轨道分析解的改进方法及其应用

doi:10.3969/j.issn.1001-506X.2020.02.23

系统工程与电子技术 ›› 2020, Vol. 42 ›› Issue (2): 427-433.doi: 10.3969/j.issn.1001-506X.2020.02.23

轨道分析解的改进方法及其应用

杨志涛^1,^2,³(), 刘静^1,³(), 刘林^3,^4,⁵()

1. 中国科学院国家天文台, 北京 100012
2. 中国科学院大学天文与空间科学学院, 北京 100049
3. 国家航天局空间碎片监测与应用中心, 北京 100012
4. 南京大学天文与空间科学学院, 江苏南京 210093
5. 南京大学空间环境与航天动力学研究所, 江苏南京 210093

收稿日期:2019-08-30 出版日期:2020-02-01 发布日期:2020-01-23
作者简介:杨志涛(1986-),男,助理研究员,博士研究生,主要研究方向为航天器轨道力学、近地天体预警及防御。E-mail:ztyang@nao.cas.cn|刘静(1970-),女,研究员,博士,主要研究方向为空间碎片监测与预警技术。E-mail:liujing@nao.cas.cn|刘林(1936-),通信作者,男,教授,博士,主要研究方向为天体力学、航天器轨道力学。E-mail:lliu@nju.edu.cn
基金资助:
国家自然科学基金(11803052);空间碎片研究专项资助课题(KJSP2016010101);空间碎片研究专项资助课题(KJSP2016020201);空间碎片研究专项资助课题(KJSP2016020301);空间碎片研究专项资助课题(KJSP2016020101)

Improved method of orbit analytical solution and its application

Zhitao YANG^1,^2,³(), Jing LIU^1,³(), Lin LIU^3,^4,⁵()

1. National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
2. School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China
3. Space Debris Observation and Data Application Center, China National Space Administration, Beijing 100012, China
4. School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China
5. Institute of Space Environment and Astronautics, Nanjing University, Nanjing 210093, China

Received:2019-08-30 Online:2020-02-01 Published:2020-01-23
Supported by:
国家自然科学基金(11803052);空间碎片研究专项资助课题(KJSP2016010101);空间碎片研究专项资助课题(KJSP2016020201);空间碎片研究专项资助课题(KJSP2016020301);空间碎片研究专项资助课题(KJSP2016020101)

摘要/Abstract

摘要：

主要介绍一种通过改进各类轨道摄动项的表达形式,以优化计算效率的轨道分析解改进方法。以低地球轨道为例,阐述了轨道分析解改进后的具体算法,并通过数值仿真分析验证了算法的有效性和实用性。算法以第一类无奇点根数作为轨道状态量,采用开普勒轨道根数计算各类摄动力的长期、长周期和短周期项,通过较简单的组合形式计算无奇点根数的对应摄动项,实现在保持分析解精度和消除小偏心率奇点的同时,提高计算效率。仿真结果表明,分析解算法的模型精度在1E-5量级,符合一阶分析解理论精度的预期;同时计算速度达到传统分析解算法的4倍左右,可有效提升空间碎片轨道预报的计算效率,具有较强的工程应用价值。

关键词: 轨道预报, 空间碎片编目, 开普勒根数, 分析解, 计算效率

Abstract:

This paper mainly introduces an improved orbital analysis solution method which can optimize the computational efficiency through improving the expression of various types of orbital perturbation terms. The low-Earth orbit is taken as an example to illustrate the improved algorithm of the orbital analysis solution, and the effectiveness and practicability are analyzed and verified through numerical simulation. The first class of nonsingular orbital elements is used as the state vector, the secular-terms, long-periodic- terms and short-periodic -terms of perturbations are calculated with Keplerian elements firstly, then the corresponding perturbation terms of the first class of nonsingular orbital elements are calculated by a certain combination form. The algorithm achieves the aim of improving computational efficiency while maintaining analytical solution accuracy and eliminating the small eccentricity singularity. The simulation results show that the model accuracy of the analytical solution algorithm is in the order of 1E-5, which accords with the theoretical expectation of the first-order analytical solution's accuracy. At the same time, the orbit prediction speed of the analytical solution algorithm can reach four times of the calculation speed of the traditional analytical solution algorithm, which can effectively improve the computational efficiency of space debris orbit prediction. Thus, the algorithm has strong engineering application values.

Key words: orbit prediction, space debris cataloging, Kepler elements, analytical solution, computational efficiency

中图分类号:

V412.4+1

杨志涛, 刘静, 刘林. 轨道分析解的改进方法及其应用[J]. 系统工程与电子技术, 2020, 42(2): 427-433.

Zhitao YANG, Jing LIU, Lin LIU. Improved method of orbit analytical solution and its application[J]. Systems Engineering and Electronics, 2020, 42(2): 427-433.

