基于可达域的解体碎片云中期演化建模方法

doi:10.7527/S1000-6893.2024.30135

Abstract

Abstract:

The breakup of satellites in orbit is one of the main sources of space debris. Accurate simulation of the dynamic evolution of the debris cloud can avoid the collision between the debris and other satellites in orbit. In this paper， a method for modeling the debris cloud based on the perturbation orbit reachable domain theory is proposed for the complex medium-term evolution of the debris cloud. In this method， the spatial distribution of the debris cloud is described by the reachable domain envelope， and the density of uniformly distributed debris is characterized by calculating the volume of the reachable domain. Then， to improve the characterization accuracy， the debris cloud is stratified according to the size of the velocity increment， and the sub clouds with different velocity increment were simulated to achieve the accurate calculation of the non-uniformly distributed debris density. The simulation results show that the spatial distribution and density magnitude of the medium-term debris cloud given by the proposed method are consistent with the corresponding results of the numerical method.

Key words: satellite breakup, debris cloud, debris density, orbit reachable domain, space security

CLC Number:

V528

Zihan JIN, Changxuan WEN, Dong QIAO. Modeling medium-term debris cloud of breakups based on reachable domain[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(21): 230135.

Figures/Tables 18

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Table 1

Parameters of 14 debris sub clouds

编号	$Δ v i$ /（m·s^-1）	$N i$	编号	$Δ v i$ /（m·s^-1）	$N i$
1	1 000	1 123	8	510	48 925
2	930	3 909	9	440	69 874
3	860	7 272	10	370	101 032
4	790	11 639	11	300	153 318
5	720	17 228	12	230	252 589
6	650	24 575	13	160	495 777
7	580	35 066	14	90	1 797 673

Table 1

Fig.10

Fig.11

Fig.12

Fig.13

Table 2

Average relative error of magnitude at different evolutionary times

演化时间/day	$x y$ 平面 $ε$ （ $N v$ ）	$x z$ 平面 $ε$ （ $N v$ ）
80	10%（267）	6%（145）
160	11%（581）	4%（294）

