USS Ariel

From Memory Alpha, the free Star Trek reference.

The USS Ariel was a Federation survey ship in service during the mid-to-late 23rd century. During the 2260s it was manned by a crew of 6 scientists.

In 2269, the Ariel was on a survey mission to planet Lactra VII under the command of Lieutenant Commander Tom Markel. When a 3-person landing party went missing on the surface, Markel ignored Starfleet orders and beamed to the surface with his remaining crew, biologist Randi Bryce and navigator Nancy Randolph.

Six weeks later, the abandoned Ariel was found in orbit by the crew of USS Enterprise, who searched the ship and its log entries. An Enterprise landing party subsequently discovered and managed to free the crew from a Lactran zoo. (TAS: "The Eye of the Beholder")

The "USS" prefix was not on screen, but the crew were definitely with Starfleet, and therefore the Ariel is likely a Starfleet vessel. Oddly, her crew wore the same insignia as the Enterprise.

She might have been named after Ariel, a moon of Uranus.