A novel approach for the computation of the spherical harmonic coefficients of the gravity field of a constant density polyhedron is presented. The proposed method is based on the expression of these coefficients as the volume integral of solid harmonics. It is well known that the divergence theorem leads to an expression of these volume integrals as surface integrals. We show that these surface integrals can be expressed as the sum of line integrals along the edges of the polyhedron. In contrast to previous approaches, the values of the spherical harmonic coefficients at a given degree and order result directly from the computation of the line integrals. The performed numerical implementation revealed the stability of the proposed algorithm up to degree 360 for a prismatic test source.

中文翻译：

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计算等密度多面体潜在谐波系数的线积分方法

提出了一种计算恒定密度多面体重力场球谐系数的新方法。所提出的方法基于将这些系数表示为固体谐波的体积积分。众所周知，散度定理导致将这些体积积分表示为表面积分。我们表明这些表面积分可以表示为沿多面体边缘的线积分的总和。与之前的方法相比，给定度数和阶数的球谐系数的值直接来自线积分的计算。所执行的数值实现揭示了所提出的算法在棱镜测试源的高达 360 度的稳定性。