Gravitational potential of a truncated inverse-radius sphere
= Gravitational potential of a truncated inverse-radius sphere
{title2=$\Phi(r)=-k^\prime(2r_0-r)$}
The sphere $\rho=k^\prime/(2\pi Gr)$ for $r<r_0$ has $M(r)=k^\prime r^2/G$ and $\Phi(r)=-k^\prime(2r_0-r)$, with zero potential at infinity. Its finite central potential contrasts with the logarithmic central divergence of a truncated inverse-square density.