Because of the Earth's revolution around the Sun, nearby stars appear to move with respect to very distant stars.
The parallax of a star is the apparent angular size of the ellipse that a nearby star appears to trace against the background stars.
Because all parallaxes are small (the stars are very far away), we can use the small angle approximation: tan (x) ~ x, for small x. If we measure the distance to the star in A.U. (astronomical units), then the parallax is given by:
A parsec is the distance at which a star would be if its parallax were exactly 1 second of arc.
1 parsec = 3.26 light years = 206,265 A.U. = 3.09 x 1018 cm .
There aren't any stars that close! The nearest star is Proxima Centauri, at 1.3 pc (or 4.3 light years).
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