\(g=-\cfrac{{G}_{o}}{(x+{r}_{eo})^2}\)
\({g}_{eo}=-\cfrac{{G}_{o}}{{r}_{eo}^2}\) = -3.980484e14/(0.00886)^2 = -5.07071e18 ms-2
And the corresponding gravity equation is,
\(g=-{g}_{eo}{e}^{-\cfrac{{g}_{eo}{r}_{eo}}{{G}_{o}}(x)}=-{g}_{eo}{e}^{-\cfrac{1}{{r}_{eo}}(x)}\)
\(g\) = -(5.07071e18)*e^(-112.86690*x)
This graph of g = -(5.07071*10^18)*e^(-112.86690*x) has been scaled in the x-axis by \(\cfrac{1}{1000}\) and in the y-axis by \(10^{14}\). But it is still possible to calculate from the formula \({x}_{e}\) when \(g={g}_{o}\) around a black hole.
9.80665 = (5.07071*10^18)*e^(-112.86690*\(x_e\))
\({x}_{e}\) = ln((5.07071*10^18)/9.80665)/112.86690 = 0.3613 m.
