空间激光干涉引力波探测器轨道修正方法

黄文涛; 师鹏; 赵育善; 武海雷

doi:10.13700/j.bh.1001-5965.2019.0177

空间激光干涉引力波探测器轨道修正方法

doi: 10.13700/j.bh.1001-5965.2019.0177

黄文涛¹,
师鹏^1, ,,
赵育善¹,
武海雷^{2, 3}

1.
北京航空航天大学宇航学院, 北京 102206
2.
上海航天控制技术研究所, 上海 201109
3.
上海市空间智能控制技术重点实验室, 上海 201109

基金项目:

国家自然科学基金 11572019

上海航天科技创新基金 SAST2017095

详细信息

作者简介:
黄文涛男, 硕士研究生。主要研究方向:航天器动力学与控制

师鹏男, 博士, 讲师, 硕士生导师。主要研究方向:航天器总体设计、航天器动力学与控制

通讯作者:
师鹏.E-mail: shipeng@buaa.edu.cn

中图分类号: V412.4
计量
- 文章访问数: 509
- HTML全文浏览量: 44
- PDF下载量: 120
- 被引次数: 0
出版历程
- 收稿日期: 2019-04-22
- 录用日期: 2019-10-11
- 网络出版日期: 2020-03-20

Orbit correction method of space-based laser interferometric gravitational wave detector

HUANG Wentao¹,
SHI Peng^{1
, ,},
ZHAO Yushan¹,
WU Hailei^{2, 3}

1.
School of Astronautics, Beihang University, Beijing 102206, China
2.
Shanghai Aerospace Control Technology Institute, Shanghai 201109, China
3.
Shanghai Key Laboratory of Aerospace Intelligence Control Technology, Shanghai 201109, China

Funds:

National Natural Science Foundation of China 11572019

Shanghai Aerospace Science and Technology Innovation Fund SAST2017095

More Information

Corresponding author: SHI Peng, E-mail:shipeng@buaa.edu.cn

摘要

摘要:
针对空间激光干涉引力波探测器轨道修正问题，提出一种基于虚拟编队构型设计的航天器轨道修正方法。空间激光干涉引力波探测器由3颗航天器组成等边三角形构型。由于入轨误差和摄动的影响，探测器的构型不稳定。假设名义轨道上运行着一颗理想航天器，实际轨道上的真实航天器与之组成虚拟编队，探测器的3颗真实航天器分别与对应的理想航天器组成3个虚拟编队。考虑探测器构型稳定性要求和摄动的影响，对虚拟编队的构型进行设计，进而求解航天器平均轨道要素修正量。求解得到的航天器平均轨道要素修正量小于偏差量，轨道修正通过四脉冲控制实现。数值仿真结果表明，该方法通过部分轨道修正满足了探测器的构型稳定性要求，具有减少燃料消耗、延长任务寿命的潜力。
- 空间激光干涉引力波探测 /
- 轨道修正 /
- 虚拟编队 /
- 摄动 /
- 天琴计划
Abstract:
Aimed at the orbit correction problem of space-based laser interferometric gravitational wave detector, a spacecraft orbit correction method based on virtual formation configuration design is proposed. The detector is composed of three spacecraft forming an equilateral triangle configuration. The configuration of the detector is unstable due to the orbit error and perturbation. It is assumed that an ideal spacecraft is running in nominal orbit, and the real spacecraft in actual orbit forms a virtual formation with the ideal spacecraft. The three spacecraft of detector form three virtual formations with their ideal spacecraft. Considering the stability requirement of detector configuration and the effect of perturbation, the configuration of the virtual formation is designed to solve the correction value of mean orbital elements of spacecraft. The orbit correction value is less than the orbit deviation value, and orbit correction is realized by four-pulse control. The numerical simulation results show that the method meets the stability requirements of the detector configuration through partial orbit correction, and has the potential to reduce fuel consumption and prolong mission life.
- space-based laser interferometric gravitational wave detection /
- orbit correction /
- virtual formation /
- perturbation /
- TianQin

HTML全文

图 1 天琴计划轨道构型示意图

Figure 1. Schematic of orbital configuration for TianQin

下载: 全尺寸图片幻灯片

图 2 天琴计划虚拟编队示意图

Figure 2. Schematic of virtual formation for TianQin

下载: 全尺寸图片幻灯片

图 3 天琴计划虚拟编队构型几何关系示意图

Figure 3. Schematic of geometric relationship of virtual formation configuration for TianQin

