Multipole expansion of the inverse-square law of gravity

We introduce the multipole expansion of the inverse-square law of gravity. The $1/R$ potential of gravity draws an immediate analogy with that of Coulomb's law and provides a powerful tool to address the effect of imperfections of instruments probing gravitational torques with high precision. We discuss our results in the context of a torsion balance experiment designed to search for non-Newtonian gravity at short-range distances.