Adaptive Gravitational Force Representation for Fast Trajectory Propagation Near Small Bodies

Abstract

We present an approximation scheme for gravitational forces near arbitrarily shaped small bodies. The approximation uses polynomial interpolation with an adaptive spatial data structure near the asteroid and spherical harmonics far from it. These data structures allow us to drive the approximation errors of the model to within userdefined thresholds, while significantly reducing the run time of trajectory integrations about small bodies. This alleviates the computational burden of Monte Carlo simulation for small-body proximity operation and mission design. We conclude with performance tests and models for the asteroid 1998 ML 14.

Reliability-Based Soft Landing Trajectory Optimization near Asteroid with Uncertain Gravitational Field

“…Its gravitational field near the asteroid could hardly be denoted by using the spherical harmonics expansion because it is only valid outside a circumscribing sphere. Assuming that the density of the asteroid is uniform, the accurate potential function of the polyhedral asteroid can be computed by the method reported in [11][12][13]. However, this method is relatively time consuming, especially when it is used in the numerical integration, and it is very difficult to use in the nonuniform density case.…”

Structure Preserving Approximations of Conservative Forces for Application to Small-Body Dynamics

“…Exactness: All conservative forces are the gradient of some potential field. The cubetree method presented in [6] does not respect this qualitative feature. This is especially important for long-term simulation where qualitative features of the trajectories are of primary interest.…”

“…Recently, a novel numerical scheme (the cubetree algorithm) for the fast evaluation of gravitational force around irregular bodies has been introduced by the authors [6] and shown to provide a significant speed improvement over other methods. The scheme exploits the availability of large storage capacities to reduce the online computations.…”

Comparisons of the Cubed-Sphere Gravity Model with the Spherical Harmonics

“…Interpolation models have been developed to make evaluation faster. Some of these models preserve the spherical coordinate system [3,4], while others drastically reformulate the evaluation of the gravity field [5,6].…”