I dunno about that one. The UFP's first mention is in the latter half of Season One (A Taste of Armageddon?) So the bulk of that season contains the Earth based references. IIRC, Seasons Two and Three are pretty consistant in referring to the UFP as political/national authorty that the Enterprise operates under. So roughly 22 as an "Earth ship" vs 40+ as a "Federation ship".STAR TREK was about the Federation. Surprisingly rarely mentioned, putting retcon to the side, more often than not not Kirk spoke of Earth, Earth ships, Earth colonies, Human achievements, Human histories. Yes, there were Federation call out too, but much less than half the time.