下载: 全尺寸图片幻灯片

图 4 天琴计划虚拟编队构型(30 d)

Figure 4. Virtual formation configuration for TianQin (30 d)

下载: 全尺寸图片幻灯片

图 5 天琴计划等边三角形构型稳定性参数变化曲线

Figure 5. Curves of stability parameters of equilateral triangular configuration for TianQin

下载: 全尺寸图片幻灯片

图 6 轨道修正后的天琴计划虚拟编队构型(30 d)

Figure 6. Virtual formation configuration for TianQin after orbit correction (30 d)

下载: 全尺寸图片幻灯片

图 7 轨道修正后的天琴计划等边三角形构型稳定性参数变化曲线

Figure 7. Curves of stability parameters of equilateral triangular configuration for TianQin after orbit correction

下载: 全尺寸图片幻灯片

表 1 天琴计划航天器名义轨道要素^[11]

Table 1. Nominal orbital elements of spacecraft for TianQin^[11]

航天器	a/km	e	i/(°)	Ω/(°)	ω/(°)	M/(°)
S₁	100 000	0	74.39	211.58	0	0
S₂	100 000	0	74.39	211.58	0	120
S₃	100 000	0	74.39	211.58	0	240

下载: 导出CSV

表 2 天琴计划等边三角形构型稳定性指标^[11]

Table 2. Stability index of equilateral triangular configuration for TianQin^[11]

参数	ΔL/km	Δθ/(°)	/(m·s^-1)
大小要求	< 1 500	< 1.5	< 9

下载: 导出CSV

表 3 平均轨道要素偏差

Table 3. Deviation of mean orbital elements

航天器	σa/km	σe	σi/(°)	σΩ/(°)	σω/(°)	σM/(°)
S₁	7	0.001	-0.04	0.03	0.03	-0.05
S₂	5	0.001	0.04	-0.03	-0.02	0.04
S₃	-8	0.001	0.05	0.02	-0.04	0.03

下载: 导出CSV

表 4 平均轨道要素修正量

Table 4. Correction value of mean orbital elements

航天器	Δa/km	Δe	Δi/(°)	ΔΩ/(°)	Δω/(°)	ΔM/(°)
S₁	-7.001 4	0	0	0	0	0.011 9
S₂	-4.998 6	0	0	0	0	-0.011 9
S₃	8.001 8	0	0	0	0	0.004 6

下载: 导出CSV

表 5 轨道修正速度脉冲

Table 5. Velocity pulse for orbit correction

航天器	(ΔV_h, u_h)	(ΔV_r₁, u_r)	(ΔV_t, ΔV_r₂, u_r+π)
S₁	(0 m/s, -)	(-0.103 9 m/s, -90°)	(-0.069 9 m/s, -0.103 9 m/s, 90°)
S₂	(0 m/s, -)	(0.103 9 m/s, -90°)	(-0.049 9 m/s, 0.103 9 m/s, 90°)
S₃	(0 m/s, -)	(-0.040 2 m/s, -90°)	(0.079 9 m/s, -0.040 2 m/s, 90°)

下载: 导出CSV

参考文献(22)

