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We derive an expression for the mutual gravitational force and torque of twobodies having arbitrary shapes and mass distributions, as an expansion in powerseries of their products of inertia and of the relative coordinates of theircentres of mass. The absolute convergence of all the power series developed isrigorously demonstrated. The absence of transcendental functions makes thisformalism suitable for fast numerical applications. The products of inertiaused here are directly related to the spherical harmonics coefficients, and weprovide a detailed analysis of this relationship.

Figure-Figure Interaction Between Bodies Having Arbitrary Shapes and Mass Distributions: A Power Series Expansion Approach