不规则形状小行星引力环境建模及球谐系数求取方法

Modeling for the gravitation potential environment of an irregular-shaped asteroid and the spherical harmonic coefficient estimation

在实施小行星探测任务之前,需要对不规则形状小行星的引力场有一个清楚的认识,以便于进行环绕或着陆小行星的轨道设计。文章提出了一种小行星引力场建模及球谐系数的求取方法。首先,由多面体模型方法重构出小行星外部的引力环境并以此作为虚拟观测量。在此基础上,根据球谐系数与引力势能间的关系,通过求解超定线性方程组得到小行星引力场的各阶次球谐系数。与传统的将小行星近似成三轴椭球体进而计算球谐系数的方法相比,该方法可大幅度提高引力场建模的精度。通过与由NEAR探测器轨道数据解算的Eros433小行星的球谐系数比较表明,其最大误差不超过6%。计算表明,该方法可以为小行星探测任务发射前的轨道设计提供更为精确的数据。

The pre-mission certification of the irregular-shaped asteroid gravitation is essential for the orbit design (in orbiting phase or landing phase).This paper proposes a novel algorithm for the irregular-shaped asteroid spherical harmonic coefficient estimation,where the gravitation potential of the asteroid is reconstructed using the polyhedral model method and is taken as the virtual measurements.Then a formula for the relationship between the spherical harmonic coefficients and the gravitation is suggested.Finally the spherical harmonic coefficients of the asteroid gravity are computed by solving the over-determined equations based on the least squares method (LSM).Compared with the traditional method which approximates the asteroid as a tri-axial ellipsoid,the algorithm proposed in this paper could obviously improve the asteroid gravitation modeling resolution.When compared with the spherical harmonic coefficients of Eros 433 derived from NEAR probe orbit data,the relative error is less than 6%.The result indicates that it is more accurate and will offer more information for pre-mission orbit design.