You also learned that knowing the analytical form of the Planck function allows mathematical derivation of a simple equation expressing this relationship. Another comparison between radiation from the sun and radiation from a blackbody comes from looking at the total energy emitted by each of them. You discovered in Project 6 that increasing the temperature of a thermal radiator causes it to get brighter at every wavelength. Application of the Stefan-Boltzmann law to the sun requires integration of the observed solar flux over all wavelengths. Because flux measurements of the sun or any star always come within limited wavelength intervals, this involves combination of observations across the entire electromagnetic spectrum.
Astronomers call the resulting quantity the bolometric flux.
The solar spectral energy distribution shown in Figure 1 derives from measurements of the solar flux received above the earth s atmosphere at numerous wavelengths. This, finally, leads to second way to define a blackbody temperature for the sun. The effective temperature of an object, particularly a star, is the temperature of a blackbody that emits the same surface flux. As you found in your explorations of the Planck Function in Project 7, the filter flux ratio between the B and V bands provides a good temperature estimate for a blackbody in a specific range of temperatures. Any pair of wavelengths would yield a similar color temperature , T c , with comparable utility and limitation.