Numerical Implementation of Empirical Distribution Models for Spacecraft Fragmentation

In-orbit collisions with space debris anduncontrolledsatellites represent an actual hazard for the safety and exploitation of Earth orbits. In case of impacts and break-ups, up to thousands of fragments may be generated; their number and distribution is directly correlated to the shapes of the collidingsatellites and the impact geometry.To date,distributions of fragments size, area-to-mass, and velocity are generated by empirical models. Several of them can be used as reference when evaluating the consequences of in-space fragmentation, including the one under development by the University of Padova. To compute the fragment distributions, this model considers both common standard parameters, such as the satellites masses and relative velocity, and new variables, namely the nature of satellites and the impact geometry. In this paper, the numerical implementation of this model developed by Stellar Project s.r.l is presented. The implemented algorithm simulates in-orbit satellite collisions, applying mathematical models to compute the fragment distributions resulting from in-orbit collisions. The algorithm accounts for the standard NASA-SBM inputs along with several other parameters, such as satellite dimensions, presence of appendices, and impact geometry; in particular, the impact point allows determining if the collision is central, on the spacecraft side or on appendices. This allows to define scaling parameters that increase the accuracy of the model prediction for glancing or non -normal impact scenarios. The implemented software permits the user to input custom collision parameters, both exact or as ranges associated to probability density functions (PDFs), depending on the user’s knowledge of the impact event. Finally, multiple simulations computed using the newly developed software are compared with the data acquired from real world events, with hypervelocity impacts data gained from laboratory experiments and with the NASA-SBM. It is shown the new model’s capability to reproduce the experimental distributions, even for glancing impacts.