Suppose that a planet were discovered between the Sun and Mercury, with a circularorbit of radius equal to 2/3 of the average orbit radius of Mercury. What would be theorbital period of such a planet? (Such a planet was once postulated, in part to explainthe precession of Mercury's orbit. It was even given the name Vulcan, although we nowhave no evidence that it actually exists. Mercury's precession has been explained bygeneral relativity.)

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