Abstract: The varied-density in the interior of a celestial body, generally results in an anisotropic gravity potential outside of the celestial. The general numerical integration method needs too much time in the potential determination to be efficiently applied in a large-scaled gravity inversion as well as the forward case. To deal with this problem, this paper proposes an updated model of spherical harmonic expansion, which is based on the generalized Fourier Transformation. Results indicate that the spherical harmonic expanded coefficients of the gravity potential can be directly estimated according to the expanded coefficients of density. Our method simplifies the potential calculation in the case of density varied in a celestial body. By applying our algorithm to the actual case, the potential from our approach shows a similar distribution with the general method, but our method spents less time in the computation than its counterpart. To the issue of lunar crustal density varied, the estimated gravity potential from our method shows the same behavior with the varied-density. Our method is validated and can be applied in the gravity inversion as well as its forward problem.

Key words: varied-density sphere, gravity potential, normalized, spherical harmonic expansion