Debris re-entry modeling using high dimensional derivative based uncertainty quantification

Well-known tools developed for satellite and debris re-entry perform break-up and trajectory simulations in a deterministic sense and do not perform any uncertainty treatment. In this paper, we present work towards implementing uncertainty treatment into a Free Open Source Tool for Re-entry of Asteroids and Space Debris (FOSTRAD). The uncertainty treatment in this work is limited to aerodynamic trajectory simulation. Results for the effect of uncertain parameters on trajectory simulation of a simple spherical object is presented. The work uses a novel uncertainty quantification approach based on a new derivation of the high dimensional model representation method. Both aleatoric and epistemic uncertainties are considered in this work. Uncertain atmospheric parameters considered include density, temperature, composition, and free-stream air heat capacity. Uncertain model parameters considered include object flight path angle, object speed, object mass, and direction angle. Drag is the only aerodynamic force considered in the planar re-entry problem. Results indicate that for initial conditions corresponding to re-entry from a circular orbit, the probabilistic distributions for the impact location are far from the typically used Gaussian or ellipsoids and the high probability impact location along the longitudinal direction can be spread over ∼2000 km, while the overall distribution can be spread over ∼4000 km. High probability impact location along the lateral direction can be spread over ∼400 km.