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Two identical stars of mass $M$ and radius $R$ are separated by a distance $d$ ($d>>R$). The two stars are in circular orbit around their combined center of mass. They are observed to be moving at a speed ${v}_{1}$.

Two other identical stars each with a mass of $2M$ (but with the same radius $R$) are found to be in the same configuration; specifically separated by a distance $d$ and orbiting their combined center of mass. They are moving at a speed ${v}_{2}$.

What is the ratio of $\cfrac {{v}_{2}}{{v}_{1}}$?

A

$\cfrac{1}{4}$

B

$1$

C

$\sqrt {2}$

D

$2$

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