= Surface tidal time scale of a spherical gravitating body
{title2=$t_{\rm tide}=\sqrt{R/g}=\sqrt{R^3/(GM)}$}
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 $2\pi t_{\rm tide}$, 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.
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