acceleration due to gravity

Question

Value of g at height h above Earth (R radius) approximately is:

RankGuru · Accepted Answer

The acceleration due to gravity ($g$) at the surface is $g = \frac{GM}{R^2}$.
- At a height $h$ above the surface, the distance from the center is $(R+h)$.
- The value $g_h = \frac{GM}{(R+h)^2}$.
- Taking the ratio: $\frac{g_h}{g} = \frac{R^2}{(R+h)^2} = \left( \frac{R}{R+h} \right)^2$.
- For $h \ll R$, this simplifies using binomial expansion to $g_h \approx g (1 - \frac{2h}{R})$.

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