Solution to 2008 Problem 53

\begin{align*}L = m r v = m r \frac{2 \pi r}{T} = \frac{2 \pi m r^2}{T}\end{align*}
The magnitude of the angular momentum L is the same for both planets, so
\begin{align*}\frac{2 \pi m_1 r_1^2}{T_1} = \frac{2 \pi m_2 r_2^2}{T_2}\end{align*}
We are told that r_1 = r_2 = R and that T_1 = 3 T_2, so
\begin{align*}\frac{m_1}{m_2} = \frac{T_1}{T_2} = \boxed{3}\end{align*}
Therefore, answer (D) is correct.

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