There "isn't another vessel in the whole quadrant" when Kruge picks up
the data from the merchantman.
STVI: Charting a new sector, the Excelsior did detailed surveys of 54 planets. Shortly after picking up Gorkon, the Enterprise is "a thousand light years" from Federation headquarters.
STVIII: The Federation is an organization of 150 worlds, spread across 8000 light years.