It looks like you're trying to analyze the characteristics of the Sun in relation to other stars. Let's clarify and correct a few points:
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Brightness and Temperature: The Sun is categorized as a medium-bright star largely because of its temperature and size compared to other stars. It is classified as a G-type main-sequence star (G dwarf star). Other types of stars exhibit varying brightness depending on their temperature.
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Hotter Stars: Typically, hotter stars (like those classified as O and B types) emit more energy overall and are much brighter, often appearing very luminous. However, this does not mean that they are "brighter" in the sense of being more visible from Earth unless they are also relatively close.
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Cooler Stars: Cooler stars (like K and M types) can emit less energy, making them less bright compared to the Sun when viewed from Earth.
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Medium Brightness: The Sun is brighter than many stars because it is relatively close to Earth, yet when compared to the vast number of stars in the universe, it falls in the middle range of brightness.
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Conclusion: While the Sun has a medium temperature (about 5,500 degrees Celsius on its surface), it is not the "biggest star." There are significantly larger stars (like supergiants) that have much greater diameters and luminosities.
The statement that "the sun has a medium temperature making it the biggest star" is inaccurate. Temperature does contribute to a star's brightness, but stars can be larger or smaller regardless of their temperature. The Sun is not the biggest star; instead, it is considered a middle-sized star in terms of temperature and size.
In summary, the Sun's classification as a medium-bright star relates to its temperature and distance from Earth, while brightness compared to other stars is influenced by both temperature and distance rather than solely by the Sun's physical characteristics.