Sulu actually calls out, "Galaxy center, Captain!" in "Magicks".
As he should: the center of the galaxy appears on their viewscreens at that moment. Further proof that they aren't in it, naturally, or they wouldn't see it.
The intent is clear in both this and STV, that they were at the galaxy's center. Anything else is fan headcanon.
Writer intent is fan headcanon. Only that which actually makes it on screen is beyond debate.
The Kronos travel time discrepancy between "Broken Bow" and Into Darkness seems the least problematic to me, since it's both the smallest discrepancy and involves the greatest difference in ship speeds--warp 5 vs. warp 8 (?), according to your chart--and while I'm sure someone can correct me about what I'm overlooking, I would have assumed that the Kelvinverse Enterprise would be booking it to Kronos at warp 9 or close.
We never hear the new hero ship being referred to as "the fastest" in the new set of movies, but we could well assume that she is well endowed in that department. "Ample nacelles" and all that.
But the problem would appear to be the reverse one here. If it only takes four days to cross the distance at warp 5, why does Kirk's ship spend relative ages (hours at least - isn't Scotty drinking in San Francisco in that night scene, whilst the heroes departed San Francisco in daylight?) at what must be a much higher warp factor?
Yet Kirk isn't in extreme hurry on his way out. He would value stealth over speed until blasting Harrison to bits, so flying out at warp 7 or whatever would be prudent. A return trip at warp 10 would then be nice, as Kirk in TOS proved even his midget ship could do that much, and Kirk in the new movies (and especially the scene in question) would be less mindful of safety.
It's amusing how TPTB installed a tachometer on the viewscreen of the new ship, and then took extreme care to frame it outside every shot to prevent the fans from nitpicking!
How long does it take the Enterprise A to go from Earth to the Klingon Empire in The Undiscovered Country?
Good question. If we disregard everything from "Flashback" as the feverish rantings of the severely affected Tuvok, we have no data whatsoever. One day, the heroes plan on leaving Earth; another, they are "a thousand lightyears out" (or is that just where Kirk got his ale, during some other adventure altogether?), right next to the Klingons, and then essentially stay there for the rest of the movie. The only trip worth a mention in the latter part of the movie is the one from Klingon space to Khitomer; Azetbuhr makes it in more time than Kirk or Chang, establishing nothing much. But Ra-Ghotarei in the meantime travels from Earth to Khitomer, making it worthwhile for us to study the latter part of the movie after all..
Now, we could say that Kirk and McCoy stood trial on the Klingon homeworld, although that's not explicated (it's just Valeris' speculation, and the Operation Retrieve chart text isn't legible without "cheating"). The time to travel there (wherever "there" is) from the border (where our heroes supposedly first met Gorkon - and they hadn't gone to warp yet, because all the beaming back and forth wouldn't fit that picture) is not described beyond the fact that Spock's posse is going to stall for 24 hours; the trial takes place within those, with the clock starting an undetermined time after the assassination (but supposedly soon after it's made public and discussed between Ra-Ghotarei and Azetbuhr).
When Kirk and McCoy end up on Rura Penthe, Spock's time is up, and "Starfleet is screaming". So those 24 hours probably passed, and now our heroes stall by saying their warp drive has failed; there's no time limit established there. Then there's at least half a (Rura Penthe) day of action, including bedtime, plus the walk out of the magnetic shield. And then comes the conclusion, the rescue, the flight to Khitomer, the fight. We're talking a minimum of three days or so between the death of Gorkon and the death of Chang (aka Ra-Ghotarei's travel time from Earth to Khitomer), but we're not talking any sort of a maximum - there is one interval where several days can be easily inserted, and that's the time Kirk and McCoy spend on Rura Penthe.
Timo Saloniemi
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