Question

If the radius of earth $\left(R_e\right)=6.38\times {10}^{6}metre$, gravitational constant (G)=$6.67\times {10}^{-11}N{m}^2/k{g}^2$ and acceleration due to gravity (g) = $9.8m/s^2$, then calculate the mass of the earth.

Answer 1

Step 1: Given data

The radius of the earth $\left(R_e\right)=6.38\times {10}^{6}metre$

The gravitational constant (G) = $6.67\times {10}^{-11}N{m}^2/k{g}^2$

Acceleration due to gravity (g) = $9.8m/s^2$

Mass of the earth $(M_{e)}$=?

Step 2: Formula used

$g=\frac{G{M}_e}{{R_e}^2}................\left(a\right)$

Step 3: Finding the mass of the earth

On, putting the given values in equation (a)

$$\begin{gathered} 9.8m/s^2=\frac{6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}\times M_e}{{\left(6.38\times {10}^{6}m\right)}^2} \\ {M}_e=\frac{9.8\times 6.38\times 6.38\times {10}^{12}}{6.67\times {10}^{-11}}=6\times {10}^{24}kg \end{gathered}$$

Hence, the mass of the earth is $6\times {10}^{24}kg.$