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Transport in Astrophysics: IX. Planck’s versus Callendar’s Distributions
Department of Physics, University of Turin, Turin, Italy
- 1 Department of Physics, University of Turin, Turin, Italy
International Journal of Astronomy and Astrophysics·Volume 16 (2026)·Pages 126–144·Published 1 June 2026·DOI10.4236/ijaa.2026.162009
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Abstract
We compare Planck’s distribution for spectral radiation with Callendar’s. We cover the two regimes of wavelengths and frequencies. In each of the four cases we evaluate the dependence of the spectral radiance on the temperature for the maximum, the standard deviation and the distance between the two inflection points. The astrophysical comparison of Planck’s and Callendar’s distributions covers the temperature of the sun, the temperature of the cosmic microwave background, the (B-V) color and the bolometric correction.
KeywordsStarsAtmospheresRadiation MechanismsGeneralBlackbody Radiation
- Planck, M. (1900) On the Theory of the Energy Distribution Law of the Normal Spectrum. Verhandlungen der Deutschen Physikalischen Gesellschaft , 2, 237-245.
- Callendar, H.L. (1913) LXVI. Note on Radiation and Specific Heat . The London , Edinburgh , and Dublin Philosophical Magazine and Journal of Science , 26, 787-791. https://doi.org/10.1080/14786441308635023
- Callendar, H.L. (1914) XCVI. Thermodynamics of Radiation . The London , Edinburgh , and Dublin Philosophical Magazine and Journal of Science , 27, 870-880. https://doi.org/10.1080/14786440508635158
- Tran, M. (2020) Planck’s and Callendar’s Blackbody Radiation Formulas and Their Fitness to Experimental Data. European Journal of Physics , 41, Article 025102. https://doi.org/10.1088/1361-6404/ab513b
- Hernandez, H. (2025) Modelling Thermal Radiation 3. Spectral Radiation, Fors Chem Research Reports, 1-17
- Mohr, P.J., Newell, D.B., Taylor, B.N. and Tiesinga, E. (2025) CODATA Recommended Values of the Fundamental Physical Constants: 2022. Reviews of Modern Physics , 97, Article No. 025002. https://doi.org/10.1103/revmodphys.97.025002
- Phillips, K.J.H. (1995) Guide to the Sun. Cambridge University Press.
- Fixsen, D.J. (2009) The Temperature of the Cosmic Microwave Background. The Astrophysical Journal , 707, 916-920. https://doi.org/10.1088/0004-637x/707/2/916
- Planck, M. (1959) The Theory of Heat Radiation. Dover Publications.
- Kraus, J.D. (1986) Radio Astronomy. Cygnus-Quasar Books.
- Rybicki, G. and Lightman, A. (1991) Radiative Processes in Astrophysics. Wiley-Interscience.
- Condon, J.J. and Ransom, S.M. (2016) Essential Radio Astronomy. Princeton University Press.
- Stefan, J. (1879) Über die beziehung der wärmestrahlungund der temperature. Sitzungs-berichte der KaiserlichenAkademie der Wissenschaften, Mathe-matische-Naturwissenschaftliche Classe Abteilung II, Vol. 79, 391-428.
- Boltzmann, L. (1884) Ableitung des stefan’schen gesetzes, betreffend die abhängigkeit der wärmestrahlung von der temperatur aus der electromagnetischen lichttheorie. Annalen der Physik , 258, 291-294. https://doi.org/10.1002/andp.18842580616
- Lambert, J.H. (1758) Observations variae in mathesin puram, Acta Helvitica , 3, 128-168.
- Olver, F.W.J., Lozier, D.W., Boisvert, R.F. and Clark, C.W. (2010) NIST Handbook of Mathematical Functions. Cambridge University Press.