Question

Calculate mass of the Earth from given data, Acceleration due to gravity $g=9.81m/s^2$, Radius of the Earth $R_e=6.37\times {10}^{6}m$, $G=6.67\times {10}^{-11}N{m}^2/k{g}^2$

Answer 1

Step 1: Given:

$g=9.81m/s^2$

$R_e=6.37\times {10}^{6}m$

$G=6.67\times {10}^{-11}N{m}^2/k{g}^2$

Mass of the Earth ($M_e$)​

Step 2: Formula used

$$\begin{gathered} F=mg=\frac{G{M}_{e}m}{{R_e}^2} \\ g=\frac{G{M}_e}{{R_e}^2} \end{gathered}$$

Step 3: Substituting the given values :

$$\begin{gathered} M_e=\frac{g{R^2}_e}{G}=\frac{9.81\times {(6.37\times {10}^6)}^2}{6.67\times {10}^{-11}} \\ =\frac{9.81\times 6.37\times 6.37\times {10}^{23}}{6.67} \\ =59.679\times {10}^{23} \\ =5.9679\times {10}^{24}kg \end{gathered}$$

Therefore the mass of the earth is $5.9679\times {10}^{24}kg$.