基于轨道间最小距离的空间环境指数

doi:10.12305/j.issn.1001-506X.2024.11.20

摘要/Abstract

摘要：

空间环境指数是描述空间碎片对空间环境长期影响的量化评估指数。用该指数可以对比分析某空间物体的在轨运行是否对其他物体乃至整体环境产生较大威胁。对现有典型空间碎片环境指数及其建模方法进行分析和比较, 并针对过去模型中平均碰撞风险计算方法的不足, 提出一种空间环境指数模型, 即基于轨道间最小距离(minimum orbital intersection distance, MOID)的空间环境指数(MOID-based space index, MBSI)。该指数综合空间碎片的质量、有效截面积等因素, 基于MOID考虑碰撞风险, 计算近地轨道(low Earth orbit, LEO) 区域中不同空间物体的MBSI指数, 并与已有的R_N指数、CSI(criticality of spacecraft index, CSI)指数的结果进行比对和分析。MBSI与R_N指数、CSI指数符合度超过60%, 而MBSI更能体现空间物体寿命期内的危险程度。

关键词: 空间碎片, 轨道间最小距离, 碰撞风险, 空间环境指数

Abstract:

The space index is a quantitative assessment index that describes the long-term impact of space debris on the space environment. This index allows for a comparative analysis of whether the in-orbit operation of a space object poses a significant threat to other objects or the overall environment. This paper analyzes and compares existing typical space indices and their modeling methods. Addressing the shortcomings in the calculation of average collision risk in previous models, a space index model based on the minimum orbital intersection distance (MOID), namely the MOID-based space index (MBSI). This index considers factors such as the mass and effective cross-sectional area of space debris and incorporates collision risk. The MBSI indices of different space objects in the low Earth orbit (LEO) are calculated and compared with the results of existing R_N and CSI indices, providing a comprehensive analysis. The results show that the conformity between MBSI and R_N and CSI indices exceeds 60%. Additionally, MBSI better reflects the danger level of space objects throughout their lifespan.

Key words: space debris, minimum orbital intersection distance (MOID), collision risk, space index

中图分类号:

武恩惠, 刘静, 杨旭. 基于轨道间最小距离的空间环境指数[J]. 系统工程与电子技术, 2024, 46(11): 3784-3791.

Enhui WU, Jing LIU, Xu YANG. Minimum orbital intersection distance based space index[J]. Systems Engineering and Electronics, 2024, 46(11): 3784-3791.

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指数名称	公式	提出机构	提出时间/年份	质量M	截面积A	空间密度F	空间通量D	寿命l	轨道倾角i
RC	RC=P·M_i	NASA Johnson Space Center	2009	√	√	√	-	-	-
EC	$\mathrm{EC}=\sum\limits_{t=t_{\text {start }}}^{t_{\text {end }}}\left(D(h) \cdot A \sum\limits_{t=t_{\text {frag }}}^{t_{\text {end }}}(\Delta D(h) \cdot A)\right) $	Technical University of Braunschweig	2014	-	√	-	√	-	-
R_N	$R_{\mathrm{N}}=\left(\frac{M}{M_0}\right)^{1.75} \cdot \frac{\overline{F(h)}}{\overline{F\left(h_0\right)}} \cdot \frac{l(h)}{l\left(h_0\right)} $	Institute of Information Science and Technologies	2014	√	-	-	√	√	-
CSI	$\operatorname{CSI}=\frac{M}{M_0} \cdot \frac{D(h)}{D_0} \cdot \frac{l(h)}{l\left(h_0\right)} \cdot \frac{1+k \varGamma(i)}{1+k} $	Institute of Applied Physics	2014	√	-	√	-	√	√
ECOB	$ \mathrm{ECOB}=\sum\limits_{j=1}^{N_{\mathrm{tar}}} w_j P_{c, j}$	University of Southampton	2016	-	√	-	√	-	-

NORADID	质量/kg	CSI	R_N	MBSI	CSI排名	R_N排名	MBSI排名
22285	8 225.97	0.262 2	79.517 1	4 321.702 1	1	1	1
19120	8 225.97	0.203 2	73.722 1	2 565.905 0	7	6	2
20625	8 225.97	0.237 0	79.517 1	2 481.016 8	4	4	3
17590	8 225.97	0.248 0	79.517 1	2 255.914 5	3	3	4
29499	4 086.00	0.007 4	1.194 9	1 426.449 4	18	18	7
22803	8 225.97	0.248 4	79.517 1	1 992.651 7	2	2	5
16182	8 225.97	0.214 1	64.239 6	1 918.211 2	6	7	6
22823	1 890.98	0.046 4	5.626 3	287.902 9	12	13	9
25260	2 730.43	0.013 4	1.419 7	701.136 8	17	16	8
23705	8 225.97	0.233 8	79.517 1	46.560 0	5	5	10
27453	1 403.00	0.029 1	2.494 9	10.317 9	14	14	14
38771	4 086.00	0.079 8	13.228 2	34.717 9	9	9	11
25400	8 225.97	0.150 5	55.115 8	32.502 8	8	8	12
12443	1 421.21	0.018 2	1.756 0	9.201 2	15	15	15
25634	2 490.00	0.061 7	9.106 9	12.187 5	10	10	13
39177	7 000.00	0.029 2	7.374 0	8.447 5	13	11	16
16682	1 421.21	0.017 0	1.402 6	6.779 9	16	17	17
25394	2 444.00	0.047 3	6.589 9	5.103 2	11	12	18

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