Planet Vulcan. Suppose that a planet were discovered between the sun and Mercury

Question

Planet Vulcan. Suppose that a planet were discovered between the sun and Mercury, with a circular orbit of radius equal to {rac{2}{3}} of the average orbit radius of Mercury. (Such a planet was once postulated, in part to explain the precession of Mercury's orbit. It was even given the name Vulcan, although we now have no evidence that it actually exists. Mercury's precession has been explained by general relativity.) The orbital period of Mercury is 88.0 days.

What would be the orbital period of such a planet?

Explanation / Answer

we know that. T^2/a^3=const a_vu=a_mer*2/3. so T1^2/T2^2=a1^3/a2^3. so T1^2/88^2=(2/3)^3. so T1=47.9(days)

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