轨道分析解的改进方法及其应用

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

Abstract

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

CLC Number:

V412.4+1

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.

Figures/Tables 6

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References 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

Improved method of orbit analytical solution and its application

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