图/表 6

图1

表1

图2

图3

表2

表3

参考文献 32

1	NATIONS U. Technical report on space debris[R]. New York: United Nations Office for Outer Space Affairs, 1999: 1-10.
2	PHILLIP A . Slann, space debris and the need for space traffic control[J]. Space Policy, 2014, 30, 40- 42. doi: 10.1016/j.spacepol.2013.10.007
3	程昊文, 汤靖师, 刘静, 等. 大面质比空间碎片在太阳光压和引力作用下的轨道演化[J]. 空间科学学报, 2013, 33 (2): 182- 187.
	CHENG H W , TANG J S , LIU J , et al. Orbital evolution of high area-to-mass ratio debris under the influence of radiation pressure and gravitational effects[J]. Chinese Journal of Space Science, 2013, 33 (2): 182- 187.
4	王歆, 刘林. 目标天体极轨道卫星的轨道寿命[J]. 宇航学报, 2001, 22 (5): 62- 65. doi: 10.3321/j.issn:1000-1328.2001.05.011
	WANG X , LIU L . Lifetime of polar-orbit satellite[J]. Journal of Astronautics, 2001, 22 (5): 62- 65. doi: 10.3321/j.issn:1000-1328.2001.05.011
5	KESSLER D J , COUR-PALAIS B G . Collision frequency of artificial satellites: the creation of a debris belt[J]. Journal of Geophysical Research Atmospheres, 1978, 83, 2637- 2646. doi: 10.1029/JA083iA06p02637
6	王晓伟, 刘静, 崔双星. 一种应用于空间碎片演化模型的碰撞概率算法[J]. 宇航学报, 2019, 40 (4): 482- 488.
	WANG X W , LIU J , CUI S X . A collision probability estimation algorithm used in space debris evolutionary model[J]. Journal of Astronautics, 2019, 40 (4): 482- 488.
7	张育林, 张斌斌, 王兆魁. 空间碎片环境的长期演化建模方法[J]. 宇航学报, 2018, 39 (12): 98- 108.
	ZHANG Y L , ZHANG B B , WANG Z K . Methods for space debris environment long-term evolution modeling[J]. Journal of Astronautics, 2018, 39 (12): 98- 108.
8	孙涛, 山秀明, 陈鲸. 空间监视相控阵雷达匹配搜索技术研究[J]. 系统工程与电子技术, 2013, 35 (6): 1183- 1187.
	SUN T , SHAN X M , CHEN J . Research on technology of match search by space surveillance phased array radar[J]. Systems Engineering and Electronics, 2013, 35 (6): 1183- 1187.
9	苏飞, 刘静, 张耀, 等. 航天器面内机动规避最优脉冲分析[J]. 系统工程与电子技术, 2018, 40 (12): 2782- 2789. doi: 10.3969/j.issn.1001-506X.2018.12.23
	SU F , LIU J , ZHANG Y , et al. Analysis of optimal impulse for in plane collision avoidance maneuver[J]. Systems Engineering and Electronics, 2018, 40 (12): 2782- 2789. doi: 10.3969/j.issn.1001-506X.2018.12.23
10	王卫杰, 李怡勇, 罗文, 等. 天基激光清除空间碎片任务分析[J]. 系统工程与电子技术, 2019, 41 (6): 1374- 1382.
	WANG W J , LI Y Y , LUO W , et al. Mission analysis on removal of space debris with space-based laser[J]. Systems Engineering and Electronics, 2019, 41 (6): 1374- 1382.
11	International Standard Organization. Space systems-estimation of orbit lifetime[S]. ISO 27852: 2010(E).
12	王大为, 汤靖师, 刘林, 等. 半分析方法在地球卫星100yr尺度长期预报中的性能评估[J]. 天文学报, 2017, 58 (1): 20- 45.
	WANG D W , TANG J S , LIU L , et al. The assessment of the semi-analytical method in the 100-year orbit prediction of earth satellites[J]. ACTA Astronomical Sinica, 2017, 58 (1): 20- 45.
13	刘林, 汤靖师. 卫星轨道理论与应用[M]. 北京: 电子工业出版社, 2015: 117.
	LIU L , TANG J S . Satellite orbit theory and application[M]. Beijing: Publishing House of Electronics Industry, 2015: 117.
14	刘林, 胡松杰, 王歆. 航天动力学引论[M]. 南京: 南京大学出版社, 2006: 147.
	LIU L , HU S J , WANG X . An introduction of astrodynamics[M]. Nanjing: Nanjing University Press, 2016: 147.
15	VALLADO D A . Fundamentals of astrodynamics and applications[M]. 3rd ed Hawthome: Microcosm Press, 2007: 515- 520.
16	NO T S , JUNG O C . Analytical solution to perturbed geosynchronous orbit[J]. Acta Astronautica, 2005, 56 (7): 641- 651. doi: 10.1016/j.actaastro.2004.11.008
17	SONG W D , WANG R L , WANG J . A simple and valid analysis method for orbit anomaly detection[J]. Advances in Space Research, 2012, 49 (2): 386- 391. doi: 10.1016/j.asr.2011.10.007
18	LUCIANO A , CARMEN P . Long-term dynamical evolution of high area-to-mass ratio debris released into high earth orbits[J]. Acta Astronautica, 2010, 67 (1): 204- 216.
