Relative error (in percentage) in force and torques arising from using second (top) and fourth order (bottom) mutual potentials. The two left-most panels show the force, and the middle and right-most panels show the torque on the primary and secondary, respectively. Each position in the xy-plane corresponds to the position of the secondary in the xy-plane of the primary. The units of the axes are units of primary radius a_p. The black dashed circles indicate the circumference of the primary, and the white region in the center corresponds to the region where the bounding spheres intersect. The color scaling is logarithmic and the color bars show numbers in percentage. The pair-wise comparisons between second and fourth order potentials share the same color scaling.