Published equation contexts

$3.08\times10^{-6}\,\mathrm{s^{-2}}$

Why this formula appears here

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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[15] Physical Geodesy ↗

Published contexts (1)

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3.08\times10^{-6}\,\mathrm{s^{-2}}

Equation 132 · Evolutionary Physics

The Bend an Elevator Cannot Fake

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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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