The periodic variations of the covariance and the effect on the probability of collision

Abstract

This research deals with the investigation of the periodic variations of the covariance of satellites and its effect on the probability of collision, P[C], between two objects in orbit about the Earth. Since the P[C] is dependent on the position covariance the time of conjunction relative to epoch can have a substantial effect on P[C]. Therefore, the effect of these periodic variations on the P[C] needs to be investigated. For these investigations space track data on actual objects were used. The objects were 5143 (Rocket Body), 6155 (OAO3), 20496 (LACE), and 25544 (ISS). The "best" element set and an orbit's state at epoch can be accurately estimated using the Analyst Workstation (AWS). The covariance of these objects at the estimated conjunction was obtained by propagating from the epoch to conjunction using the Geometric Method state transition matrix for linearized relative motion equations that include the effects of J₂. Assuming the encounter geometry was constant the probability of collision was computed at each time step. This study shows the effect of the periodic variations of the covariance on P[C], and how the phasing of the last track before conjunction affects P[C].