A Grid-Based, Bayesian Approach to Uncertainty Propagation for Icy-Moon Missions

The orbital and in situ exploration of the icy moons of Jupiter and Saturn is currently at the forefront of planetary science, with the NASA Europa Clipper mission scheduled for launch in 2024 and the proposed Enceladus Orbilander ranking as the third highest priority Flagship mission in the 2023-2032 Decadal Survey. While the theory for plotting a gravity flyby tour through the satellite systems is well understood and has been implemented, our knowledge about the dynamical evolution of orbits and their uncertainties in the vicinity of these moons is still incomplete. NASA’s planetary protection guidelines, moreover, require that spacecraft avoid biologically contaminating these potentially habitable worlds; a significant challenge for multi-body mission design, where the orbital phase space is dominated by chaotic trajectories. To accurately propagate the state uncertainty of icy-moon mission satellites, a more refined method for nonlinear state estimation is needed. The proposed research seeks to develop a grid-based framework for uncertainty propagation of chaotic space trajectories that utilizes novel orbital element state representations and efficient data structures paired with parallelization for computational feasibility. This work adopts and extends a Grid-based Bayesian Estimation Exploiting Sparsity (GBEES) methodology, which approximates the Fokker-Planck solution, and has been shown to accurately propagate Gaussian uncertainty along the Lorentz attractor. Hitherto, this algorithm has only been used in low-dimensional systems, but will be extended here to treat to the full six-dimensional state that characterizes the space vehicles trajectories. This technique could reveal new options for trajectory design and disposal that, up to now, have been obscured by the complexities introduced by the complicated multi-body environments. This will permit a detailed study of orbital stability in the presence of close encounters and orbital resonances and could feed-forward into Clipper or future icy-moon missions.

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