Eric R. George (The Aerospace Corporation), F. Kenneth Chan (Independent Consultant)
Keywords: Astrodynamics
Abstract:
Several relationships are developed relating object size, initial covariance and range at closest approach to probability of collision. These relationships address the following questions: – Given the objects initial covariance and combined hard body size, what is the maximum possible value of the probability of collision (Pc)? – Given the objects initial covariance, what is the maximum combined hard body radius for which the probability of collision does not exceed the tolerance limit? – Given the objects initial covariance and the combined hard body radius, what is the minimum miss distance for which the probability of collision does not exceed the tolerance limit? – Given the objects initial covariance and the miss distance, what is the maximum combined hard body radius for which the probability of collision does not exceed the tolerance limit? The first relationship above allows the elimination of object pairs from conjunction analysis (CA) on the basis of the initial covariance and hard-body sizes of the objects. The application of this pre-filter to present day catalogs with estimated covariance results in the elimination of approximately 35% of object pairs as unable to ever conjunct with a probability of collision exceeding 1×10-6. Because Pc is directly proportional to object size and inversely proportional to covariance size, this pre-filter will have a significantly larger impact on future catalogs, which are expected to contain a much larger fraction of small debris tracked only by a limited subset of available sensors. This relationship also provides a mathematically rigorous basis for eliminating objects from analysis entirely based on element set age or quality a practice commonly done by rough rules of thumb today. Further, these relations can be used to determine the required geometric screening radius for all objects. This analysis reveals the screening volumes for small objects are much larger than needed, while the screening volumes for pairs of large objects may be inadequate. These relationships may also form the basis of an important metric for catalog maintenance by defining the maximum allowable covariance size for effective conjunction analysis. The application of these techniques promises to greatly improve the efficiency and completeness of conjunction analysis.
Date of Conference: September 11-14, 2012
Track: Astrodynamics