Suppose that a planet were discoveredbetween the sun and Mercury, with a circular orbit of radius equalto {\frac{2}{3}} of the average orbit radius of Mercury. (Such aplanet was once postulated, in part to explain the precession ofMercury's orbit. It was even given the name Vulcan, although we nowhave no evidence that it actually exists. Mercury's precession hasbeen explained by general relativity.) The orbital period ofMercury is 88.0 days.
What would be the orbital period of such aplanet?