Using Chebyshev polynomials interpolation to improve the computation efficiency of gravity near an irregular-shaped asteroid

TL;DR

This paper introduces an adaptive Chebyshev polynomial interpolation method to efficiently compute the gravitational field of irregular-shaped asteroids, significantly reducing calculation time compared to traditional methods.

Contribution

The authors develop a novel adaptive interpolation approach using Chebyshev polynomials and error-adaptive octree division for irregular asteroid gravity modeling.

Findings

Efficiency increased by hundreds to thousands times

Method applicable to various irregular asteroids

Improved interpolation precision near the surface

Abstract

In asteroid rendezvous missions, the dynamical environment near the asteroid's surface should be made clear prior to the mission launch. However, most of the asteroids have irregular shapes, which lower the efficiency of calculating their gravitational field by adopting the traditional polyhedral method. In this work, we propose a method to partition the space near the asteroid adaptively along three spherical coordinates and use Chebyshev polynomials interpolation to represent the gravitational acceleration in each cell. Moreover, we compare four different interpolation schemes to obtain the best precision with the identical initial parameters. An error-adaptive octree division is combined to improve the interpolation precision near the surface. As an example, we take the typical irregular-shaped near-Earth asteroid 4179 Toutatis to show the advantage of this method, as a result, we show that the efficiency can be increased by hundreds to thousands times with our method. In a word, this method can be applicable to other irregular-shaped asteroids and can greatly improve the evaluation efficiency.