It orbits the red dwarf known as LHS 2520 in the constellation Corvus
Krypton, the home planet of Kal-El, known more formally as Superman, and his kind is a place that exists. Well, it exists now that it's been picked by well-known and well liked astrophysicist Neil deGrasse Tyson.This didn't just happen at random, he was picked by DC Comics, the publisher of Superman comics, to find a likely candidate star to fill in the role of the star in Superman's origin story.
In return, he got to make a cameo in the most recent Action Comics issue. In the comic, Superman is looking for his birthplace and asks for Tyson's help. In real life, DC Comics did the same and Tyson delivered.
Krypton, it turns out, is in the constellation Corvus, about 27.1 light years away, a close-by neighbor, orbiting the red dwarf known as LHS 2520.
The star is smaller and cooler than the sun, it has about a quarter of the mass, a third of the diameter and is half as cold. Its luminosity is only 1 percent of the sun's, so even though it's very near to us, you won't be able to see it without a telescope.
DC Comics and Tyson actually went to some trouble to get the science right. Still, the star is so cold that a planet orbiting closer than the Earth around it would still be incredibly cold.