Orbit Databases and Fast Gravity Fields for Rapid Trajectory Design Near Small Bodies

Mission design in the vicinity of small celestial bodies must grapple with significant uncertainty in the body’s physical parameters and dynamical complexity, particularly near the body surface. This research aims to develop fast modeling approaches and tools for analyzing internal density distributions in order to accelerate the mission design lifecycle both before and after a spacecraft arrives at a target small body. The research objectives originally encompassed leveraging such tools to build out orbit databases to serve as good initial guesses for trajectory optimization, but such work is left to the future due to the time constraints of the project. The work completed took place in three main phases: the first phase focused on developing a hybrid discrete-element approach for small body gravity modeling that would provide fast and accurate proxy models for state-of-the-art polyhedral gravity models. Work involved development of a novel shape model packing algorithm and trade studies of potential-fitting algorithms to improve the accuracy of the hybrid gravity models. The second phase of research improved the tools developed in the first by adapting the packing procedure for robustness to extreme nonconvexity in the body shape and developing a systematic approach to identifying optimal model configurations for several small bodies of interest. The third phase tackled the problem of modeling the near-surface small body gravity field and estimating internal density distributions when a spherical harmonics reference field exists. Regionally-divided mascon models were employed to represent internal density heterogeneities in an approach that fitted the total mascon potential to the reference spherical harmonic potential. The first phase of work resulted in hybrid gravity models for 433 Eros that were shown in published research to offer up to order-of-magnitude computational speed-ups relative to state-of-the-art reduced resolution polyhedral gravity models of equivalent accuracy. Several such models were identified along a performance Pareto front, demonstrating the potential to generate several model alternatives adapted to specific use-cases. Similar computational benefits were demonstrated in the second phase for the asteroids 216 Kleopatra and 25143 Itokawa and Comet 67P/Churyumov-Gerasimenko, representing a broad range of shape and dynamical characteristics. Hybrid gravity model alternatives for these bodies will be publicly available in short order, along with simple Fortran driver routines for their evaluation. Overall, the gravity field modeling methods implemented in the first two research phases were shown to result in efficient proxy models for state-of-the-art polyhedral models that are typically employed as references in the pre-arrival phase of the mission lifecycle. Providing accelerated gravity field evaluations at little accuracy cost has the potential to accelerate mission design efforts from conceptual design through the approach phase. The third phase of research demonstrated the estimation of feasible heterogeneous mascon models for small bodies that are statistically consistent with a reference spherical harmonics field. In practice, the reference field would likely result from orbit determination efforts and represent (albeit with significant uncertainty) information about the body’s true gravity field. By applying a carefully tuned constant-density prior, the density estimation method results in all-positive density distributions. In addition, the gravity fields of the estimated regional mascon models can be evaluated within the Brillouin sphere and (for best-case models) have Stokes’ coefficients that fall within one standard deviation of the reference coefficients. In other words, the estimated regional mascon models provide a fast, statistically consistent proxy for the reference spherical harmonics field that can be used for near-surface trajectory design and analysis.