One goal of the Russian space program is to illuminate
Chapter 34, Problem 59(choose chapter or problem)
One goal of the Russian space program is to illuminate dark northern cities with sunlight reflected to the Earth from a 200-m diameter mirrored surface in orbit. Several smaller prototypes have already been constructed and put into orbit.
(a) Assume that sunlight with intensity \(1 370 \mathrm{~W} / \mathrm{m}^{2}\) falls on the mirror nearly perpendicularly and that the atmosphere of the Earth allows 74.6% of the energy of sunlight to pass though it in clear weather. What is the power received by a city when the space mirror is reflecting light to it?
(b) The plan is for the reflected sunlight to cover a circle of diameter 8.00 km. What is the intensity of light (the average magnitude of the Poynting vector) received by the city?
(c) This intensity is what percentage of the vertical component of sunlight at St. Petersburg in January, when the sun reaches an angle of \(7.00^{\circ}\) above the horizon at noon?
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