An analytic method to determine future close approaches between satellites

Abstract

The calculation of the times of future close approaches between pairs of satellites has been formulated using analytical techniques. The resulting analytical equations are solved using numerical iterative techniques similar to solving Kepler's equation. A solution is obtained in a very efficient manner by use of a series of prefilters which eliminate many cases from further consideration. The method is valid for all values of eccentricities less than one and all relative geometries between the two orbits. This approach produces results in a very efficient and reliable manner.