Respuesta :
Answer:
118.06 days
Explanation:
d = distance of the center of moon from surface of planet = 2.315 x 10⁵ km = 2.315 x 10⁸ m
R = radius of the planet = 4.15 x 10³ km = 4.15 x 10⁵ m
r = center to center distance between the planet and moon = R + d
M = mass of the planet = 7.15 x 10²² kg
T = Time period of revolution around the planet
Using Kepler's third law
[tex]T^{2}=\frac{4\pi ^{2}r^{3}}{GM}[/tex]
[tex]T^{2}=\frac{4\pi ^{2}(R + d)^{3}}{GM}[/tex]
[tex]T^{2}=\frac{4(3.14)^{2}((4.15\times 10^{5}) + (2.315\times 10^{8}))^{3}}{(6.67\times 10^{-11})(7.15\times 10^{22})}[/tex]
T = 1.02 x 10⁷ sec
we know that , 1 day = 24 h = 24 x 3600 sec = 86400 sec
T = [tex](1.02 \times 10^{7} sec)\frac{1 day}{86400 sec}[/tex]
T = 118.06 days
