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h=2 σyϕ,zz=1.414×10−183.43×10−23 m−2≈203 mh = \sqrt{\frac{\sqrt2\,\sigma_y}{\phi_{,zz}}} = \sqrt{\frac{1.414\times10^{-18}}{3.43\times10^{-23}\,\mathrm{m^{-2}}}} \approx 203\,\mathrm m

Why this formula appears here

​ σ y ​ , gives h=2 σyϕ,zz=1.414×10−183.43×10−23 m−2≈203 mh = \sqrt{\frac{\sqrt2\,\sigma_y}{\phi_{,zz}}} = \sqrt{\frac{1.414\times10^{-18}}{3.43\times10^{-23}\,\mathrm{m^{-2}}}} \approx 203\,\mathrm m. The fourth-derivative Taylor remainder at this height is smaller than the leading term by a factor of roughly 10^{-8} , confirming that the quadratic approximation used above is, for this purpose, exact. Two hundred metres of half-spacing — roughly four hundred metres end to end — is not a laboratory bench, but it is not exotic either: it is close to the height difference a transportable optical lattice clock actually used, linked to a second clock at the base of the Tokyo Skytree tower by fibre, to measure the ordinary first-derivative geopotential difference directly against independent levelling [ 9 ] . Comparable transportable-clock campaigns have…

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hh

Symbol h

h occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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σy\sigma_y

Symbol sigma_y

sigmaya_y occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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ϕ,zz\phi_{,zz}

Symbol phi_,zz

phi_,zz occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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3.43×10−23 m−23.43\times10^{-23}\,\mathrm{m^{-2}}

Denominator: 3.43 × 10^-23mathrmm^-2

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Its accuracy depends on the assumptions and range of use described in the article. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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h=2 σyϕ,zz=1.414×10−183.43×10−23 m−2≈203 m.h = \sqrt{\frac{\sqrt2\,\sigma_y}{\phi_{,zz}}} = \sqrt{\frac{1.414\times10^{-18}}{3.43\times10^{-23}\,\mathrm{m^{-2}}}} \approx 203\,\mathrm m.

Equation 140 · Evolutionary Physics

The Bend an Elevator Cannot Fake

This equation gives an approximation: it relates the quantities while allowing an approximation.

​ σ y ​ , gives h=2 σyϕ,zz=1.414×10−183.43×10−23 m−2≈203 mh = \sqrt{\frac{\sqrt2\,\sigma_y}{\phi_{,zz}}} = \sqrt{\frac{1.414\times10^{-18}}{3.43\times10^{-23}\,\mathrm{m^{-2}}}} \approx 203\,\mathrm m. The fourth-derivative Taylor remainder at this height is smaller than the leading term by a factor of roughly 10^{-8} , confirming that the quadratic approximation used above is, for this purpose, exact. Two hundred metres of half-spacing — roughly four hundred metres end to end — is not a laboratory bench, but it is not exotic either: it is close to the height difference a transportable optical lattice clock actually used, linked to a second clock at the base of the Tokyo Skytree tower by fibre, to measure the ordinary first-derivative geopotential difference directly against independent levelling [ 9 ] . Comparable transportable-clock campaigns have…

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