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The Universe is vast, consisting of 100s of billions of galaxies. Our galaxy is vast, consisting of 100s of billions of stars. The stars within 10 light years (ly) of us? Not so vast...Here's a list, from closest to farthest.
Star (Distance in LY)

Proxima Centauri (4.24)
-likely part of a triple system that includes the binary star system
Alpha Centauri. A red dwarf with an apparent magnitude of 11.05.
Alpha Centauri
(4.36) - a binary star system, it appears to be a single star to the
naked eye and has an apparent magnitude of -0.27, which makes it the
third brightest star in the sky: 1. Sirius (-1.46), 2. Canopus (-0.72)
3. Alpha Centauri (-0.27)
Barnard's Star
(5.96) - red dwarf star named for E.E. Barnard. Dim with an apparent
magnitude of 9.54, it is the selected target of Project Daedalus.
Luhman 16 (6.59) - a
binary star system consisting of brown dwarfs. Discovered just recently
(2013), the system appears close to the galactic plane and thus
difficult to detect.
Wolf 359 (7.78) - a red dwarf named for Max Wolf, the star has an apparent magnitude of 7.1. It is a flare star.
Lalande 21185 (8.29) - a red dwarf star with an apparent magnitude of 7.52. In about 20,000 years this star will be about 4.65 ly away.
Sirius (8.58) -
Brightest star in the night sky, has an apparent magnitude of -1.46.
Its name is derived from the ancient greek "Seirios" which means
"glowing" or "scorcher". The star is actually a binary star system
consisting of a white main-sequence star and a white dwarf companion.
Sometimes called the "Dog Star" because it is the brightest star in the
constellation Canis Major (Greater Dog).
Luyten 726-8
(8.73) - a binary star system consisting of two red dwarfs, both of which
are flare stars. The apparent magnitude of the system is 12.57. In
32,000 years it will have a close encounter (within 1 ly) with Epsilon
Eirdani (10.52 ly away from us).
Ross 154 (9.68) - a
red dwarf and a flare star. It has an apparent magnitude of 10.44. It
is estimated to be 24% of our Suns radius and 17% of it's mass. It
radiates only 0.38% of our Sun's luminosity.
Some Useful Diagrams

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