 Surface tidal time scale of a spherical gravitating body

At radius $R$ outside a spherical mass $M$, the Newtonian relative-acceleration tensor has eigenvalues $-g/R,-g/R,2g/R$ with $g=GM/R^2$. It compresses free fall separations tangentially and stretches them radially. The displayed time scale is the inverse square root of the curvature scale controlling this tidal evolution. An ideal circular orbit at that radius has period $2\pi t_{\mathrm{tide}}$, providing a second physical interpretation. For Earth's surface it is about $806$ seconds, while the corresponding ideal low-orbit period is about $84$ minutes. A uniform gravitational acceleration does not determine this relative motion; spatial variation of the field does.