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 $g_h\approx g(1-\frac{2h}{R})$.