Let $b(r) = -G \iiint \frac {r-r_0}{||r-r_0||^3} dm$ be the gravitational acceleration, where $r_0$ is the center of mass of a rigid body. Show that $\lim_{r\to\infty} b(r) = 0$.
What is the geometrical interpretation for this?
I'm very new to this field of study and do not have much experience with this. It would be so helpful if somebody could explain the derivation for this.