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answers:
Flouride say: cher.
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Clive say: Sun. Because it's THE Sun and that's what it's always been called, in English at any rate.
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Brigalow Bloke say: There are dozens of languages on Earth, each will have a word for the Sun. There is one ENGLISH word and that is "Sun".
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stevan say: solar molar
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Nyx say: Hot Stuff
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poldi say: Not all stars in the galaxy have a name.
Earth's sun is called the Sun - that is its name.
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Tom S say: The Sun.
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Mutt say: Some people mistakenly claim "Sol" is the official name. But according to the IAU, our sun's official/proper name is "Sun", just as our moon's proper name is "Moon".
Notice how I capitalized "Sun" and "Moon" above when referring to the names of the two? That is because they are the proper names, so they should be capitalized, just as you would with Jim, New York City, France, and any other proper names. However, these two can also be used as more generic terms, such as "moons of Jupiter" or the sun of some exoplanet. These are lower case names (unless first in the sentence), just as sometimes "earth" is lower case if you are referring to dirt.
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fairly smart say: Sol.
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Starrysky say: If? They don't. With 2 to 400 billion of them, not possible.
Our "sun" has had various names in different languages. The one in Latin is "sol". We call our family of planets and our sun the "solar system".
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mike1942-f say: No they don't all have a name, because we haven't named them - too many. our Sun has lots of names including Sol and Helios.
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Davros say: It is just "Sun."
Like the Moon it is the thing for which it is named because it's the first one Humanity looked at. Other examples came later. It's what the internet generation would call the Trope Namer.