One goal of the Russian space program is to illuminate dark northern cities by sunlight reflected to the Earth from a200 m diameter mirrored surface in orbit. Several smaller prototypes have already been constructed and put into orbit.
1) Assume 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 though it in clear weather. What is the power received with a city when the space mirror is reflecting light to it?
2) 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?
3) 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?