If the acceleration due to gravity at a height 1 km above the earth is similar to a depth d below the surface

Question

If the acceleration due to gravity at a height 1 km above the earth is similar to a depth d below the surface of the earth, then:

Accepted Answer

The acceleration due to gravity at a height $h$ (where $h << R_e$) is given by $g_h pprox g(1 - rac{2h}{R_e})$. 
The acceleration due to gravity at a depth $d$ is given by $g_d = g(1 - rac{d}{R_e})$. 
Given that $g_h = g_d$: 
$g(1 - rac{2h}{R_e}) = g(1 - rac{d}{R_e})$ 
$rac{2h}{R_e} = rac{d}{R_e} \implies d = 2h$. 
Given $h = 1$ km, we find $d = 2 	imes 1 	ext{ km} = 2$ km.

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