015: 99-100.
[18] 周新耀, 陶勇鹏, 曾亮,等. 空间轨道交会非线性优化方法研究[J]. 上海航天, 2018, 35(1): 54-58.
[19] DAVID A. Fundamentals of astrodynamics and application[M]. 2nd ed. EI Segundo: Microcosm Press, 2004: 20-25.
[20] HOST F R, ROEHRICH R L. Space track report No.3: models for propagation of norad element sets[R]. Peterson: Aerospace Defense Command, United States Air Force, 1980: 1-79.
[21] 李彬. 空间碎片快速精密轨道确定与预报若干关键问题研究[D]. 武汉:武汉大学, 2017.
[22] 贺波勇, 顾绍景, 黄海兵,等. 中秋节载人登月任务窗口与转移轨道设计研究[J]. 上海航天, 2017, 34(5): 9-15.
[23] CHAN K. Collision probability analysis for earth orbiting satellites[J]. Space Cooperation into the 21st Century, 1997, 14(6): 1033-1048.
[24] CHAN F K. Spacecraft collision probability[M]. El Segundo, CA: Aerospace Press, 2008: 34-56.
[25] 齐跃, 李怡勇, 来嘉哲. 航天器碰撞解体模型分析比较[J]. 兵工自动化, 2018, 37(2): 74-77.