A fast Chebyshev polynomial method for calculating asteroid gravitational fields using space partitioning and cosine sampling

This paper presents a computationally fast method for solving gravitational accelerations near irregularly-shaped asteroids. This method is based on analytical three-dimensional Chebyshev polynomial approximation of the polyhedral gravity. For the purpose of improving the approximation accuracy, space partitioning schemes based on practical flight zones is used to avoid interpolation the whole space around the target asteroid. Specifically, a minimum ellipsoid close to the asteroid surface is defined to select the space for surrounding trajectories with safe distance and a cone connected to the surface is defined to select the space for descent trajectories. Moreover, interpolation points are sampled in a cosine sampling fashion according to the Chebyshev-Gauss-Lobatto nodes and a radial adaption technique. The performance of different space partitioning schemes is analyzed. The effectiveness of the proposed method is validated through simulations of solving gravitational accelerations at the test points near different shaped asteroids 1996 HW1, 433 Eros, 25143 Itokawa and 101955 Bennu.