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Expected Collision Rates for Tracked Satellites
Journal of Spacecraft and Rockets ( IF 1.6 ) Pub Date : 2021-02-01 , DOI: 10.2514/1.a34919
Doyle T. Hall 1
Affiliation  

This analysis estimates collision risks between tracked satellites based on the statistically expected collision rate N˙c and number of collisions Nc, which are closely related to the collision probability Pc. For isolated encounters, Nc equals Pc. For multi-encounter interactions, Nc can exceed Pc and is significantly easier to approximate semi-analytically. Estimating Nc requires integrating the collision rate over time throughout an interaction, with each required N˙c value calculated as a statistical expectation value based on the uncertainty distributions of initial orbital states. The uncertainty distributions are estimated from orbit determination analyses of satellite trajectory measurements. The formulation accounts for the nonlinear orbital motion of the satellites, and derives Nc and N˙c expressions for Monte Carlo simulations as well as semi-analytical approximations for single- and multi-encounter interactions.



中文翻译:

跟踪卫星的预期碰撞率

该分析根据统计上的预期碰撞率估算跟踪卫星之间的碰撞风险 ñ˙C 和碰撞次数 ñC,这与碰撞概率密切相关 PC。对于孤立的遭遇,ñC 等于 PC。对于多人互动,ñC 可以超过 PC并且非常容易进行半解析近似。估算ñC 需要在整个互动过程中整合碰撞率随时间的推移, ñ˙C基于初始轨道状态的不确定性分布计算为统计期望值的值。不确定性分布是根据卫星轨迹测量的轨道确定分析估计的。该公式考虑了卫星的非线性轨道运动,并得出ñCñ˙C 蒙特卡洛模拟的表达式以及单次和多次遇到的相互作用的半解析近似。

更新日期:2021-02-01
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