superscript

The passage around this formula

For Earth modelled as a point mass, $\Phi(r)$ = -GM/r gives a radial second derivative of magnitude 2GM/$R^3$ and, since $\Phi$ is harmonic in vacuum, transverse second derivatives of magnitude GM/$R^3$ with the opposite sign — a trace-free tensor in the exact ratio 2:{-1}:{-1} . With the standard gravitational parameter G$M_\oplus$ = 3.986$\times$10^{14}\,$\mathrm{m^3\,s^{-2}}$ and mean radius $R_\oplus$ = 6.371$\times$10^{6}\,$\mathrm m$ , this gives G$M_\oplus$/$R_\oplus^3$ $\approx$ 1.541$\times$10^{-6}\,$\mathrm{s^{-2}}$ and a radial magnitude of 3.08$\times$10^{-6}\,$\mathrm{s^{-2}}$ , matching the standard geodetic free-air gravity gradient of about 3.086$\times$10^{-6}\,$\mathrm{s^{-2}}$ , or 0.3086 milligal per metre,…

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