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When Did People First Realize That the Sun is a Star?

It is likely that the idea that the Sun might be a star surfaced many times in the ancient world, but humans were not in a position to begin to prove it until the nineteenth century, and before then there were plenty of competing ideas. The Eurocentric view is that Anaxagoras around the 450 B.C. gets credit for being the first to suggest that stars are far-away Suns. You have to ask yourself whether this is at all representative of a date for the idea or whether it is an abribtrary assignment. (For example, do you think that if the Greeks borrowed the word algebra from arabic, that they didn't borrow anything else? Ooh that's a nice word, I think we'll use that. Oh... err... ooh... what's that? $a^{2} \ + $...c'mon let's have a look? Ahh $a^{2} + b^{2} = $...? Ooh $c^{2}$. Of course, one of our guys had aleady figured that out!)

In the nineteenth century it became possible to breakdown the light from stars and the Sun into many colors (in jargon, the result is a spectrum, and the activity is called spectroscopy). These studies, and the monumental task of classification of stars based on observational features, was a collective effort that spread across a period of over a century. Much of the classification was done before the physics of stars was understood so classification schemes underwent revision processes as the physics was gradually revealed.

Notable amongst the first observers who observed the “decomposed light” (spectra) of stars and the Sun was Joseph Fraunhofer, in 1814. See, for example, various discussions on the spectroscopy of stars in and Stellar Spectral Classification by R. O. Gray, C. J. Corbally, and A. J. Burgasser, and Spectral Classification; Old and Contemporary (2010) by S. Giridhar. Note that the first distance measured to a star other than our Sun was achieved in 1838, see: F. W. Bessel, “On the Parallax of 61 Cygni,” Monthly Notices of the Royal Astronomical Society 4 (1838), 152-161. A milestone in the understanding of the nuclear physics in stars was reached in the late 1950s, marked by the seminal paper: E. M. Burbidge, G. R. Burbidge, W. A. Fowler, and F. A. Hoyle, “Synthesis of the Elements,” Reviews of Modern Physics 29, 4 (1957), 547-650.

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Deducing the physics of stellar structure and evolution, and relating those findings to the observational properties and classification scheme of the stars is actually still an ongoing refinement process. The idea that nuclear fusion could account for the energy generation mechanism in stars was floated as early as 1920 by Arthur Eddington. However, there were many hurdles to clear before reaching the point of a satisfactory working theory of stellar structure and evolution that was driven by nuclear energy generation. By the late 1950s, the critical problems had been solved.

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