## College Physics (7th Edition)

$F=G\frac{mM_{e}}{R^{2}}$ m = mass of an object on earth's surface. R=radius of earth at that point. Again, $F=mg$ Thus, $mg=G\frac{mM_{e}}{R^{2}}$ or, $g=G\frac{M_{e}}{R^{2}}$ So, mass of the earth $=M_{e}=\frac{gR^{2}}{G}$ Since all the quantities on the right side are known, we can find mass of the earth.