Transformation of Satellite Breakup Distribution for Probabilistic Orbital Collision Hazard Analysis

Abstract

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Analytical Propagation of Space Debris Density for Collisions near Sun-Synchronous Orbits

“…Therefore, it is necessary to carry out a transform from the set of orbits into density in a continuous form. Thanks to the work of Kessler [27], Izzo [28,29], and Frey and Colombo [12], the density function can be expressed in terms of either the Cartesian coordinates or the orbital elements, which are equivalent in some sense. To be precise, one can perform a change of variables to transform from one form to the other.…”

“…The body of these work in [6][7][8][9][10][11] made an extensive contribution to the research on orbital evolution of debris clouds. Recently, a complete description of the satellite breakup events based on the probabilistic analysis method was provided by Frey and Colombo [12]. The reachable domain theory was applied to model early medium-term evolution and collision probability of debris clouds by Wen and Gurfil [13] and Wen and Qiao [14].…”

Investigating the risks of debris-generating ASAT tests in the presence of megaconstellations

“…The NSBM is implemented following [15], which yields probability distributions for parameters that describe debris formed from an explosion or collision. The distributions that we use correspond to the parameterizations for a collision.…”

“…The choice is intended to better represent the energetics of the India 2019 ASAT test, which used a kinetic kill vehicle rather than an explosive warhead. Distribution parameters can be found in Appendix B of [15].…”

“…These PDFs are sampled to obtain a distribution of A/M ratios. The area and mass for the fragment is obtained using its A/M ratio and equations (42a,b) of [15]. The initial number distribution ∆N(L c ) is normalized using the ratio of the target payload mass to the total fragment mass m t /m frag,tot , the A/M and mass distributions are re-sampled, and this process is done iteratively until m frag,tot ≤ M e , resulting in a total number of fragments N tot and an updated mass of fragments M * e = m frag,tot .…”