Keplers Law: Practice Problem & Solution

Solution Explained:

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

Areal velocity is given by \(\frac{dA}{dt} = \frac{L}{2m} = \frac{vr}{2} = \frac{\sqrt{GMr}}{2}\). Since areal velocity is proportional to \(\sqrt{r}\), the ratio is \(\sqrt{\frac{R}{4R}} = \frac{1}{2}\) or 1 : 2.