Answer:
The mass of the earth, [tex]M=6.023\times 10^{24}\ kg[/tex]
Explanation:
It is given that,
Time taken by the moon to orbit the earth, [tex]T=27.3\ days=2358720\ m[/tex]
Distance between moon and the earth,[tex]r=384000\ km=384\times 10^6\ m[/tex]
We need to find the mass of the Earth using Kepler's third law of motion as :
[tex]T^2=\dfrac{4\pi^2}{GM}r^3[/tex]
[tex]M=\dfrac{4\pi^2r^3}{T^2G}[/tex]
[tex]M=\dfrac{4\pi^2\times (384\times 10^6)^3}{(2358720)^2\times 6.67\times 10^{-11}}[/tex]
[tex]M=6.023\times 10^{24}\ kg[/tex]
So, the mass of the earth is [tex]6.023\times 10^{24}\ kg[/tex]. Hence, this is the required solution.
