By Jaan Kalda (TalTech).
Consider a satellite that has a shape of a plate of surface area A and of thickness d\ll \sqrt A. The surface normal of the plate is turned towards Sun. The satellite has to convert solar energy into electrical energy and charge the onboard batteries. At the position of the satellite, the solar energy flux density is S. What is the theoretically maximal constant charging power if any devices can be installed inside the satellite, but its outer coating can be only a gray painting (from white to black), i.e. the emissivity has to be independent of the wavelength? Different parts of the satellite can be painted differently. Neglect the cosmic microwave background.
Any numeric values in your final answer should have at least 4 significant digits.