Explicit Expression Of Collision Probability In Terms Of Rsw And Ntw Components Of Relative Position
September 15, 2013 - Bai, Xian-Zong; Chen, Lei; Tang, Guo-Jin
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EmailJournal or Book Title: ADVANCES IN SPACE RESEARCH
Volume/Issue: 52
Year Published: 2013
The existing analytical and numerical computing methods for collision probability (P-c) provide sufficiently accurate results, but do not reveal the direct connection between P-c and conjunction geometry or error covariance. This paper derived an explicit expression of P-c under the circular orbit assumption, based on analysis of closest approach distance and Chan's analytical formulae for P-c. The P-c was expressed as an explicit function of the radial, in-track, cross-track components of relative position and error covariance. The explicit expression is simple and compact, relates P-c with components of relative position, which are two kinds of important conjunction risk criteria. By introducing non-zero flight-path angle and ratio of velocity's magnitude, a modified expression of P-c was presented for objects in eccentric orbits. For objects with eccentricity less than 0.01 (which account for 62% of all LEO objects), the relative error of the explicit expression is less than 0.107, or 0.252 for typical conjunction cases. What really matters in conjunction risk assessment is the order of magnitude rather than the specific value of P-c, the precision of the explicit expression is sufficient for conjunction risk assessment and decision-making for most LEO objects. (C) 2013 COSPAR. Published by Elsevier Ltd. All rights reserved.
DOI: 10.1016/j.asr.2013.05.034
Type of Publication: Article