Table 2

Table 3

Fig.14

Fig.15

References 32

1	CelesTrak： SATCAT Boxscore［EB/OL］. （2024-03-10）［2024-03-10］. .
2	PARDINI C， ANSELMO L. Review of past on-orbit collisions among cataloged objects and examination of the catastrophic fragmentation concept［J］. Acta Astronautica， 2014， 100： 30-39.
3	PHILLIP A， JOHN O. History of on-orbit satellite fragmentations［EB/OL］. （2023-01-20）［2024-03-10］. .
4	BARROWS S P， SWINERD G G， CROWTHER R. Review of debris-cloud modeling techniques［J］. Journal of Spacecraft and Rockets， 1996， 33（4）： 550-555.
5	MCKNIGHT D， LORENZEN G. Collision matrix for low earth orbit satellites［J］. Journal of Spacecraft and Rockets， 1989， 26（2）： 90-94.
6	JEHN R. Dispersion of debris clouds from on-orbit fragmentation events［C］∥41st， International Astronautical Congress（IAF）； Dresden， Federal Republic of Germany. 1990.
7	CHOBOTOV V. Dynamics of orbiting debris clouds and the resulting collision hazard to spacecraft［J］. Journal of the British Interplanetary Society， 1990， 43（5）： 187-194.
8	SPENCER D B. The effects of eccentricity on the evolution of an orbiting debris cloud［C］∥Proceedings of the AAS/AIAA Astrodynamics Conference. San Diego， CA： UNIVELT INC， 1988： 791-807.
9	BARROWS S. Evolution of artificial space debris clouds［D］. Southampton： University of Southampton， 1996： 30-37.
10	HUJSAK R S. Nonlinear dynamical model of relative motion for the orbiting debris problem［J］. Journal of Guidance， Control， and Dynamics， 1991， 14（2）： 460-465.
11	HOUSEN K R. The short-term evolution of orbital debris clouds［J］. Journal of the Astronautical Sciences， 1992， 40（2）： 203-213.
12	BARROWS S， SWINERD G， CROWTHER R. Assessment of the short-term collision hazard resulting from an on-orbit fragmentation event-Polar platform case study［C］∥Astrodynamics Conference. Reston： AIAA， 1994.
13	HEALY L， KINDL S， BINZ C. Spatial density maps from a debris cloud［C］∥7th European Conference on Space Debris. Darmstadt： ESA Space Debris Office， 2017： 1-15.
14	HEARD W B. Dispersion of ensembles of non-interacting particles［J］. Astrophysics and Space Science， 1976， 43（1）： 63-82.
15	MCINNES C R. An analytical model for the catastrophic production of orbital debris.［J］. ESA Jour-nal， 1993， 17（4）： 293-305.
16	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）： 1408-1418.
	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）： 1408-1418 （in Chinese）.
17	LETIZIA F， COLOMBO C， LEWIS H G. Analytical model for the propagation of small-debris-object clouds after fragmentations［J］. Journal of Guidance， Control， and Dynamics， 2015， 38（8）： 1478-1491.
18	WEN C X， GURFIL P. Modeling early medium-term evolution of debris clouds using the reachable domain method［J］. Journal of Guidance， Control， and Dynamics， 2016， 39（12）： 2649-2660.
19	LETIZIA F， COLOMBO C， LEWIS H G. Multidimensional extension of the continuity equation method for debris clouds evolution［J］. Advances in Space Research， 2016， 57（8）： 1624-1640.
20	JEHN R. Dispersion of debris clouds from in-orbit fragmentation events［J］. ESA Journal， 1991， 15（1）： 63-77.
21	VALLADO D A. Fundamentals of astrodynamics and applications［M］. 4th ed. Portland Oregon： Microcosm Press， 2013： 525-594.
22	WEISSTEIN E W. Sphere point picking［EB/OL］. （2017-03-14）［2023-12-25］. .
23	CHOBOTOV V， SPENCER D， SCHMITT D， et al. Dynamics of debris motion and the collision hazard to spacecraft resulting from an orbital breakup： TR SD-TR-88-96［R］. El Segundo： Aerospace Corp.， 1988.
24	龚自正，赵秋艳，李明，等. 空间碎片防护研究前沿问题与展望［J］. 空间碎片研究， 2019， 19（3）： 2-13.
	GONG Z Z， ZHAO Q Y， LI M， et al. The frontier problem and prospect of space debris protection research［J］. Space Debris Research， 2019， 19（3）： 2-13 （in Chinese）.
25	FREY S， COLOMBO C. Transformation of satellite breakup distribution for probabilistic orbital collision hazard analysis［J］. Journal of Guidance， Control， and Dynamics， 2020， 44（1）： 88-105.
26	彭科科. 近地轨道空间碎片环境工程模型建模技术研究［D］. 哈尔滨：哈尔滨工业大学， 2015： 70-71.
	PENG K K. Research on modeling technology of space debris environmental engineering model in near-earth orbit［D］. Harbin： Harbin Institute of Technology， 2015： 70-71 （in Chinese）.
27	VINH N X， GILBERT E G， HOWE R M， et al. Reachable domain for interception at hyperbolic speeds［J］. Acta Astronautica， 1995， 35（1）： 0094576594001326.
28	XUE D， LI J F， BAOYIN H X， et al. Reachable domain for spacecraft with a single impulse［J］. Journal of Guidance， Control， and Dynamics， 2010， 33（3）： 934-942.
29	WEN C X， SUN Y， PENG C， et al. Reachable domain under J2 perturbation for satellites with a single impulse［J］. Journal of Guidance， Control， and Dynamics， 2022， 46（1）： 64-79.
30	BEYERW H. CRC standard mathematical tables［M］. Boca Raton： CRC Press， 1984.
31	BOURKE P. Polygons and meshes［EB/OL］. （1998-03-01）［2023-11-21］. .
32	GIUDICI L， TRISOLINI M， COLOMBO C. Probabilistic multi-dimensional debris cloud propagation subject to non-linear dynamics［J］. Advances in Space Research， 2023， 72（2）： 129-151.

演化时间/day	可达域方法用时/s	数值方法用时/s
80	51.69	8 513.37
160	51.84	15 923.79

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Modeling medium-term debris cloud of breakups based on reachable domain

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