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A Star's Temperature And Luminosity Analysis

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According to the book, "If you know a star’s temperature and luminosity, you can determine its radius" (Seeds 151). The luminosity of a star is related to its absolute magnitude, and its spectral class has a relation to the star's temperature. So, in order to estimate the size of Betelgeuse, we would need both its luminosity (in which we can substitute its absolute magnitude) and its temperature (spectral class), which we have been provided. The absolute magnitude refers to the brightness of a star "if it were 10 pc away" (Seeds 145), and the lower the number the brighter the star (and vice versa). According to the spectral sequence, which goes O, B, A, F, G, K, then M, "O stars are the hottest...M stars, the coolest" (Seeds 148), with M stars being orange/red in color.

From here, one would use the Hertzsprung-Russell Diagram, which compares luminosity and spectral class in order to estimate a star's size. A H-R diagram possesses
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So what does this mean in regards to Betelgeuse's size? Well, there is only one explanation: "Although they are cool, they are luminous, and that must mean they are larger and have more surface area than main sequence stars of the same temperature" (Seeds 154). This means that Betelgeuse is a red giant, which "are roughly 10 to 100 times larger than the sun" (Seeds 154). In fact, according to the H-R diagram on page 155, Betelgeuse is even considered a supergiant, which "are over a thousand times the sun’s diameter" (Seeds 154). In conclusion, one can estimate the size of roughly any star if the absolute magnitude (or luminosity) and spectral class (or temperature) is known using the H-R diagram! In Betelgeuse's case, we can estimate that it is an extremely large supergiant star based on its position on the H-R
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