Hybrid model of gravitational fields around small bodies for efficient trajectory propagations

When modeling the gravitational fields around small bodies, the highly irregular shapes of such objects make it difficult to balance accuracy with efficiency. In this paper, a novel and general hybrid model for evaluating the gravity of a small body is proposed with the aim of reducing errors and the computational cost. The hybrid model separates dominant effects and smaller undulations. The dominant effects are represented by the gravity-best-fit ellipsoid, which is generated by solving an optimization problem in the sense of minimizing the contribution of undulations. The undulations are then approximated using the serendipity interpolation technique, which is computationally efficient. Furthermore, a discretization scheme for the region of interest is developed, and this guarantees the evaluation of gravity in the close proximity of a small body. Based on this discretization strategy, a rapid element tracking scheme is developed to improve the efficiency of trajectory propagations. The most remarkable advantage of this tracking strategy is that the runtime for identifying elements remains the same when the region of interest is arbitrarily broadened. Simulations on asteroids 1999 KW₄ and 1620 Geographos show that the hybrid model is highly accurate and around 196 times faster than the conventional polyhedral model.