A non-perturbative method for gravitational potential calculations within heterogeneous and aspherical planets

Abstract

We present a numerically exact method for calculating the internal and external gravitational potential of aspherical and heterogeneous planets. Our approach is based on the transformation of Poisson?s equation into an equivalent equation posed on a spherical computational domain. This new problem is solved in an efficient iterative manner based on a hybrid pseudospectral/ spectral element discretization. Themain advantage of our method is that its computational cost reflects the planet?s geometric and structural complexity, being in many situations only marginally more expensive than boundary perturbation theory. Several numerical examples are presented to illustrate the method?s efficacy and potential range of applications.