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It's not correct to say that the sun is a star of average size and brightness. In fact, the sun is larger and brighter than 96% of all stars.
The closest star to Earth is the sun. After that, the closest star(s) are three stars in the Alpha Centauri system. The two main stars are Alpha Centauri A and Alpha Centauri B, which form a binary pair. They are approximately 4.3 light-years from Earth. The third star is Proxima Centauri. It is about 4.22 light-years from Earth and is the closest star other than the sun.
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