We apply three spherical-harmonic-based techniques to deliver external gravitational field models of the asteroid (101955) Bennu within its circumscribing sphere. This region is known to be peculiar for external spherical harmonic expansions, because it may lead to a divergent series. The studied approaches are (i) spectral gravity forward modelling via external spherical harmonics, (ii) the least-squares estimation from surface gravitational data using external spherical harmonics and (iii) the combination of internal and external series expansions. While the first method diverges beyond any reasonable doubts, we show that the other two methods may ensure relative accuracy from \({\sim }10^{-6}\) to \(10^{-8}\) in the vicinity of Bennu. This is possible even with the second method, despite the fact that it relies on a single series of external spherical harmonics. Our main motivation was to study conceptual differences between spherical harmonic coefficients from satellite data (analogy to the first method) and from surface gravitational data (the second method). Such coefficients are available through the popular spherical-harmonic-based models of the Earth’s gravitational field and often are combined together. We show that the coefficients from terrestrial data may lead to a divergence effect of partial sums, though excellent accuracy can be achieved when such model is used in full. Under (presently) extreme but realistic conditions, the divergence effect of partial sums may affect many near-surface geoscientific applications, such as the geoid/quasigeoid computation or residual terrain modelling. Computer codes (Fortran, MATLAB) and data produced within the study are made freely available at http://edisk.cvt.stuba.sk/~xbuchab/.

我们应用了三种基于球谐函数的技术来在其外接球体内提供小行星（101955）Bennu的外部重力场模型。已知该区域对于外部球形谐波扩展是特殊的，因为它可能导致发散级数。研究的方法是（i）通过外部球谐函数进行频谱重力正演建模；（ii）使用外部球谐函数从表面引力数据进行最小二乘估计；以及（iii）内部和外部序列展开的组合。尽管第一种方法有任何合理的疑问，但我们证明了另外两种方法可以确保从\（{\ sim} 10 ^ {-6} \）到\（10 ^ {-8} \）的相对准确性。 在本努附近。即使使用第二种方法，也可以做到这一点，尽管它依赖于一系列外部球谐函数。我们的主要动机是研究卫星数据（类似于第一方法）与表面重力数据（第二方法）之间的球谐系数之间的概念差异。可以通过流行的基于地球重力场的基于球谐函数的模型获得这些系数，并且通常将它们组合在一起。我们表明，尽管当完全使用这种模型时可以实现极好的精度，但来自地面数据的系数可能会导致部分和的发散效果。在（目前）极端但现实的条件下，部分总和的发散效应可能会影响许多近地表地球科学应用，例如大地水准面/准大地水准面计算或残余地形建模。研究中产生的计算机代码（Fortran，MATLAB）和数据可从http://edisk.cvt.stuba.sk/~xbuchab/免费获得。