Some of the comments in this thread suggest that some people are a little uncertain about the passage of time in "The Menagerie".
So here I go again.
When Spock (or an illusion of Spock) si with PIke (or an illusion of PIke) near the begining:
SPOCK: Captain Pike, may I remain for a moment? (flash, the others leave) You know why I've come, Captain. It's only six days away at maximum warp and I have it well-planned. (flash, flash) I have never disobeyed your orders before, Captain, but this time I must. (flash, flash) I know. I know it is treachery and it's mutiny. but I must do this. (flash, flash) I have no choice. (flash, flash)
So according to that possibly false statement by Spock (or an illusion of Spock), the minimum travel time from Starbase 11 (or an illusion of Starbase 11) to Talos IV (or an illusion of TAlos IV) is 6 days, and that at maximum warp.
Later the Enterprise apparently warps out of orbit around Starbase 11 and apparently heads for Talos IV. And later, aboard the real or illusionary shuttlecraft:
MENDEZ: Pulling ahead of us fast. Fuel is down to sixty three point three. If we turn back now, we've just got barely enough to get us back to the base.
On the bridge, later (?):
SPOCK: Stop. How long before shuttlecraft's fuel supply forces return to starbase?
COMPUTER: Computed. Shuttlecraft is already past point of safe return.
Some time later, after Kirk apparently comes aboard the apparent Enterprise:
Captain's log, stardate 3012.4. Despite our best efforts to disengage computers, the Enterprise is still locked on a heading for the mysterious planet Talos Four. Meanwhile, as required by Starfleet General Orders, a preliminary hearing on Lieutenant Commander Spock is being convened. And in all the years of my service, this is the most painful moment I've ever faced.
Spock requests immediate court martial, since Kirk, Mendz, and PIke are enough command officers for a court martial board. So sometime later:
Captain's log, stardate 3012.6. General Court-Martial convened. Mister Spock has again waived counsel and has entered a plea of guilty.
Later, meendez declares the court in recess. And the first part of the episode ends.
http://www.chakoteya.net/StarTrek/16.htm
"The Menagerie Part 2" begins with:
Personal log, stardate 3013.1. I find it hard to believe the events of the past twenty four hours or the plea of Mister Spock standing general court-martial.
Tha tis followed by a recap of the events in "The Menagerie Part 1", and is followed by a shot of the hearing room and:
KIRK [OC]: The court-martial of Mister Spock has been convened in closed session. Despite all we can do, images continue to be transmitted to us from Talos Four.
:
I believe that this is a direct continuation of Kirk's personal log on stardate 3013.1, and that this scene thus begins on 3013.1.
So the scene which begins with this voice over by Kirk should begin on stardate 3013.1, which should be about 24 hours or less since the beginning of the events which Kirk finds it hard to believe.
And I suppose that when Kirk mentions "the events of the past twenty four hours" he is rounding a bit and the time span could be between about 22 hours and about 26 hours.
When in the story did the events which Kirk finds it hard to believe start?
1) I think that the events which Kirk finds it hard to believe probably started before the first scene, at the time when a message calling them to Starbase 11 was reported to be received.
2) Or possibly some people might think that the events which Kirk finds it hard to believe started when the Enterprise apparently left orbit around Starbase 11.
3) Or possibly some people might think that the events which Kirk finds it hard to believe started when Kirk apparenlty reached the Enterprise..
5) Or possibly some people might think that the events which Kirk finds it hard to believe started at Spock's preliminary hear on stardate 3012.4.
6) Or possibly some people might think that the events which Kirk finds it hard to believe started at Spock's court martial on stardate 3012.6.
In # 5, there would be about 22 to 26 hours in about 0.7 stardate units from 3012.4 to 3013.1, at a rate of about 31.4 to 37.14 hours per stardate unit.
in # 6, there would be about 22 to 26 hours in about 0.5 stardate units from 3012.6 to 3013.1, at a rate of about 44 to 52 hours per stardate unit.
And if the 24 hours began earlier in the story, there would be few hours per stardate unit.
After the Talosians show more images of Pike's experiences on Talos IV, they stop.
MENDEZ: What is it? Why have they stopped the images?
SPOCK: Because they know that Captain Pike is fatigued. We can reconvene later.
After an unspecified interval:
Personal log, stardate 3013.2. Reconvening court-martial of Mister Spock and the strangest trial evidence ever heard aboard a starship. From the mysterious planet now only one hour ahead of us, the story of Captain Pike's imprisonment there.
http://www.chakoteya.net/StarTrek/16b.htm
Obviously,If Kirk said "one hour ahead of us" when the planet was between 0.5 and 2.0 hours away, the estimated time of arrival would be stardate 3013.2 plus 0.5 to 2.0 hours times the ratio of hours to stardates. So the stardate of arrival at Talos IV would be between about 3013.2096 and stardate 3013.2318.
Of course if Kirk's 24 hours began earlier in the story than stardate 3012.4 the ratio of hurs to stardate units would be smaller and there would be a larger fraction of a stardate unit per hour.
So the voyage to Talos IV is said to take 6 days at maximum warp, and the dated part of the voyage seems to take only 0.8 stardate units and ends about an hour away from Talos IV.
Assuming that the total voyage was 5 to 7 Earth days and took 0.8 to 1.2 stardate units, there would be 4.16666 to 8.75 Earth days, or 99.999 to 210 Earth hours, per stardate unit.
