This problem considers an Earth-like planet but with no atmosphere or ocean, which simplifies the energy balance calculations of surface temperature. Consider this planet to have a constant albedo A, unless a different value is given in the part of the question you're solving. Use A=0.31 so this planet reflects about the same fraction of sunlight as Earth on average. Calculate Ts for the given values of solar input using an energy balance (i.e. Fin=Fout or in words energy flux in = energy flux out). The discussion part of each question emphasizes physical understanding by comparing Earth to this simple planet. It is useful to convert absolute temperature to values in degrees C. [10 points total]
a) The inverse square law is used to calculate the decrease in radiation intensity due to an increase in distance away from the radiation source. Given that the earth receives ~1370 W/m² of solar radiation (i.e. the solar constant So=1370 W/m²) at a distance ro = rs-e = 1.5 x 10¹¹ m, what is the distance between our Earth-like planet and the Sun (our shared energy source) knowing that the global average solar flux is S/4 = 342 W/m² on this planet? [1 point]
b) Calculate Ts for S/4 = 342 W/m², the global average input. Compare to the global average Ts on Earth, which is about 15°C. Besides distance away from the sun, what is the single main effect that makes Earth's Ts differ from the Ts you calculated? [2 points]
