Question

How far above the earth's surface must an astronaut in space be if they are to feel a gravitational acceleration that is half what they would feel on the surface of the earth?

• A. $R_{Earth}$
• B. $2R_{Earth}$
• C. $\frac{R_{Earth}}{2}$
• D. $\sqrt{2}{R}_{Earth}$
• E. $\sqrt{2}{R}_{Earth}-R_{Earth}$

Answer 1

The correct option is E $\sqrt{2}{R}_{Earth}-R_{Earth}$

Let the radius of earth be $R_{Earth}$ and acceleration due to gravity at the surface be $g$.

Thus acceleration due to gravity at a height h above the surface $g^{\prime }=g\frac{R_{Earth}^2}{(R_{Earth}+h{)}^2}$

$\therefore$ $\frac{g}{2}=g\frac{R_{Earth}^2}{(R_{Earth}+h{)}^2}$

OR $R_{Earth}+h=\sqrt{2}{R}_{Earth}$ $⟹h=\sqrt{2}{R}_{Earth}-R_{Earth}$