A science-fiction tale describes and artificial planet in the form of a band completely encircling a sun

A science-fiction tale describes and artificial €œplanet€ in the form of a band completely encircling a sun (Fig.5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce and apparent gravity of g as on Earth. What will be the period of revolution, this planet€™s year, in Earth days?

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Sun