5. A GPS satellite is stationed at a fixed position outside the atmospheric layer and face to the surface of earth. The satellite can be simplified as a large disc of composite material, with temperature-dependent conductivity along its thickness and given internal heating source distribution. Assuming the earth temperature is about 280 K and space environment is about 4 K. Establish a model for the transient surface temperatures of sun-lit surface and earth facing surface during the daylight time (between sun-rise and sun-set) of a given day. Assume the emissivity of surface material is diffuse but spectrum dependent (not a gray surface). The time is based on local solar time, and the solar constant is known.