19	KUANG D , DESAI S , SIBTHORPE A , et al. Measuring atmospheric density using GPS-LEO tracking data[J]. Advances in Space Research, 2014, 53 (2): 243- 256. doi: 10.1016/j.asr.2013.11.022
20	HE C , YANG Y , CARTER B , et al. Review and comparison of empirical thermospheric mass density models[J]. Progress in Aerospace Sciences, 2018, 103 (11): 31- 51.
21	CALABIA A , JIN S . Thermospheric density estimation and responses to the March 2013 geomagnetic storm from GRACE GPS-determined precise orbits[J]. Atmospheric and Solar-Terrestrial Physics, 2017, 154 (2): 167- 179.
22	LI A , CLOSE S . Mean thermospheric density estimation derived from satellite constellations[J]. Advances in Space Research, 2015, 56 (8): 1645- 1657. doi: 10.1016/j.asr.2015.07.022
23	EXERTIER P , BOIS E . Analytical solution of the perturbed circular motion: an extended formulation for various perturbations[J]. Planetary and Space Science, 1995, 43 (7): 863- 874. doi: 10.1016/0032-0633(94)00216-E
24	ALIMOV G , GREB A , KUZNETSOV E , et al. Approximate analytical theory of satellite orbit prediction presented in spherical coordinates frame[J]. Celestial Mechanics and Dynamical Astronomy, 2001, 81 (3): 219- 234. doi: 10.1023/A:1013252917957
25	EXERTIER P , BONNEFOND P . Analytical solution of perturbed circular motion: application to satellite geodesy[J]. Journal of Geodesy, 1997, 71 (3): 149- 159. doi: 10.1007/s001900050083
26	WNUK E . Recent progress in analytical orbit theories[J]. Advances in Space Research, 1999, 23 (4): 677- 687. doi: 10.1016/S0273-1177(99)00148-9
27	MAHAJAN B, VADALI S R, ALFRIEND K T. Analytic solution for satellite relative mtion with zonal gravity perturbations[C]// Proc.of the 26th AAS/AIAA Space Flight Mechanics Meeting, 2016: 3325-3348.
28	MAHAJAN B, VADALI S R, ALFRIEND K T. Analytic solution for satellite relative mtion: The complete zonal gravitational problem[C]//Proc.of the 26th AAS/AIAA Space Flight Mechanics Meeting, 2016: 3325-3348.
29	AARON J R , DESPOINA K S , KLEOMENIS T , et al. Dynamical cartography of Earth satellite orbits[J]. Advances in Space Research, 2019, 63 (1): 443- 460. doi: 10.1016/j.asr.2018.09.004
30	GKOLIAS I , DAQUIN J , GACHET F , et al. From order to chaos in Earth satellite orbits[J]. Astronomical Journal, 2016, 152 (5): 119- 134. doi: 10.3847/0004-6256/152/5/119
31	ELY T A , HOWELL K C . Dynamics of artificial satellite orbits with tesseral resonances including the effects of luni-solar perturbations[J]. Dynamical Systems an International Journal, 1997, 12 (4): 243- 269. doi: 10.1080/02681119708806247
32	LANTUKH D , RUSSELL R P , BROSCHART S . Heliotropic orbits at oblate asteroids: balancing solar radiation pressure and J₂ perturbations[J]. Celestial Mechanics and Dynamical Astronomy, 2015, 121 (2): 171- 190. doi: 10.1007/s10569-014-9596-x

参数项	参数值
轨道历元	2016 05 20 00 00 0.0
轨道初值	a∈[500 km, 2 000 km], e=0.001i=Ω=ω=M=45°
预报期/h	24
步长/s	30
面质比/(m²/kg)	0.01

轨道高度/km	所提方法耗/s	传统方法耗时/s	速度比
500	0.921	3.495	3.8
550	0.845	3.371	4.0
600	0.798	3.29	4.1
650	0.855	3.077	3.6
700	0.789	3.231	4.1
750	0.737	3.398	4.6
800	0.616	3.906	6.3
850	0.848	3.427	4.0
900	0.76	3.102	4.1
950	0.878	3.409	3.9
1 000	0.798	3.443	4.3
平均	0.804	3.377	4.3

偏心率	所提方法耗时/s	传统方法耗时/s	速度比
0.001	0.833	3.567	4.3
0.005	0.822	2.784	3.4
0.01	0.903	3.158	3.5
0.05	0.759	3.163	4.2
0.1	0.779	3.502	4.5
平均	0.819	3.235	4.0

轨道分析解的改进方法及其应用

Improved method of orbit analytical solution and its application

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 6

参考文献 32

相关文章 1

编辑推荐

Metrics

本文评价