Gravity gradiometry
= Gravity gradiometry
<Gravity gradiometry> measures spatial differences of <gravitational acceleration>. Two simultaneous measurements along a <unit vector> $\mathbf e$, separated by $L\mathbf e$, give
$$
\frac{\mathbf e\cdot[\mathbf g(\mathbf R+L\mathbf e)-\mathbf g(\mathbf R)]}{L}\simeq\mathbf e^{\mathsf T}T\mathbf e.
$$
This measures one directional component of the <tidal tensor>, not its whole <matrix>. Any identical platform <acceleration> cancels in the difference. Unequal instrument responses, changing geometry and <rotating reference frames> can spoil that cancellation. For a large baseline, the quotient is an average of the directional <tidal tensor> along the baseline, rather than its exact value at one point.