Mass of the earth:

Consider a body of mass m on the surface of the Earth. Let the mass of the Earth be M_e and the radius of the Earth be R. According to the law of gravitation, the gravitational force F of the Earth acting on a the the the the the the body is given by

$F=G \: m \frac{Me}{R^{2}}$ ………….  (i)

But the force with which Earth attracts a body

towards its center is equal to its weight W.

Therefore,

F = W = mg

$mg= \:G \: m \frac{Me}{R^{2}}$

$g= \:G \: \frac{Me}{R^{2}}$

and   $Me=R^{2}\frac{g}{G}$

Mass $M\epsilon$ of the Earth can be determined on putting the values in equation

$Me=\left(6.4\times10^{6}m\right)^{2}\times\frac{10ms^{-2}}{6.673}\times10^{-11}Nm^{2}kg^{-2}$
$=6.0\times10^{24}kg$

Thus, the mass of the Earth is  $=6.0\times10^{24}kg$