Question

A satellite is orbiting around the Earth at a distance $5times$ the radius of the Earth from its centre. If the acceleration due to gravity on the Earth is $9.8m{s}^{-2}$, calculate the acceleration due to gravity acting of spaceship.

Answer 1

Step 1: Given data

$R\text{'}=5R$

$g_{Earth}=9.8m{s}^{-2}$

$g_{Spaceship}=?$

Step 2: Calculating the acceleration due to gravity acting of spaceship

$g_{Earth}=\frac{G\times M}{R^2}$------------------------------------------------(1)

$g_{Spaceship}=\frac{G\times M}{R{\text{'}}^2}=\frac{G\times M}{{\left(5R\right)}^2}=\frac{G\times M}{25R^2}$--------------------(2)

Dividing (2) by (1), we get

$$\begin{gathered} \frac{g_{Spaceship}}{g_{Earth}}=\frac{G\times M}{25R^2}\times \frac{R^2}{G\times M} \\ \Rightarrow \frac{g_{Spaceship}}{g_{Earth}}=\frac{1}{25} \\ \Rightarrow g_{Spaceship}=\frac{g_{Earth}}{25} \\ \Rightarrow g_{Spaceship}=\frac{9.8m{s}^{-2}}{25}=0.392m{s}^{-2} \end{gathered}$$

Hence, the acceleration due to gravity acting of spaceship is $0.392m{s}^{-2}$