A body weighs $63 ext{ N}$ on the surface of the Earth. What is the gravitational force on it due t

Question

A body weighs $63	ext{ N}$ on the surface of the Earth. What is the gravitational force on it due to the Earth at a height equal to half the radius of the Earth?

Professor PC Thomas Classes · Answer

The acceleration due to gravity at a height $h$ (comparable to $R$) is $g' = \frac{g}{(1 + h/R)^2}$. For $h = R/2$, $g' = \frac{g}{(1 + 1/2)^2} = \frac{4}{9}g$. Therefore, the new weight is $W' = \frac{4}{9}W = \frac{4}{9} 	imes 63 = 28	ext{ N}$.