The gravitational force acting on Earth due to Sun is $F = \frac{G M_{S} M_{E}}{r^{2}}, r \rightarrow$ mean orbital radius of the earth around the sun. Now, the centripetal force acting on the earth due to the Sun is $F_{c} = M_{E} r \omega^{2} = M_{E} r \frac{4 \pi^{2}}{T^{2}}, \omega \rightarrow$ angular velocity Since, this centripetal force is provided by the gravitational pull of the Sun on the Earth, so,$\because r = 1.5 \times 10^{8} \text{ km}$$= 1.5 \times 10^{11} \text{ m},$$T = 365 \text{ days}$$= 365 \times 24 \times 60 \times 60 \text{ s}$ $\simeq 2 \times 10^{30} \text{ kg}.$