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Published equation contexts

Ω2≈5.32×10−9 s−2\Omega^2 \approx 5.32\times10^{-9}\,\mathrm{s^{-2}}

Why this formula appears here

Earth’s own centrifugal contribution is the concrete case worth sizing, precisely because it is not negligible enough to ignore by assumption. With Ω\Omega ≈\approx 7.292×\times10^{-5}\,rad s−1\mathrm{rad\,s^{-1}} fixed by astrometry to far more figures than any clock network could hope to determine on its own [ 10 ] , the centrifugal Hessian has magnitude Ω2\Omega^2 ≈\approx 5.32×\times10^{-9}\,s−2\mathrm{s^{-2}} — smaller than the radial tidal magnitude computed above by a factor of nearly six hundred, but not so much smaller that a network aiming to certify the 2:{-1}:{-1} ratio to good precision can skip subtracting it. Left in, it would masquerade as roughly a fifth of one percent of the genuine tidal…

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Ω2\Omega^2

Symbol Omega^2

Omega2a^2 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

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Published contexts (1)

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Ω2≈5.32×10−9 s−2\Omega^2 \approx 5.32\times10^{-9}\,\mathrm{s^{-2}}

Equation 151 · Evolutionary Physics

The Bend an Elevator Cannot Fake

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

Earth’s own centrifugal contribution is the concrete case worth sizing, precisely because it is not negligible enough to ignore by assumption. With Ω\Omega ≈\approx 7.292×\times10^{-5}\,rad s−1\mathrm{rad\,s^{-1}} fixed by astrometry to far more figures than any clock network could hope to determine on its own [ 10 ] , the centrifugal Hessian has magnitude Ω2\Omega^2 ≈\approx 5.32×\times10^{-9}\,s−2\mathrm{s^{-2}} — smaller than the radial tidal magnitude computed above by a factor of nearly six hundred, but not so much smaller that a network aiming to certify the 2:{-1}:{-1} ratio to good precision can skip subtracting it. Left in, it would masquerade as roughly a fifth of one percent of the genuine tidal…

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