Determination of close approaches based on ellipsoidal threat volumes

摘要

A method for computing close approach events for space objects having ellipsoidal threat volumes is presented. An event is deemed to occur whenever the closest distance between the an ellipsoid about a satellite of interest and an ellipsoid about another orbiting object is less than an user-specified threshold. The dimensions of each ellipsoid, representing the position uncertainty of an object, is also user-specified. Both fixed and time-varying ellipsoids are considered. We first describe the solution to the problem of computing the closest distance between a point and an ellipsoid. We then use this solution in an iterative scheme to compute the closest distance between two ellipsoids.