If you want to REALLY go for a loop re - the TOS timeframe as stated in the series itself, it's all over te place.
In The Squire of Gothos Spock informs Kirk that Trelane is viewing events 800 years in Earth's past (the planet was 800 light years from Earth and Spock states that Trilane is not taking the speed at which light travels into account; thus the Napoleonic Era trappings). Since the accepected 'era of the Napoleonic war is 1799 -1815; this FIRMLY places TOS in 2599 - 2615 (aka the early 27th century).
Yet, later in the first season we have Tomorrow Is Yesterday; and a scene between a USAF Captain, and the arrested Captain Kirk, where the USAF Captain states:
"I'm got enough to lock you up for the next couple of centuries..."
"That outta be just about right"
this placing TOS in the mid 22nd century.
Then we have Space Seed with Khan's vessel launched in 1996 and the line from Kirk in response to Khan's
"How looong...."
"A little over 2 centuries..."
Which places TOS in the late 22nd, early 23rd century.
The most interesting thing to me in all the various continuity violation debate is that nearly everyone takes Spock's description of the Romulan War era of technology as sacrosanct; yet when the century of the TOS era was firmly laid down in the motion picture; NOBODY was citing the Squire of Goths Spock dialogue that crealy put TOS in the late 26th to early 27th century.
So, while I LOVE TOS (it's my favorite series); it's so internally inconsistent at times that I honestly can't tale a lot of what people claim as clear canon violations in later series seriously. And BTW, the arguement that 1960ies TV shows didn't place a lot of emphasis on internl consistency and continuity; sorry, there were others that did, like The FBI and QM's Invaders. IF GR and the gang had cared about internal consistency for TOS, they could have done it - but they didn't and instead chose to have the 'facts' serve the story when a contradiction arose (which is fine). Again, I just do find it interesting that some people like to state 'if they cared they would have watch TOS' for the later series, when often they DID; but again, TOS was not overall very consistent itself with a lot of its own 'historical backstory'.
Spock the precise didn't suggest that "Squire of Gothos" was 900 years after 1804 or later; Jaeger and Kirk did speculate that Trelane was using some telescopic like device to see actions from the past, but the fact that Trelane knew Earth worlds and names proves their theory wrong.
The line in "Space Seed" is "two centuries we estimate", and the 200 years is repeated in the episode and in WOK.
^^ These keep being thrown out there, but most of them can be rationalized.
In "Tomorrow Is Yesterday" the 200 year reference doesn't have to be taken literally. Just look at Kirk's expression. "That outta be just about right." The Colonel is exaggerating to make a point and Kirk's sarcasm plays into it. No problem.
In "Space Seed" it gets dicier to rationalize, but if accept that the Botany Bay reached a decent percentage of light than their "about two hundreds" year sleep could be explained as relativistic time dilation. I put the events of "Space Seed" in 2272. If the Botany Bay left Earth and the Sol system no earlier than 1996 than it's 276 years (realtime) before it's found by the Enterprise. Put that together and you can rationalize the "two centuries we estimate."
WNMHGB makes two references to the Valiant of about two centuries give or take a bit. I put the events of WNMHGB in 2270. Minus about two hundred years and you're in the latter part of the 21st century. That's just enough for the Valiant to be an early warp capable ship.
In "The Squire Of Gothos" Trelane's planet is stated to be 900 light years from Earth. Trelane claims to have been studying Earth's past. There's no reason to believe that he studied only one small part of Earth's history during late 18th and early 19th century. He could have been studying all the way back to the 14th century and chose only to imitate the trappings of the 18th to early 19th centuries when the Enterprise came along.
The idea that the Botany Bay was travelling at relativistic speed would mean that it would reach a preselected Earth like exoplanet in 50 or 100 years Earth time. If they traveled about 200 years aboard the ship at relativistic speeds speeds the elapsed time outside the ship could have been several times 200 years.
It is simpler to assume that since we don't know how precise Kirk was with two centuries he meant more than one century but less than three centuries - 100 to 300 years. Since it was believed that Khan left Earth about 1990 to 1996 in the "Space Seed" calendar that puts the year of "Space Seed" about 2090 to 2296 in the "Space Seed" calendar.
WNMHGB has a statement that Tarbolde was on the Canopius Planet in 1996, which was sometime during "the last couple of centuries", putting WNMHGB about 2096 to 2196 in the calendar used in that episode. It also says that the
Valiant was lost in space over 200 years before, and thus before some moment in the period of 2096 to 2196 in the calendar used in WNMHGB.
Your explanation for "Squire of Gothos" is good.
My explanation is that Kirk and Jaeger weren't too good with mental math. They speculated that Trelane was using some sort of super telescope equivalent to watch Earth history and thus assumed that since Gothos was now 900 light years from Earth Trelane was watching events 900 years earlier. If they had properly calculated the time since the Napoleonic era they would have realized that light from that era on Earth wouldn't reach Gothos for centuries.
But because the United Earth government constantly changes, for political reasons, the official United Earth calendar, and the Earth year sometimes changes from 2785 to 1354, for example, or from 957 to 3015, for example, Kirk and Jaegar aren't too sure how many centuries ago the Napoleonic era was.
And those of you interest in chronology, which this thread is about, might want to go to my thread:
https://www.trekbbs.com/threads/how...-chronologies-are-there.295793/#post-12605940
And perhaps mention various other chronologies they know about.