基于半分析法的改进SOLEM模型与空间碎片长期演化分析

doi:10.12305/j.issn.1001-506X.2025.09.24

系统工程与电子技术 ›› 2025, Vol. 47 ›› Issue (9): 3031-3040.doi: 10.12305/j.issn.1001-506X.2025.09.24

• 制导、导航与控制 • 上一篇

基于半分析法的改进SOLEM模型与空间碎片长期演化分析

郑峰椿¹, 张耀¹^,²^,*, 刘静¹^,², 甘庆波¹^,², 程昊文¹^,², 汤靖师³

1. 中国科学院国家天文台，北京 100101
2. 中国科学院大学天文与空间科学学院，北京 100101
3. 南京大学天文与空间科学学院，江苏南京 210023

收稿日期:2024-08-08 出版日期:2025-09-25 发布日期:2025-09-16
通讯作者: 张耀
作者简介:郑峰椿（1998—），男，助理工程师，硕士，主要研究方向为空间碎片环境长期演化、空间碎片轨道预报
刘　静（1970—），女，研究员，博士，主要研究方向为空间碎片监测和预警
甘庆波（1982—），男，研究员，博士，主要研究方向为天体测量与天体力学
程昊文（1984—），男，高级工程师，博士，主要研究方向为天体测量与天体力学
汤靖师（1983—），男，副教授，博士，主要研究方向为航天器轨道动力学理论及应用
基金资助:
空间碎片与近地小行星防御专项科研（KJSP2020020205）资助课题

Modified SOLEM model based on semi-analytical method and long-term evolution analysis of space debris

Fengchun ZHENG¹, Yao ZHANG¹^,²^,*, Jing LIU¹^,², Qingbo GAN¹^,², Haowen CHENG¹^,², Jingshi TANG³

1. National Astronomical Observatories，Chinese Academy of Sciences，Beijing 100101，China
2. School of Astronomy and Space Science，University of Chinese Academy of Sciences，Beijing 100101，China
3. School of Astronomy and Space Science，Nanjing University，Nanjing 210023，China

Received:2024-08-08 Online:2025-09-25 Published:2025-09-16
Contact: Yao ZHANG

摘要/Abstract

摘要：

针对空间碎片环境长期演化计算中速度和精度难以兼容的问题，提出使用一种半分析方法进行长期轨道预报。对半分析法预报精度和速度进行测试，与数值法相比，10年内低轨半长轴偏差小于7 km，预报耗时小于0.11%。为评估半分析法轨道预报的适用性，对有45年轨道数据的千余碎片进行预报，分析在轨碎片数量演化趋势。结果表明，截至2024年7月的碎片数量误差为2.4%。基于半分析法轨道预报，对空间物件长期演化模型（space object long-term evolution model, SOLEM）进行改进，并与国际典型模型进行对比，验证了改进模型的可信度较高。

关键词: 半分析法轨道预报, 空间碎片, 长期演化, 空间物件长期演化模型

Abstract:

In order to solve the problem of compatibility between calculation speed and accuracy of space debris environmental long-term evolution, a semi-analytical method is proposed for long-term orbital prediction. The prediction accuracy and speed of the semi-analytical method are tested. Compared with the numerical method, the semi-major axis deviation of the low Earth orbit in 10 years is less than 7 km, and the consumed time of prediction is less than 0.11%. To evaluate the applicability of the semi-analytical method, orbital prediction is carried out for more than 1000 space debris with 45 years of orbital data, and the evolutionary trend of the number of debris in orbit is analyzed. The result indicates that the error of the debris number as of July 2024 is 2.4%. Based on the semi-analytical orbital prediction, the space object long-term evolution model （SOLEM） is improved, and comparison with representative international models verifies the higher reliability of the improved model.

Key words: semi-analytical orbital prediction, space debris, long-term evolution, space object long-term evolution model （SOLEM）

中图分类号:

P 139

郑峰椿, 张耀, 刘静, 甘庆波, 程昊文, 汤靖师. 基于半分析法的改进SOLEM模型与空间碎片长期演化分析[J]. 系统工程与电子技术, 2025, 47(9): 3031-3040.

Fengchun ZHENG, Yao ZHANG, Jing LIU, Qingbo GAN, Haowen CHENG, Jingshi TANG. Modified SOLEM model based on semi-analytical method and long-term evolution analysis of space debris[J]. Systems Engineering and Electronics, 2025, 47(9): 3031-3040.

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摄动力	低轨	中轨	地球同步轨道	大偏心率轨道
地球非球形引力	${J_2},{J_3},{J_4},{J_{2,2}}$	${J_2},{J_3},{J_4},{J_{2,2}}$	${J_2},{J_3},{J_4},{J_{2,2}}$	${J_2},{J_3},{J_4},{J_{2,2}}$
日、月引力	√	√	√	√
大气阻力	√	×	×	√
太阳光压	√	√	√	√

轨道类型	初始轨道
LEO	[7 500 km, 0.0001, 50°, 50°, 50°, 50°]
MEO	[26 500 km, 0.0001, 50°, 50°, 50°, 50°]
GEO	[42 378 km, 0.0001, 0°, 50°, 50°, 50°]
HEO	[26 500 km, 0.2, 50°, 50°, 50°, 50°]

轨道类型	分析法/s	半分析法/s	数值法/s	耗时比例/%
LEO	0.53	2.48	2 310.90	0.11
MEO	0.44	1.57	2 281.40	0.07
GEO	0.32	0.27	2 290.26	0.01
HEO	0.46	2.58	2 376.85	0.11

模型参数	说明
演化时长/年	200
初始空间碎片环境数据	2018年2月1日的空间碎片环境，包括LEO和穿过 LEO轨道的尺寸大于10 cm的物体，总计26 317个
卫星发射模型	2010年1月1日至2017年12月31日的卫星发射信息，在演化期间每隔8年循环发射
卫星在轨任务期/年	8
任务后处置成功率/%	90
空间环境参数	F10.7具有11年周期，且每月更新1次；Ap=9
蒙特卡罗仿真次数	50

模型	说明
初始空间碎片环境数据	2023年1月1日的空间碎片环境，包括LEO和穿过 LEO轨道的尺寸大于10 cm的物体，总计25 980个
卫星发射模型	2017年1月1日至2022年12月31日的卫星发射信息，在演化期间循环发射
星座发射模型	2023—2223年总计发射244 708颗
星座中卫星任务期/年	5
星座碰撞规避	任务期间考虑人工碰撞规避，与其他碎片不产生碰撞
蒙特卡罗仿真次数	50

基于半分析法的改进SOLEM模型与空间碎片长期演化分析

Modified SOLEM model based on semi-analytical method and long-term evolution analysis of space debris

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