Gravitational field modelling near irregularly shaped bodies using spherical harmonics: a case study for the asteroid (101955) Bennu

Abstract

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/ .