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 diagram 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, by 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.