New insights into black bodies

Planck's law describes the radiation of black bodies. The study of its properties is of special interest, as black bodies are a good description for the behavior of many phenomena. In this work a new mathematical study of Planck's law is performed and new properties of this old acquaintance are obtained. As a result, the exact form for the locus in a color-color diagrams has been deduced, and an analytical formula to determine with precision the black body temperature of an object from any pair of measurements has been developed. Thus, using two images of the same field obtained with different filters, one can compute a fast estimation of black body temperatures for every pixel in the image, that is, a new image of the black body temperatures for all the objects in the field. Once these temperatures are obtained, the method allows, as a consequence, a quick estimation of their emission in other frequencies, assuming a black body behavior. These results provide new tools for data analysis.