The International Space Station is being designed to perform debris avoidance maneuvers based on certain criteria developed from the probability of collision Pc. Existing methods to determine the Pc are based on the dee nitionofacollision/conjunctionplanethatcontainsallofthepositionuncertaintyassociatedwiththeproblem.In thispaperwedevelopa directand more naturalway of obtaining probability ofcollision and presentanalternative but equivalent dee nition for Pc 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. HE International Space Station (ISS) shall continuously face the threat of collision with orbiting debris. Hence, there needs to be a comprehensive methodology that can assess the risks posed byindividualdebrisencountersand suggestmaneuverswhenneces- sary. Such a study shall not only benee t the ISS, but also any future orbital asset placed in low Earth orbits. Thus, although we refer to the ISS in the rest of our paper, the analysis presented here holds true for any other orbiting asset of size and orbit comparable with that of the upcoming ISS. Space shuttle (SS) maneuvers are commanded to avoid poten- tial collisions with cataloged space objects (maintained by the U.S. Space Command ) whenever the estimated conjunction with an ob- jectfalls within a box centered on the estimated SSposition. The di- mensionsofthisconjunctionboxare §5 kmin thein-track direction and §2kmintheradialandout-of-planedirections.Thedimensions of such a conjunction box are probably based on prior estimates of position error covariances. The determination was made that this simple criterion, or any other known deterministic criterion 1,2 when applied to the ISS, would result in too many maneuvers. 3 In addi- tion, unnecessary maneuvers waste fuel and hamper the micrograv- ity experiments onboard the ISS. Although the size of the conjunc- tion box could be decreased to decrease the manuever rate, such a step clearly increases the risk to unacceptable levels. Therefore, the ISS needs a more rigorous probability-based approach for collision avoidance. 4