Method of intersecting detection of ellipsoids between launching vehicles and space objects

In order to precisely assess collision risk between space objects and launch vehicles, the method of detecting the intersection of two space ellipsoids surrounded with the two objects is discussed. The matrix formulae for the ellipsoids of space objects and launch vehicles are acquired. The eigenvalues for an associated matrix of the two ellipsoids are used to determine the status of overlapping, touching and separated. The principle for the special overlapping which means one ellipsoid includes the other is discussed. A satellite launching-safety example shows that, the method presented by the paper is useful to reduce the highly false alarm, which can be easily caused by the distance detecting during the launch-safety analysis.