[1]	罗子人, 白姗, 边星, 等.空间激光干涉引力波探测[J].力学进展, 2013, 43(4):415-447. http://d.old.wanfangdata.com.cn/Periodical/twxjz201501004 LUO Z R, BAI S, BIAN X, et al.Space laser interferometry gravitational wave detection[J].Advances in Mechanics, 2013, 43(4):415-447(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/twxjz201501004
[2]	WEBER J.Observation of the thermal fluctuations of a gravitational-wave detector[J].Physical Review Letters, 1966, 17(24):1228-1230. doi: 10.1103/PhysRevLett.17.1228
[3]	BLAIR D, JU L, ZHAO C N, et al.Gravitational wave astronomy:The current status[J].Science China Physics Mechanics & Astronomy, 2015, 58(12):120402. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ0221825959/
[4]	ABBOTT B P, ABBOTT R, ABBOTT T D, et al.Observation of gravitational waves from a binary black hole merger[J].Physical Review Letters, 2016, 116(6):061102. doi: 10.1103/PhysRevLett.116.061102
[5]	CORNELISSE J W.LISA mission and system design[J].Classical and Quantum Gravity, 1996, 13(11A):A251-A258. doi: 10.1088/0264-9381/13/11A/034
[6]	ARMANO M, AUDLEY H, BAIRD J, et al.Beyond the required LISA free-fall performance:New LISA pathfinder results down to 20 μHz[J].Physical Review Letters, 2018, 120(6):061101. doi: 10.1103/PhysRevLett.120.061101
[7]	WU A M, NI W T.Deployment and simulation of the ASTROD-GW formation[J].International Journal of Modern Physics D, 2013, 22(1):1341005. doi: 10.1142/S0218271813410058
[8]	JIN G.Program in space detection of gravitational wave in Chinese Academy of Sciences[C]//11th International LISA Symposium.Bristol: IOP Publishing, 2017, 840(1): 012009.
[9]	LUO J, CHEN L S, DUAN H Z, et al.TianQin:A space-borne gravitational wave detector[J].Classical and Quantum Gravity, 2016, 33(3):035010. doi: 10.1088/0264-9381/33/3/035010
[10]	HU X C, LI X H, WANG Y, et al.Fundamentals of the orbit and response for TianQin[J].Classical and Quantum Gravity, 2018, 35(9):095008. doi: 10.1088/1361-6382/aab52f
[11]	万小波, 张晓敏, 黎明.天琴计划轨道构型长期漂移特性分析[J].中国空间科学技术, 2017, 37(3):110-116. http://d.old.wanfangdata.com.cn/Periodical/zgkjkxjs201703014 WAN X B, ZHANG X M, LI M.Analysis of long-period drift characteristics for orbit configuration of TianQin Mission[J].Chinese Space Science and Technology, 2017, 37(3):110-116(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/zgkjkxjs201703014
[12]	YE B B, ZHANG X, ZHOU M Y, et al.Optimizing orbits for TianQin[J].International Journal of Modern Physics D, 2019, 28(9):1950121. doi: 10.1142/S0218271819501219
[13]	YANG C, ZHNAG H.Formation flight design for a LISA-like gravitational wave observatory via Cascade optimization[J].Astrodynamics, 2019, 3(2):155-171. doi: 10.1007/s42064-018-0042-9
[14]	唐文林.中国空间引力波探测计划卫星轨道设计的初步研究[D].北京: 中国科学院大学, 2014: 17-31. TANG W L, Preliminary study of the orbit design of the Chinese mission to detect the gravitational wave in space[D].Beijing: University of Chinese Academy of Sciences, 2014: 17-31(in Chinese).
[15]	WANG G, NI W T.Orbit optimization for ASTROD-GW and its time delay interferometry with two arms using CGC ephemeris[J].Chinese Physics B, 2013, 22(4):571-579. http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_1205.5175
[16]	刘林, 汤靖师.卫星轨道理论与应用[M].北京:电子工业出版社, 2015:227-243. LIU L, TANG J S.Theory and application of satellite orbit[M].Beijing:Publishing House of Electronics Industry, 2015:227-243(in Chinese).
[17]	PRADO B D A, FERNANDO A.Third-body perturbation in orbits around natural satellites[J].Journal of Guidance, Control, and Dynamics, 2003, 26(1):33-40. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=5817fa93351ace7e47d84e6b5548b5fa
[18]	杜耀珂, 杨盛庆, 完备, 等.近地卫星严格回归轨道保持控制[J].航空学报, 2018, 39(12):322449. http://d.old.wanfangdata.com.cn/Periodical/hkxb201812029 DU Y K, YANG S Q, WAN B, et al.Strictly-regressive orbit maintenance control of near earth satellites[J].Acta Aeronautica et Astronautica Sinica, 2018, 39(12):322449(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/hkxb201812029
[19]	孟云鹤.航天器编队飞行导论[M].北京:国防工业出版社, 2014:28-32. MENG Y H.Introduction to spacecraft formation flying[M].Beijing:National Defense Industry Press, 2014:28-32(in Chinese).
[20]	HOU X Y, ZHAO Y H, LIU L.Formation flying in elliptic orbits with the J2 perturbation[J].Research in Astronomy and Astrophysics, 2012, 12(11):1563. doi: 10.1088/1674-4527/12/11/010
[21]	ROSCOE C W T, VADALI S R, ALFRIEND K T.Third-body perturbation effects on satellite formations[J].Journal of the Astronautical Sciences, 2013, 60(3-4):408-433. doi: 10.1007/s40295-015-0057-x
[22]	曹喜滨, 张锦绣, 王峰.航天器编队动力学与控制[M].北京:国防工业出版社, 2013:103-121. CAO X B, ZHANF J X, WANG F.The dynamics and control of spacecraft formation flying[M].Beijing:National Defense Industry Press, 2013:103-121(in Chinese).