Two computational strategies for the evaluation of the spherical harmonic coefficients of the gravitational potential due to a generally shaped homogeneous polyhedral source are examined in detail. The techniques are implemented numerically for the known asteroid shape models of Eros and Didymos. The aim of the investigation is to quantify specific numerical aspects of the two algorithms, such as the accuracy of the techniques compared to a closed analytical solution for varying distance between source and computation point, the band-limited spectral analysis of the obtained spherical harmonic models and the convergence behavior of the corresponding series expansion in the vicinity of the characteristic Brillouin sphere. From a computational point of view, the line integral approach demands approximately three times the CPU time of Werner’s method. The two sets of spherical harmonic coefficients are 100% correlated up to degree 45 for Eros and up to degree 49 for Didymos. Approaching degree 100, the correlation by degree decreases by 0.0004% for Eros and by 0.004% for Didymos, the corresponding values for the correlation by order being 0.0002% and 0.304%. Inside the Brillouin sphere and approaching its boundary, the numerical agreement of the gravitational potential between the line integral method and the analytical solution is at the 1E-4 level, while with Werner’s approach at the 1E-7 level. At a distance of 33.5 km outside the Brillouin sphere for Eros and 2.2 km for Didymos, both methods are identical, reaching an agreement level with the analytical solution of 1E-11 level for Eros and 1E-14 for Didymos. In terms of spherical harmonic representation, the series defined by the line integral approach converges faster to the analytical value for the gravitational potential by 4 degrees.

详细研究了两种计算策略，用于评估由于一般形状的均匀多面体源而产生的引力势的球谐系数。这些技术已针对已知的 Eros 和 Didymos 小行星形状模型进行了数值实施。研究的目的是量化这两种算法的具体数值方面，例如与源和计算点之间的距离变化的封闭解析解相比，技术的准确性、所获得的球谐模型的带限谱分析以及特征布里渊球附近相应级数展开的收敛行为。从计算的角度来看，线积分方法所需的 CPU 时间大约是 Werner 方法的三倍。两组球谐系数 100% 相关，Eros 的相关度高达 45 度，Didymos 的相关度高达 49 度。接近 100 度时，Eros 的度数相关性降低了 0.0004%，Didymos 降低了 0.004%，相应的顺序相关性值为 0.0002% 和 0.304%。在布里渊球内部并接近其边界，线积分法与解析解之间的引力势数值一致性处于1E-4水平，而与Werner方法的数值一致性处于1E-7水平。在Eros布里渊球外33.5 km处和Didymos布里渊球外2.2 km处，两种方法完全相同，与Eros 1E-11级和Didymos 1E-14级解析解达到一致水平。就球谐表示而言，