Maximum collision probability considering variable size, shape, and orientation of covariance ellipse

摘要

When engaging in the maximum collision probability (P_(cmax)) analysis for short-term conjunctions between two orbiting objects, it is important to clarify and understand the assumptions for obtaining P_(cmax). Based on Chan's analytical formulae and analysis of covariance ellipse's variation of orientation, shape, and size in the two-dimensional conjunction plane, this paper proposes a clear and comprehensive analysis of maximum collision probability when considering these variables. Eight situations will be considered when calculating P_(cmax) according to the varied orientation, shape, and size of the covariance ellipse. Three of the situations are not practical or meaningful; the remaining ones were completely or partially discussed in some of the previous works. These situations are discussed with uniform definitions and symbols and they are derived independently in this paper. The consequences are compared and validated by the results from previous works. Finally, a practical conjunction event is presented as a test case to demonstrate the effectiveness of methodology. Comparison of the P_(cmax) presented in this paper with the empirical results from the curve or surface calculated by numerical method indicates that the relative error of P_(cmax) is less than 0.0039%.