Question

Calculate the acceleration due to gravity when a spaceship is at a distance equal to twice the earth' radius from the centre of gravity.

Answer 1

$$\begin{gathered} \mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{r}}^2} \\ \mathrm{Hence}, \\ \frac{\mathrm{g}\text{'}}{\mathrm{g}}={\left(\frac{\mathrm{r}}{\mathrm{r}\text{'}}\right)}^2 \\ ={\left[\frac{\mathrm{R}}{2\mathrm{R}}\right]}^2 \\ =\frac{1}{4} \\ \mathrm{So},\mathrm{g}\text{'}=\frac{\mathrm{g}}{4} \\ =\frac{9.8}{4} \\ =2.45\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$