(covers information from several alternate timelines)
The Vostok 1 was an early Earth spacecraft launched by the Union of Soviet Socialist Republics during the mid-20th century. In 1961, Vostok 1 carried the first Human into space, concluding with a single successful orbit.
An image depicting Vostok 1 was contained in the library computer aboard the USS Enterprise. This data was flashed on a viewscreen when the Talosians scanned the Enterprise computer in 2254. (TOS-R: "The Cage")
The first Human who was launched into space and orbited Earth was named Yuri Gagarin. The 22nd century starship VK Yuri Gagarin and the planet Gagarin IV were named for him (see also: Yuri Gagarin Hall).
The Artisan prop and model shop of Quantum Mechanix, QMx FX Cinema Arts, was asked to illustrate the history of space flight with models for the film. They constructed fourteen models in total. On their website, there was a picture of the Vostok model. According to the site, the model was damaged on set, resulting in the loss of several antennae.