= Tidal field
{title2=$T_{ij}=\partial_jg_i$}
A <tidal field> describes the spatial variation of <gravitational acceleration> across an extended body. With $g_i=-\partial_i\Phi$, a small separation $\xi$ gives relative <acceleration> $\delta g_i=T_{ij}\xi_j$, where $T_{ij}=-\partial_i\partial_j\Phi$.
For a <point mass>, a radial separation is stretched at rate coefficient $2GM/r^3$, while transverse separations are compressed with coefficient $-GM/r^3$. The common <acceleration> can be removed by choosing a freely falling frame; these relative <accelerations> remain. This makes tides a probe of gravitational inhomogeneity rather than merely the strength of the local <acceleration>.
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