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Proxima Centauri
Nearest star to the Sun
Proxima Centauri is a small red dwarf about 4.2 light-years away, which is around 40 trillion km. Light from it takes more than four years to reach us.
Proxima Centauri was found in 1915 by the Scottish astronomer Robert Innes, who noticed that it moves across the sky in step with the bright pair Alpha Centauri A and B. Its distance is worked out by parallax, the tiny apparent shift in a star's position as Earth moves around the Sun. The result is about 4.24 light-years, or roughly 40 trillion kilometres.
It is a red dwarf with only a small fraction of the Sun's mass, and it shines very faintly. Its brightness is far below the limit of human eyesight, so you need a telescope even though it is the closest known star to the Sun. Red dwarfs like it often produce sudden flares, which can strongly affect any planets close by.
In 2016 astronomers announced Proxima b, a planet roughly Earth-sized in mass that orbits within the star's habitable zone, where liquid water could in principle exist. Whether it is actually habitable is unknown, since the flares and the planet's closeness to the star raise real doubts.
Proxima is thought to be gravitationally linked to the Alpha Centauri pair, though it would take on the order of hundreds of thousands of years to circle them. Even the fastest spacecraft built so far would need many thousands of years to reach it.