Gravity of a concentric hollow sphere ($g(r)=GM(<r)/r^2$)

For constant mass density $\rho$ on $a<r<b$, the shell theorem gives zero gravitational field for $r\le a$, inward magnitude $4\pi G\rho (r^3-a^3)/(3r^2)$ for $a<r<b$, and $4\pi G\rho (b^3-a^3)/(3r^2)$ outside. These formulas agree continuously at both boundaries. The empty cavity has zero gravitational field but generally nonzero constant gravitational potential.