Spacecraft collision analysis for long-term encounter in close-range

A novel method for close-range spacecraft collision analysis based on the concept of relative reachable domain (RRD) is proposed. The RRD describes the minimum position volume enclosing all the possible location that the spacecraft may arrive. It can be obtained by integrating the time-varying error ellipsoids of spacecraft, which calculated by covariance analysis description equation technique (CADET), in the given time interval. Comparisons between the solved envelope of RRD and the results of a certain amount of Monte Carlo trajectories, which can be regarded as the true results, are presented to demonstrate the feasibility of the RRD method. Spacecrafts may collide with each other when their RRD envelope overlapping. An algebraic condition for estimate whether there is an overlap between the two RRDs is presented subsequently. The algebraic condition can be used to assess the possibility of collision in the given probability threshold. Simulation results indicate that the algebraic method is convenient and feasible for the long-term encounter collision problem.