Probability of collision between space objects

The International Space Station is being designed to perform debris avoidance maneuvers based on certain criteria developed from the probability of collision P-c. Existing methods to determine the P-c are based on the definition of a collision/conjunction plane that contains all of the position uncertainty associated with the problem. In this paper we develop a direct and more natural way of obtaining probability of collision and present an alternative but equivalent definition for P-c that leads to the same results obtained earlier. Because debris avoidance is crucial for every orbiting asset in low Earth orbit, a study of this nature helps to establish the equivalence of different methods for risk assessment and evaluation.