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Variation of G Due to Height and Depth

Find what wil...

Question

Find what will be the change in the value of $g$ while going $h$ height over the earth's surface where $h$ is in the order of $R e$ .

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Solution

Force of attraction between two masses, $F = \frac{G M m}{r^{2}}$
where, $r$ is the distance from earth center.

$m a = \frac{G M_{e} m}{r^{2}}$

$a = \frac{G M_{e}}{{(h + R_{e})}^{2}}$

Hence, acceleration above height h from earth surface is $\frac{G M}{{(h + R_{e})}^{2}}$

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