Accurate Uncertainty Characterization of Impulsive Thrust Maneuvers in the Restricted Three Body Problem

Uncertainty propagation in the circular restricted three body problem is traditionally carried out using Cartesian coordinates. In that case, both magnitude and direction information of velocity are embedded into the Cartesian components, and are inherently propagated together. An alternate model is proposed in this work for the propagation of velocity direction independent of its magnitude. The advantage of this feature for uncertainty characterization, especially for impulsive transfers, is discussed in this work with the help of case studies. In order to carry out these studies, computationally efficient strategies to propagate the statistical moments using deterministic sampling, and to evaluate the sensitivities of a reference trajectory through a non-intrusive data-driven approach are outlined. These sensitivities facilitate a polynomial approximation of the states rapidly, in the neighborhood of the reference trajectory, thereby allowing the generation of state histograms to study future consequences of initial uncertainties.