Safety analysis for shallow controlled re-entries through reduced order modeling and inputs' statistics method

Abstract In recent years, the interest and demand for small satellites have grown exponentially. While in the past the end-of-life design for this type of spacecraft was often approximated or totally neglected, it has recently become increasingly important. Indeed, small spacecraft able to achieve advanced mission objectives are more frequently on the worldwide space agenda. They may contain components which might withstand the re-entry conditions and reach the ground. In addition, these spacecraft are usually limited to shallow re-entries which are more sensitive to atmospheric model uncertainties and thus have larger debris fields. The objective of this work is to provide a reliable and efficient statistical analysis to estimate the risk to aeronautic and maritime traffic as well as to ground based populations. A simple geometric safety assessment is proposed, based on the safety boxes concept introduced in the ESA Space Debris Mitigation Compliance Verification Guidelines. Correctly estimating the dimensions of a safety box and locating it over uninhabited regions, such as the oceans, guarantees a casualty risk below a prescribed value. Furthermore, by estimating the probability of debris landing outside the largest possible safety box within which there is a zero casualty risk, the maximum probability of control failure admissible for the mission can be estimated. This proposed safety analysis is achieved using two re-entry models of differing complexity. The high fidelity model includes both the aerodynamic and aerothermodynamic effects that occur during re-entry and is used to statistically characterize “high level’’ uncertain variables such as the ballistic coefficient and the demise altitude. The reduced order model is based on these high level variables and captures the spacecraft fragmentation behavior and its re-entry dynamics with significantly less computation time than the high fidelity model. Coupled with advanced statistical techniques designed to estimate very low probabilities such as the Inputs' Statistics Method, a reliable safety analysis can be conducted with a limited overall computational burden. The proposed safety analysis is applied to a fictitious 2U CubeSat mission that performs a controlled re-entry using the Drag De-orbit Device developed by the ADAMUS laboratory at the University of Florida.