  We derive an expression for the mutual gravitational force and torque of two
bodies having arbitrary shapes and mass distributions, as an expansion in power
series of their products of inertia and of the relative coordinates of their
centres of mass. The absolute convergence of all the power series developed is
rigorously demonstrated. The absence of transcendental functions makes this
formalism suitable for fast numerical applications. The products of inertia
used here are directly related to the spherical harmonics coefficients, and we
provide a detailed analysis of this relationship.
