Jupiter Ascending

Classical Mechanics Level 3

Two moons of Jupiter, Callisto and Europa of masses $m_C$ and $m_E$ are orbiting in circular paths of radius $r_C$ and $r_E$ respectively about Jupiter. The radii are measured from the Jupiter’s centre of mass and the respective moons’ centre of masses.

What is the ratio of their velocities $\dfrac{v_C}{v_E}$ in terms of the given variables?

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