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:

According to Kepler's Third Law, \(T^2 \propto R^3\). Thus, \(\left(\frac{T'}{T}\right)^2 = \left(\frac{R'}{R}\right)^3 = \left(\frac{1}{2}\right)^3 = \frac{1}{8}\), which gives \(T' = \frac{365}{\sqrt{8}} \approx 129\text{ days}\).