Answer:
0.19245 lunar months
Explanation:
T = Orbital time
r = Radius
[tex]r_2=\dfrac{1}{3}r_1[/tex]
1 denotes the moon
2 denotes the satellite
From Kepler's law we have
[tex]T^2=\dfrac{4\pi^2r^3}{GM}[/tex]
So,
[tex]\\\Rightarrow T\propto \sqrt{r^3}[/tex]
[tex]\dfrac{T_2}{T_1}=\sqrt{\dfrac{r_2^3}{r_1^3}}\\\Rightarrow \dfrac{T_2}{T_1}=\sqrt{\dfrac{\left(\dfrac{1}{3}r_1\right)^3}{r_1^3}}\\\Rightarrow \dfrac{T_2}{T_1}=0.19245\\\Rightarrow T_2=0.19245T_1[/tex]
The period of revolution of the satellite is 0.19245 lunar months
