Find the magnitude of acceleration due to gravity at height of $10\, km$ from the surface of earth.
Find the magnitude of acceleration due to gravity at height of $10\, km$ from the surface of earth.
In equation $\mathrm{g}_{h}=\mathrm{g}_{e}\left(1-\frac{2 h}{\mathrm{R}_{e}}\right), h=10 \mathrm{~km}=10^{4} \mathrm{~m}$ $\mathrm{Re}=6.4 \times 10^{6} \mathrm{~m}$ and $\mathrm{g}_{e}=9.8 \mathrm{~ms}^{-2}$
$\therefore \mathrm{g}_{h}=9.8\left[1-\frac{2 \times 10^{4}}{6.4 \times 10^{6}}\right]$
$\therefore \mathrm{g}_{h}=9.8[1-0.003125]$
$\therefore \mathrm{g}_{h}=9.8[0.996875]$
$\therefore \mathrm{g}_{h}=9.769375 \mathrm{~ms}^{-2}$
$\therefore \mathrm{g}_{h}=9.8 \mathrm{~ms}^{-2}$
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