Dynamic scaling of fragment populations in orbital breakup modelling

The modelling of on-orbit fragmentations is becoming increasingly relevant for assessing the consequences of fragmentation events and the ensuing risk to active spacecraft nearby, as well as the long-term stability of the orbital environment. The fragmentation model currently used at the Institute of Space Systems at TU Braunschweig is based on ESA’s MASTER tool suite, which provides a statistical size distribution of the generated fragments from a breakup, and relies heavily on dynamic scaling of this distribution in order to set the true number of generated debris. We present improvements made to three main aspects of this dynamic scaling: first, considerations for the time delay between the occurrence of a fragmentation event and when most, or all of its detectable fragments have been catalogued, which enables a thorough fragmentation analysis within a short time after an event. Furthermore, the current implementation of the Henize factor, which takes into account fragments that remain unobserved by sensor networks at long timescales after the event, is overhauled and re-implemented as a dynamic scaling function intended to more accurately reflect the original data it is based on. Finally, a method for the derivation of an empirical equation for the minimum diameter trackable by sensor networks as a function of the altitude is presented. This minimum trackable diameter is the reference point at which the dynamic scaling of the fragment size distribution from a breakup is performed. Amendments to these three aspects of the scaling greatly influences the accuracy and validity of the later steps in the institute’s fragmentation model, improving the subsequent assessments of the risk and remaining lifetime of the generated fragments.