If the acceleration due to gravity experienced by a point mass at a height $h$ above the surface of earth is same as that of the acceleration due to gravity at a depth $\alpha h \left( h \ll R _ { e } \right)$ from the earth surface. The value of $\alpha$ will be $\_\_\_\_$.\\
(use $R _ { e } = 6400 \mathrm {~km}$)