Answer:
27.5 days
0.92 month
Explanation:
[tex]r[/tex] = radius of the orbit of moon around the earth = [tex]3.85\times10^{8} m[/tex]
[tex]M[/tex] = Mass of earth = [tex]5.98\times10^{24} m[/tex]
[tex]T[/tex] = Time period of moon's motion
According to Kepler's third law, Time period is related to radius of orbit as
[tex]T^{2} = \frac{4\pi ^{2} r^{3} }{GM}[/tex]
inserting the values, we get
[tex]T^{2} = \frac{4(3.14)^{2} (3.85\times10^{8})^{3} }{(6.67\times10^{-11})(5.98\times10^{24})}\\T = 2.3754\times10^{6} sec[/tex]
we know that
1 day = 24 hours = 24 x 3600 sec = 86400 s
[tex]T = 2.3754\times10^{6} sec \frac{1 day}{86400 sec} \\T = 27.5 days[/tex]
1 month = 30 days
[tex]T = 27.5 days \frac{1 month}{30 days} \\T = 0.92 month[/tex]
