Theoretical and empirical analysis of the average cross-sectional areas of breakup fragments

Abstract: This paper compares two different approaches to calculate the average cross-sectional area of breakup fragments. The first one is described in the NASA standard breakup model 1998 revision. This approach visually classifies fragments into several shapes, and then applies formulae developed for each shape to calculate the average cross-sectional area. The second approach was developed jointly by the Kyushu University and the NASA Orbital Debris Program Office. This new approach automatically classifies fragments into plate- or irregular-shapes based on their aspect ratio and thickness, and then applies formulae developed for each shape to calculate the average cross-sectional area. The comparison between the two approaches is demonstrated in the area-to-mass ratio (A/m) distribution of fragments from two microsatellite impact experiments completed in early 2008. A major difference between the two approaches comes from the calculation of the average cross-sectional area of plates. In order to determine which of the two approaches provides a better description of the actual A/m distribution of breakup fragments, a theoretical analysis in the calculation of the average cross-sectional area of an ideal plate is conducted. This paper also investigates the average cross-sectional area of multi-layer insulation fragments. The average cross-sectional area of 214 multi-layer insulation fragments was measured by a planimeter, and then the data were used to benchmark the average cross-sectional areas estimated by the two approaches. The uncertainty in the calculation of the average cross-sectional area with the two approaches is also discussed in terms of size and thickness. [Copyright &y& Elsevier]