Satellite Collision and Fragmentation Probabilities Using Radar-Based Size and Mass Estimates

Most conjunctions between Earth-orbiting satellites involve unknown objects, typically debris created by explosions or collisions. This study formulates methods to estimate probabilities of collision and fragmentation for such conjunctions, which depend on the estimated sizes and masses of the unknown objects. Analysis of radar cross-section (RCS) measurements provides estimated sizes, found to be accurate at the 90% confidence level to within a factor of 0.59 for potential underestimations and to within a factor of 3.1 for potential overestimations. For satellites that experience measurable atmospheric drag orbital perturbations, combining RCS data with orbit determination ballistic coefficients provides mass estimates accurate to within factors of 0.47 to 10.9 at the 90% confidence level. For satellites with perigee altitudes above 450 km, combining RCS data with solar radiation pressure coefficients provides mass estimates accurate to within factors of 0.44 to 5.6 at 90% confidence. The collision and fragmentation risk assessment formulation accounts for these size and mass estimation uncertainties. Specifically, conjunction collision probabilities formulated as statistically expected values account for the RCS-based size estimation uncertainties. Fragmentation probabilities, which measure the likelihood of producing more than a threshold number of collision fragments, account for both size and mass estimation uncertainties.