Quantifying Shortcomings in the 2-D Pc Calculation

The probability of collision, Pc, between two Earth-orbiting satellites can often, but not always, be approximated adequately using the "2D-Pc" formulation. The objective is to find a set of "boundary conditions" that ensure the 2D-Pc approximation be sufficiently accurate, so that it may be determined when computationally-intensive Brute Force Monte Carlo1 (BFMC) Pc estimates are required. We critically examine the assumptions used in the formulation of the 2D-Pc approximation and then formulate 2D-Pc boundary condition tests to check if these assumptions are satisfied adequately.