A non-homogeneous sphere as a model of the planets. Internal points of maximum gravity

We obtained the criterion for the existence of gravitational potential inflection points within a inhomogeneous spherical planet. According to the criterion obtained, inflection points (the point of local maximum gravity) can exist only at such a distance $r$ from the center, at which the matter density is two-thirds of the average density of the inner ball with a specified radius. The criterion is defined for the axial moment of the planet inertia too.