Fundamentals Of Debris Collision Avoidance

Collision avoidance maneuvering is one method of mitigating the risk from orbital debris and can be quite economically effective for some space vehicles. However, maneuvering also has associated costs and risks and should not be used in all cases. A holistic approach to debris collision avoidance maneuvering is required for a safe and effective process. This paper develops formalism for quantifying risk and residual risk based on a maneuvering strategy and position and position uncertainty for the tracked conjunction population. Position and position uncertainty predictions of the conjunction population need to be sufficiently accurate so that the cost of maneuvering a spacecraft is at least comparable to the value of the mitigated risk. A process based on an exclusion volume is compared with a process based on collision probability. The use of 2 line element sets for debris avoidance is also discussed. Before adapting any debris collision avoidance strategy for any vehicle, the associated risk and residual risk should be determined. A debris avoidance process based on collision probability offers the possibility of identifying the infrequent high collision probability conjunctions for which action should be taken if at all possible. Such a process has been adopted for both the International Space Station and for the Space Shuttle. INTRODUCTION The statistical risk of a collision between a spacecraft and tracked space debris is generally small for a given conjunction. However, even this small risk may be unacceptable for a variety of reasons. In particular the integrated risk over time may not be so small. Both the “exclusion volume” and “maneuver threshold” methods have been carefully investigated by performing detailed calculations of debris risk over time and debris avoidance maneuver rate for the Space Transport System (STS) Orbiter and the International Space Station (ISS). The exclusion volume and the threshold methods are inseparably related. The underlying mathematics of the two methods is identical. Also, conjunction screening is based upon an exclusion volume; the efficiency of the screening exclusion volume is the limiting efficiency of the debris avoidance process, whether the threshold method or the exclusion box method is employed in the final decision process. This analysis shows the threshold method to have the advantages of somewhat better risk reduction and far fewer maneuvers. All computations are based on empirically determined covariance distributions for STS and the orbital debris population. The covariance of the ISS is assumed to be that of an orbital debris object, subject to the same atmospheric drag as the ISS. State vector covariances for STS were determined from recent tracking data for 2, 4, 8, and 12 hour propagation times for low, moderate, and high vehicle activity. These covariances were combined with the debris covariances to determine the maneuver rate and fractional residual risk associated with different 54th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law 29 September 3 October 2003, Bremen, Germany IAC-03-IAA.5.3.03 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. 2 screening box shapes and sizes and different collision probability maneuver thresholds. The exclusion volume calculations, performed here, supersede all previous calculations. Before, the ratio of the exclusion volume to the volume of an ellipsoidal surface with a constant collision probability, equal to that of a maneuver threshold, was calculated. That ratio, weighted over the distribution of debris position uncertainty, was taken to be the exclusion volume efficiency. The exclusion volume calculations in this work, again weighted over the distribution of debris and space vehicle uncertainty, are mathematically precise. In this paper the STS covariance data is discussed, followed by presentation of the results of the debris covariance distribution determined in Reference 1. The expression for the collision probability is then given. The exclusion volume and threshold methods are explained and their interrelation is shown. The exclusion volume method is then applied to both ISS and STS followed by application of the threshold method. The last section of the paper contains a general discussion of results. STS STATE VECTOR COVARIANCES Post Flight Attitude and Trajectory History (PATH) ephemeris data from flights STS82, STS85, STS87, STS88, STS90 and STS92 was analyzed to provide a covariance matrix for low, moderate and high vehicle activity, for propagation times from epoch of 2, 4 8, and 12 hours. The 6x6 covariance matrix was calculated from the state vector deviations from prediction ∆S as