In order to simulate the red sun at the horizon we need to evaluate the average density of matter along a line of sight characterized by a given elevation angle. The decrease in frequency or the increase in wavelength of the light is modeled by the Bouguer-Beer-Lambert law and as a consequence, all the Planck spectrum is shifted toward lower frequencies or longer wavelengths.
References
[1]
Planck, M. (1901) Ueber das Gesetz der Energieverteilung im Normalspectrum. Annalen der Physik, 309, 553-563. https://doi.org/10.1002/andp.19013090310
[2]
Kramm, G. and Mölders, N. (2009) Planck’s Blackbody Radiation Law: Presentation in Different Domains and Determination of the Related Dimensional Constants. https://arxiv.org/vc/arxiv/papers/0901/0901.1863v1.pdf
[3]
Stewart, S.M. (2011) Wien Peaks and the Lambert W Function. Revista Brasileira de Ensino de Fsica, 33, 6 p. https://doi.org/10.1590/S1806-11172011000300008
[4]
Stewart, S.M. (2012) Spectral Peaks and Wien’s Displacement Law. Journal of Thermophysics and Heat Transfer, 26, 689. https://doi.org/10.2514/1.T3789
[5]
Calcaneo-Roldan, C., Salcido, O. and Santana, D. (2017) A Semi-Analytical Approach to Black Body Radiation. European Journal of Physics, 38, 055807. https://doi.org/10.1088/1361-6404/aa7d1d
[6]
Stávek, J. (2023) What Is Hidden in the Planck Distribution Function and the Wien’s Peaks? I. Three Features of the Solar Photons. European Journal of Applied Physics, 5, 1. https://doi.org/10.24018/ejphysics.2023.5.2.240
[7]
Planck, M. (1959) The Theory of Heat Radiation. Dover Publications, New York.
[8]
Mohr, P.J., Newell, D.B. and Taylor, B.N. (2016) CODATA Recommended Values of the Fundamental Physical Constants: 2014. Reviews of Modern Physics, 88, 035009. https://doi.org/10.1103/RevModPhys.88.035009
Bouguer, P. (1729) Essai d'optique sur la gradation de la lumière. Claude Jombert, Paris.
[11]
Lambert, J.H. (1760) Photometria sive de mensura et gradibus luminis, colorum et umbrae.
[12]
Beer, A. (1852) Bestimmung der Absorption des rothen Lichts in farbigen Flüssigkeiten. Annalen der Physik, 162, 78-88. https://doi.org/10.1002/andp.18521620505
[13]
Mayerhöfer, T.G., Pahlow, S. and Popp, J. (2020) The Bouguer-Beer-Lambert Law: Shining Light on the Obscure ChemPhysChem, 21, 2029-2046. https://doi.org/10.1002/cphc.202000464
[14]
Kragh, H. (2017) Is the Universe Expanding? Fritz Zwicky and Early Tired-Light Hypotheses. Journal of Astronomical History and Heritage, 20, 2-12. https://doi.org/10.3724/SP.J.1440-2807.2017.01.01
[15]
Xu, G., Ke, Z., Zhuang, C., Li, Y., Cai, R., Yang, Y. and Du, X. (2023) Measurements and Analysis of Solar Spectrum in Near Space. Energy Reports, 9, 1764-1173. https://doi.org/10.1016/j.egyr.2023.04.229
[16]
Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992) Numerical Recipes in FORTRAN. The Art of Scientific Computing. Cambridge University Press, Cambridge, UK.
