Because of their mutual gravitational attraction, four identical planets each of mass $$m$$ are orbiting in a circular path of radius $$r$$ in the same sense, angular direction. The magnitude of the velocity of each planet is

A

$$\left[\frac{Gm}{r}\left(\frac{1 + 2\sqrt{2}}{4}\right)\right]^{1/2}$$

B

$$3\sqrt{\frac{Gm}{r}}$$

C

$$\sqrt{\frac{Gm}{r}\left(1 + 2\sqrt{2}\right)}$$

D

$$\left[\frac{1}{2}\frac{Gm}{r}\left(\frac{1 + \sqrt{2}}{2}\right)\right]^{1/2}$$