leads to information about each of the higher moments. The first moment of the mean intensity is constant regardless of optical depth: The second moment of the mean intensity is then given by: Note that the Eddington approximation is a direct consequence of these assumptions. Defining an effective temperature for the Eddington flux and applying the Stefan–Boltzmann law, realized this relation between the externally observed effective temperature and the internal blackbody temperature of the medium. The results of the grey atmosphere solution: The observed temperature is a good measure of the true temperature at an optical depth and the atmosphere top temperature is . This approximation makes the source function linear in optical depth. References Observational astronomy Astrophysics