Aurora (NC-17740)
The Aurora (NC-17740) was a 23rd century Federation Class J space cruiser. ()

History 
In 2269, the Aurora was stolen by Dr. Sevrin and his followers, who were traveling in search of the mythical planet Eden. Consequently, it was pursued by the . 

When the Aurora approached the Romulan Neutral Zone in an attempt to evade pursuit, Captain Kirk deemed it necessary to tractor in the ship. In response, the crew of the Aurora pushed the ship to its limit, causing its engines to seriously overheat. The vessel was destroyed as the Enterprise transported the vessel's complement of six aboard. ()

Appendices

Background information 

The script draft of 12 November 1968, described the ship as "(...) small, rather like the Enterprise shuttlecraft." In that draft version the ship was still called Argo. (Scenes 3 & 5, p. 2) In the draft version of 18 November, the name was changed to Aurora and the description abbreviated to "space cruiser". (Scenes 3 & 4, p. 1)

The studio model used in the original edition of "The Way to Eden" for the Aurora was a modification of one of the two  studio models that previously appeared in . For its 2008 remastered counterpart, it was replaced by a newly conceived CGI model.

The registry of the Aurora was the tail number of the  cabin cruiser biplane owned by Matt Jefferies. ()

The Aurora was listed as  Aurora in the ship list. ()

For further information on the model(s), see Class J starship studio model.

Apocrypha 
An explanation of the strange original version look of the Aurora was attempted in the Star Trek Maps, which stated:
"Space cruisers like the S.S. Aurora have been in use for over a century, and are based on a Vulcan design originally used for interplanetary travel. Essentially a 21-meter-long space yacht, space cruisers have a range of several dozen parsecs and can carry provisions for up to six passengers and crew."

The diagram, appearing on Chart B, depicts the Aurora with a registry of NCC-C1200, and a nacelle-style more akin to those found on a class F shuttlecraft.

External link 
 

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Aurora
Retconned material in background