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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