Question

Find the mass of the earth given that $g=9.8m{s}^{-2}$, radius of earth is$6.4\times {10}^{6}m$and $G=6.66\times {10}^{-11}N{m}^{2}k{g}^{-2}$.

Answer 1

Step 1: Given data

Given,

$$\begin{gathered} g=9.8m{s}^{-2} \\ Radiusofearth,R=6.4\times {10}^{6}m \\ G=6.66\times {10}^{-11}N{m}^{2}k{g}^{-2} \\ Massofearth,M=? \end{gathered}$$

Step 2: Formula for acceleration due to gravity

$g=\frac{G\times M}{R^2}$

$M=\frac{g\times R^2}{G}$

Step 3: Substituting the values given

$$\begin{gathered} M=\frac{g\times R^2}{G} \\ =\frac{9.8m{s}^{-2}\times {(6.4\times {10}^{6}m)}^2}{6.66\times {10}^{-11}N{m}^{2}k{g}^{-2}} \\ =6.027\times {10}^{24}kg \end{gathered}$$

Hence, the mass of Earth comes out to be $6.027\times {10}^{24}kg$.