The period of moon around the earth is 28 days and radius of its orbit is 4×10^5 km Find - Physics - Gravitation

Question

The period of moon around the earth is 28 days and radius of its
orbit is 4×10^5 km Find the mass of earth

Ved Prakash Lakhera · Accepted Answer

The formula of period of moon around the earth is,                T = 2πR+x3GMOR           M = 4π2R+x3GT2
We are given  T= 28×24×3600 s,  R+x=4×108m and   G= 6
67×10-11Nm2/Kg2, so          M = 4×3
14×3 14×64×10246
67×10-11×28×24×3600×28×24×3600            M=6
46×1024Kg

The period of moon around the earth is 28 days and radius of its orbit is 4×10^5 km. Find the mass of earth.