Gravitational Fields of Polyhedral Bodies with 3D Polynomial Density Contrast

For polyhedral mass bodies bodies having arbitrary shape and density distribution of polynomial type we present a tensorial approach to derive analytical expressions of the gravitational potential and gravity vector. They are evaluated at an arbitrary point by means of formulas, referred to a Cartesian reference frame having an arbitrary origin, that are shown to be singularityfree whatever is the position of the observation point with respect to the body. The solution is expressed as a sum of algebraic quantities depending solely upon the 3D coordinates of the polyhedron vertices and the coefficients of the polynomial density function. Hence, no recursive expression needs to be invoked as in the recent contribution by Ren et al. Moreover, the tensorial formalism developed in the paper allows one to obtain more concise, coordinate-free expressions that can also be extended to address polynomial functions of greater order. The analytical expressions of the gravitational potential and gravity vector are numerically validated and compared with alternativemethods retrieved from the literature