Answer:
[tex]G=6.66\times 10^{-11}\ m^3kg^{-1}s^{-2}[/tex]
Explanation:
The centripetal acceleration of the Moon around the Earth is, [tex]a_c=2.74\times 10^{-3}\ m/s^2[/tex]
Mass of the Earth, [tex]M=5.97\times 10^{24}\ kg[/tex]
The mean distance between the centers of the Earth and Moon, [tex]r=3.81\times 10^{8}\ m[/tex]
The centripetal acceleration of the Moon around the Earth is given by the formula as :
[tex]a=\dfrac{GM}{r^2}[/tex]
[tex]G=\dfrac{ar^2}{M}[/tex]
[tex]G=\dfrac{2.74\times 10^{-3}\times (3.81\times 10^{8})^2}{5.97\times 10^{24}}[/tex]
[tex]G=6.66\times 10^{-11}\ m^3kg^{-1}s^{-2}[/tex]
Hence, this is the required solution.
