Equation 123 · Part 1 · The Bend an Elevator Cannot Fake

Symbol y_2

y_2 - y_1 = \phi_{,zz}\,h^2 + O(h^4).

y_2

What this part means

$y_2$ is part of the quantity the equation computes from the expression on the right.

Its job in the formula

$y_2$ is part of the quantity the equation computes from the expression on the right.

Full expressionSymbol y_2Article meaning

The passage around this formula

An exact analytic evaluation, not a simulation, fixes the scale this actually requires. Take three clocks stacked vertically at heights -h , 0 , and +h near Earth’s surface, giving two edges $y_1$ = $\phi(0)$ - $\phi(-h)$ and $y_2$ = $\phi(h)$ - $\phi(0)$ . Their difference is an exact finite-difference identity up to a Taylor remainder of order $h^4$ : $y_2 - y_1 = \phi_{,zz}\,h^2 + O(h^4)$ . 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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

[15] Physical Geodesy ↗

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