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A "binary star" is the word used for two stars that orbit each other around their common center of mass. For example, Alpha Centauri A and Alpha Centauri B are a "binary star" that is the 2nd closest stars to our Sun. (The red dwarf Proxima Centauri is a little closer, but is so dim that it is invisible to the naked eye.)

Two stars that appear to be very close to each other in the sky but are at different distances are a "double star". They aren't associated with each other; they are merely in the same direction.

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Q: What is a pair of stars which appear to form a double star but do not?
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