<h2>AAS 99-170</h2>
<h2>Determination of Close Approaches Based on Ellipsoidal Threat Volumes                                                                            </h2>
<h4>V.T. Coppola, J. Woodburn                                                                                                                                                           </h4>
Analytical Graphics, Inc., Malvern, PA                                                                                                                                    
<h2> Abstract </h2>
We describe a method for computing close approach events for space objects having ellipsoidal threat volumes. An event is deemed to occur whenever the closest distance between the primary ellipsoid and a secondary ellipsoid is less that a user-specified threshold. The size 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 the two ellipsoids.