Over the past few centuries, a small number of stars have been named after individual people. It is common in astronomy for objects to be given names, in accordance with accepted astronomical naming conventions. However, most stars are not given proper names, relying on either long-standing traditional names (usually from the Arabic), or star catalogue numbers.
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Nomenclature
The naming of astronomical bodies is controlled by the International Astronomical Union (IAU), which lays down strict standards for this naming.
In July 2014 the IAU launched a process for giving proper names to exoplanets and their host stars, the outcome of which was announced in December 2015. As a result, the IAU approved the names Cervantes (honoring the writer Miguel de Cervantes Saavedra) and Copernicus (honoring the astronomer Nicolaus Copernicus) for the stars Mu Arae and 55 Cancri A, respectively.
In 2016, the IAU organized a Working Group on Star Names (WGSN) which will catalog cultural and historical names for bright stars to help preserve astronomical world heritage, and maintain a catalog of IAU-approved unique proper names for stars. The WGSN's first bulletin of July 2016 set out its terms of reference and naming guidelines. All approved names are included on the current IAU Catalog of Star Names, last updated on 1 February 2017. The IAU approved the name Cor Caroli (Latin for 'heart of Charles') for the star Alpha Canum Venaticorum, so named in honour of King Charles I of England by Sir Charles Scarborough, his physician. The IAU also approved the historical name of Barnard's Star, named after the American astronomer E. E. Barnard.
Whilst many private companies will offer the "right" to name a star, for a fee, they have no legal standing to assign any star a name, and can offer no guarantee of the name being noted. The IAU does not recognize this practice and its website uses the word charlatanry in this context.
Apart from the few formally approved by the IAU, and leaving aside commercial attempts, stars named after individuals fall broadly into two groups. The first group, mostly older stars, are those named openly for an individual connected with them in some way. The second, somewhat more obscurely, are those named after an individual but without explicitly making this clear.
Openly named stars
There is a small group of stars whose common names honour individuals. Many of these were highly significant in some way when discovered, usually through having some unusual characteristic.
In addition, many stars have catalogue designations that contain the name of their compiler. This includes Wolf, Ross, Bradley, Piazzi, Lacaille, Struve, Groombridge, Lalande, Krueger, Mayer, Weisse, Gould, Luyten and others. For example, Wolf 359, discovered by Max Wolf. These are not strictly named after that person, although it may seem that way, but merely given a star designation in the star catalogue in which Wolf published his discoveries.
(Note that Pandora's Star and Ratner's Star are the names of novels, not actual stars.)
Covertly named stars
However, some names have been given unofficially, and worked their way into star catalogues and thus to informal acceptance.
The earliest noted example was Sualocin and Rotanev (α and β Delphini), two stars which appeared in the Palermo star catalogue of 1814. They were eventually identified as the reversed spelling of Nicolaus Venator, a Latinised name of Nicolò Cacciatore, assistant to the astronomer Giuseppe Piazzi. It is not clear whether Piazzi intended to name the stars after his assistant, or if Cacciatore made the names up himself.
More recently, during the Apollo program, it was common for astronauts to be trained in celestial navigation, and to use a list of naked-eye stars from which to take bearings. As a practical joke, Gus Grissom gave names to three stars on this list — Navi (γ Cassiopeiae), Dnoces (ι Ursae Majoris), and Regor (γ Velorum). The names stuck, and were used through the rest of the program. Unknown to Grissom, these stars already had traditional names; however, those were not generally used, allowing the three other names to make their way into other records. Today, they are generally considered disused – some sources listing them as "traditional".
The three names are references to the three Apollo 1 crew:
It is possible, though unlikely, that more "traditional" names are in fact hidden names such as these, not yet identified; etymologies for most star names are not currently known.