  A model for the static weak-field macroscopic medium is analyzed and the
equation for the macroscopic gravitational potential is derived. This is a
biharmonic equation which is a non-trivial generalization of the Poisson
equation of Newtonian gravity. In case of the strong gravitational quadrupole
polarization it essentially holds inside a macroscopic matter source. Outside
the source the gravitational potential fades away exponentially. The equation
is equivalent to a system of the Poisson equation and the nonhomogeneous
modified Helmholtz equations. The general solution to this system is obtained
by using Green's function method and it does not have a limit to Newtonian
gravity. In case of the insignificant gravitational quadrupole polarization the
equation for macroscopic gravitational potential becomes the Poisson equation
with the matter density renormalized by the factor including the value of the
quadrupole gravitational polarization of the source. The general solution to
this equation obtained by using Green's function method has a limit to
Newtonian gravity.
