Planet and Satellite: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Planet and Satellite. Understanding the underlying formula is key to arriving at the correct answer below:

Using Kepler's Third Law, \(T^2 \propto r^3 \Rightarrow \frac{T_1}{T_2} = \left(\frac{r_1}{r_2}\right)^{3/2} = \left(\frac{3R}{6R}\right)^{3/2} = \left(\frac{1}{2}\right)^{1.5} = \frac{1}{2^{1.5}}\). Hence, the ratio is 1 : \(2^{1.5}\).