\({g}_{o}\) = 9.80663 ms-2, \({r}_{e}\) = 6371000 m
\({G}_{o}\) = 3.980484e14, \(\cfrac{{g}_{o}{r}_{e}}{{G}_{o}}\) = 1.56961e−7
\(g=-{g}_{o}{e}^{-\cfrac{{g}_{o}{r}_{e}}{{G}_{o}}(x)}\)
\(g=-{g}_{o}{e}^{-\cfrac{1}{{r}_{e}}(x)}\)
\(g\) = -9.80665*e^((-1.56961e−7)*x)
And so,
\(\gamma(x)=\sqrt{1-\cfrac{2{G}_{o}}{{c}^{2}{r}_{e}}{e}^{-\cfrac{{g}_{o}{r}_{e}}{{G}_{o}}(x)}}\)
\(\gamma(x)=\sqrt{1-1.3903267*10^{-9}{e}^{-1.56961*{10}^{−7}}(x)}\)
The following show \(\gamma(x)\) with \(x\) scaled by 1000.
As far living on earth is concern, time dilation is very small and it changes very little with the corresponding decrease in gravity as we move away from the gravitational field.
