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In this article, we present a free-vertex tetrahedral finite-element representation of irregularly shaped small bodies, which provides an alternative solution for estimating asteroid density distribution. We derived the transformations between gravitational potentials expressed by the free-vertex tetrahedral finite elements and the spherical harmonic functions. Inversely, the density of each free-vertex tetrahedral finite element can be estimated via the least-squares method, assuming adoi:10.3390/aerospace8120371 fatcat:zkfyiep6bvapbc4irrr3mbtnhy