One goal of the Russian space program is to illuminate dark northern cities by sunlight reflected to the Earth from a 200 m diameter mirrored surface in orbit. Some smaller prototypes have already been constructed and put into orbit.
a) Suppose that sunlight with intensity 1340W/m2 falls on the mirror nearly perpendicularly and that the atmosphere of the Earth allows 83.3% of the energy of sunlight to pass although it in clear weather. What is the power received by a city when the space mirror is reflecting light to it?
______________ W
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 Pointing vector) received by the city?
______________ W/m2
c) This intensity is what percentage of the vertical component of sunlight at St. Petersburg in winter, when the sun reaches an angle of 8.80° above the horizon at noon?
______________ %