The Copernicus was a Federation Type 7 shuttlecraft that was in service with Starfleet in the mid-24th century, attached to the USS Enterprise-D. It was designated as Shuttle 03. (TNG: "Coming of Age")
In 2364, Jake Kurland was distressed over having failed to qualify for the Starfleet Academy selection process decided to steal a shuttle and plot a course for Beltane IX where he could sign on as a crewmember for a freighter. As the shuttlecraft flew over Relva VII, Kurland's inexperience in flying a shuttle caused him to accidentally power down the dilithium core. Fearing a death from reentry burn in the planet's atmosphere, the young man was guided by Captain Jean-Luc Picard into saving the shuttle by piloting it into a shallow reentry trajectory. In this trajectory, the Copernicus rebounded off Relva VII's atmosphere. The Enterprise later recovered the shuttle. The friction and heat from the contact with the atmosphere left the shuttle somewhat damaged, but Commander William Riker tasked Kurland with repairing it as part of a lesson in self-discipline ordered by Picard. (TNG: "Coming of Age")
The name and registry are from the Star Trek: The Next Generation Companion (stating the ship was originally named Copernicus III by Andrew Probert) and are confirmed on the studio model. In the remastered episode, the registry is seen very briefly on the left rear of the shuttle as it approaches the planet. Previously, the number was blurred by the motion of the model.
This is the first appearance of the studio model. There are differences between this model and later appearances of the Type 7 shuttle. The most visible differences are the lack of a recessed area in the aft section as seen in the Enterprise shuttlecraft 13 full build model and the greater detail seen in the shuttle's dorsal surface (for example, the D'Alison).
Prior to this appearance, the Type 7 shuttle had appearances in LCARS displays. (TNG: "The Naked Now", "The Last Outpost", "Datalore") A variation of this type had been seen in a matte painting of the interior of Starbase 74. (TNG: "11001001")