This work proposes a continuum-based approach for the propagation of
uncertainties in the initial conditions and parameters for the analysis and
prediction of spacecraft re-entries. Using the continuity equation together
with the re-entry dynamics, the joint probability distribution of the
uncertainties is propagated in time for specific sampled points. At each time
instant, the joint probability distribution function is then reconstructed from
the scattered data using a gradient-enhanced linear interpolation based on a
simplicial representation of the state space. Uncertainties in the initial
conditions at re-entry and in the ballistic coefficient for three
representative test cases are considered: a three-state and a six-state steep
Earth re-entry and a six-state unguided lifting entry at Mars. The paper shows
the comparison of the proposed method with Monte Carlo based techniques in
terms of quality of the obtained marginal distributions and runtime as a
function of the number of samples used
