Geometric considerations on planetary surface temperatures

We propose a formula for computing the average planetary surface temperatures based solely on the solar irradiance and the bond albedo. The formula is empirically derived from data on Earth, Venus and Titan, and a model is proposed to justify it. We introduce the concept of planetary inner albedo, as a complement to the usual bond albedo. A geometric proof is given for the main finding of the paper, which can be summarized as follows: the ratio of the inner to outer albedo is a constant, related to the universal parabolic constant. Furthermore, we extend the surface temperature formula to gas giants, giving the temperature at which condensates (e.g., of ammonia) start forming within their atmosphere, particularly for Jupiter, Saturn and Uranus. Based on model complexity, applicability and accuracy, the heating mechanism via atmospheric reflectivity (a mirror effect) performs much better than the alternatives.