Collision criterion for two satellites on Keplerian orbits

This paper analyzes the collision possibility for two satellites on Keplerian orbits. Coplanar and noncoplanar cases are considered, respectively. For each case, the problem of collision possibility analysis can be solved through two steps: First, to determine whether there is any intersection point of the two orbits; if there is no intersection point, the conclusion can be given directly that collision never happens. Secondly, if the two orbits do intersect, the collision possibility in the given time-scale can be studied in terms of the relationship between the two orbital periods and time. Numerical simulations for both cases, each including several situations, are given to prove the validity of the proposed collision criterion.