In that case the previousl "24 hours" before stardate 3013.1, if they were 22 to 26 hours, would begin 0.104 to 0.26 stardate units earlier, and thus between stardate 3012.84 and 3012.996. That would be after both 3012.4 and 3012.6, which would mean that Kirk wasnot shocked by events between those stardates, but by events after stardate 3012.6. And presumably hours after the first testimony session in the court martial, which began on 3012.6, but should have lasted just 5 to 15 minutes based on what was seen in the episode.
I note that on stardate 3013.1 Kirk said:
Personal log, stardate 3013.1. I find it hard to believe the events of the past twenty four hours or the plea of Mister Spock standing general court-martial.
And Kirk does not state that the events of the last 24 hours began about 24 hours earlier, merely that they began some time during the last 24 hours. Or the 24 hours could have begun with earlier events in the story before stardate 3012.4. Either would mean that stardate 3012.6,and even stardate 3012.4, would have been a lot less than 24 hours before. stardate 3013.1. Thus thhere could have been fewer hours during the intervals between the stated stardates, and the ratio of hours to stardates calculated from the intervals between the stated stardateswas actually an upper limit.
If a ratio of 31.4 to 52 hours per stardate unit is the upper limit, the real ratio of hours to stardate units could be no higher, and culd be much lower, than 31.4 to 52 hours per stardate unit. Assuming that the voyage from Starbase II to Talos IV takes 6 earth days requires that there should be about 99.9999 to 210 hours per stardate unit.
So it seems impossible for the voyage to take the stated "6 days at maximum warp".
Possible explanations are:
1) Time passes much slower on a dtsrship at warp (Pike did set the "time warp drive" at factor 7 during the first voyage to Talos IV). Thus.6 days could have passed on Starbase 11, and the changing stardates there would be based on that, and only 1 day could have passed on the Enterprise, and the stardates on the Enterprise, based on the passage of time aboard, were more consistent with one day passing on the ship.
2) It took Kirk about 1 day to reach the Enterprise. Kirk spent the rest of that day and most of the next 4 days trying to regain control of the ship. The hearing and then the courtmartial began late on the 5th day, and reconvened on the 6th day when the Enterprise was about to reach Talos IV. Thi requires that the events which Kirk couldn't believe did not include Spock hijacting the ship, but instead began with the revelaitons in Spock's courtmartial, or even possibly some events which happened offscreen after the courtmartial recessed (possibly an attempt by enginnering which Kirk thought was certain to regain control while Spock was distracted by the courtmartial turned out to be a failure. after the ocurtmartial recessed)
3) Possibly everyone could look up the coordinates of Talos IV and how far it was from Starbase 11 and thus calculate how long - 6 days - it would take to reach Talos IV from Starbase 11. So Spock had to tell PIke the voyage would take 6 days.
But possibly the scenes on starbase 11 were illusions and they were not on Starbase 11 but were much closer to talos IV. Thus the voyage to Talos IV took only about 1 days.
4) Possibly everyone could look up the coordinates of Talos IV and how far it was from Starbase 11 and thus calculate how long- 6 days - it would take to reach Talos IV from Starbase 11. So Spock had to tell PIke the voyage would take 6 days.
But possibly the Enterprise reaching Talos IV was an illusion and they arrived at someplace else which wa sa lot closer to Starbase 11 than TAlos IV was.
5) Possibly everyone could look up the coordinates of Talos IV and how far it was from Starbase 11 and thus calculate how long - 6 days - it would take to reach Talos IV from Starbase 11. So Spock had to tell PIke the voyage would take 6 days.
But possibly the Enterprise traveled from a place which was not Starbase 11 to a place which was not Talos IV and it was only an illusion that they were travelling from Starbase 11 to Talos IV.
6) Possibly everyone could look up the coordinates of Talos IV and how far it was from Starbase 11 and thus calculate how long - only 1 day - it would take to reach Talos IV from Starbase 11. But the Talosians gave everyone the illusion that the trip would take 6 days, even at maximum warp, so Kirk would think that he had more time to regain control than he actually did.
7) Posssibly the trip did take 6 days, but the Talosians pulled a
Groundhog Day on everyone, giving everyone the illusion that they were experiencing the first day of Spock's court martial over and over again until the 6th day when they experienced the 2nd day of Spock's court martial until reaching Talos IV or some other destination.
And maybe the Talosians varied the plot on the different repeats of the first day of Spock's court martial.
I note that at the beginning of Spock's court martial:
Captain's log, stardate 3012.6. General Court-Martial convened. Mister Spock has again waived counsel and has entered a plea of guilty.
MENDEZ: Mister Spock, are you aware in pleading guilty that a further charge involving the death penalty must be held against you should this vessel enter the Talos star group?
But on the second day of Spock's Court martial:
MENDEZ: Guilty, yes or no, Captain? (flash) Yes. I must also vote guilty as charged. And you, Captain?
KIRK: Guilty as charged.
How could they vote on Spock's guilt or innocence if Spock already pleaded guildty? Thus I suspect that this scene from the alleged second day was actually a sequel to a different illusion of the beginning of the court martial, where Spock did not plead guildity at the begining but pleaded innocent instead.
So if so much of the events in "The Menagerie" might be illusions, how can anyone hope to know anything about how fast the shuttlecraft could travel based on the rather contradictory evidence about that in this episode?