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Mudd's stolen starshipEdit
As it was "unregistered" and "unidentified", Mudd's ship was hotly pursued by the Starfleet vessel. While attempting to escape the Enterprise, Mudd burned his ship's engines out, leaving the vessel powerless and adrift in an asteroid belt. Although Mudd and his "cargo" of three women were transported to safety by the Enterprise, his ship was destroyed after it impacted with an asteroid moments later.
In the final draft script of "Mudd's Women", this ship was referred to as "Earth vessel composition. About the size of the old Class 'J' cargo ships," rather than actually being a class J cargo ship itself.
In the original version of "Mudd's Women", a simple gold-colored ovoid shape was used to represent Mudd's ship until it pulsated and exploded. More indistinct optical elements were used for the final shots of the ship. During the 2008 remastering of the episode, Visual Effects Producer Michael Okuda made use of the opportunity to retcon a new CG ship into the episode. He took great care to keep its onscreen appearance barely discernible and distant in order to maintain the "feel" of the original visual effects.
Michael Okuda named the ship "Stella", an ironic and humorous echo of Harry Mudd's caustic comments about his estranged wife in "I, Mudd". Had the ship been seen more clearly on screen, Okuda would have labeled the production-used CG model with this name. 
For further information on the model, see class J starship studio model.
Starfleet training vesselEdit
During a training mission aboard this vessel, one of the ship's baffle plates ruptured and exposed the engine room to delta radiation. Fleet Captain Christopher Pike suffered severe radiation exposure and eventual paralysis due to his attempts to rescue the cadets who were trapped in the room. (TOS: "The Menagerie, Part I")