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Determining & Evaluating High Risk Conjunction Events Improving Space Operations Workshop Boulder, CO 5 – 6 April 2011

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Introduction Conjunction Assessment Process Collision Probability Sigma Level Analysis Alignment of Radial Vectors Collision Probability Sensitivity Maximum Collision Probability High Risk Events

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Conjunction Assessment Process (1/2) Conjunction assessment is performed based on state and state uncertainty data generated and disseminated by the JSpOC. Close approach predictions are generated based on a 5-day screening span. Results are sent out daily, or more frequently for high risk conjunction events. Predictions are made using data from the JSpOC high- accuracy space object catalog.

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Conjunction Assessment Process (2/2) The typical conjunction assessment process for a satellite program is to receive Orbital Conjunction Messages (OCMs) for secondary objects that are predicted to violate a designated screening volume around the primary satellite. OCMs contain sufficient data to calculate a Pc value; i.e., state vector and state uncertainty data. The screening volume must be large enough to capture close approaches with objects with a wide range of covariance sizes—this can result in large amounts of data and many conjunction events that are not a threat.

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Collision Probability (1/2) Collision probability (Pc) is a measure of the overlap of the error distribution of the two objects, where the error distribution is given by the covariance matrix. When the covariances of the objects are combined, Pc can be thought of as the relationship of the miss vector to the combined covariance. Primary & Secondary object with covariance ellipsoids Combined covariance with keep-out region positioned by miss vector

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Collision Probability (2/2) Pc is used as the primary measure of risk since it captures the miss distance, the relative geometry, and the associated uncertainty of the close approach. A conjunction assessment process based on miss distance alone does not account for the uncertainty inherent in the problem. Miss distance is used as the basis of the screening process, leading to the receipt of many OCMs for conjunction events with zero Pc values. This approach can lead to large amounts of data; especially for satellites in LEO.

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Sigma Level Analysis (1/2)

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Sigma Level Analysis (2/2)

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Sigma Level Analysis Results Sample report of data required: Sample results with corresponding collision probability: Predicted Miss DistancesPrimary Error at TCASecondary Error at TCA TotalRadialIntrackCross- track RadialIntrackCross- track RadialIntrackCross- track CaseRadial Sigma Level In-plane Sigma Level Collision Probability 12.290.357.78e-5 21.133.425.18e-9 3-9.290.050 40.840.361.18e-3 54.170.094.74e-012

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Alignment of Radial Vectors The Radial unit vectors of the two objects nearly align for conjunction events, therefore, the Radial direction can be decoupled from the Intrack and Crosstrack directions.

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Collision Probability Sensitivity Covariance size can be scaled to determine the sensitivity of the Pc value. Since covariance is propagated from OD epoch to Time of Close Approach (TCA), a reduction in covariance size gives an indication of how the Pc will evolve. This calculation is performed with a static miss distance.

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Maximum Collision Probability The Pc sensitivity curve allows evaluation of the Pc max condition. Pc max tends to occur when the miss vector lies on the 1-sigma uncertainty ellipsoid. Most conjunction events evolve to the left of the Pc max condition. Those that don’t tend to be of concern … Notice that in this example the covariance was enlarged to show Pc max.

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High Risk Events Some conjunction events show little change in Pc as the covariance is contracted. This occurs when the miss vector is within the 1 or 2-sigma of the combined covariance ellipsoid. This condition can be a sign that the conjunction event will remain a threat as the TCA approaches.

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