Something that was edited out of
The Menagerie from
The Cage is the time it took to travel the 18 light years to Talos. It's in the scene where Pike and Vina have a picnic
PIKE: Tango! You old devil, you. I'm sorry I don't have any sugar. Well, they think of everything, don't they? (feeds lumps to the horse)
VINA: Hey, your coffee. Is it good to be home?
PIKE: They read our minds very well. Home, anything else I want, if I co-operate, is that it?
VINA: Have you forgotten my headaches, darling? I get them when you talk strangely like this.
PIKE: Look, I'm sorry they punish you, but we can't let them
VINA: My, it turned out to be a lovely day, didn't it?
PIKE: It's funny. It's about twenty four hours ago I was telling the ship's doctor how much I wanted something else not very different from what we have here.
18 light years in 24 hours is very close to the 0.73 LY/hour that Roddenberry put in his initial series bible for the Enterprise's typical cruising speed. It would also mean that they'd easily cross 100 light years in less than a week (at Time-Warp 7 anyway)
However, in the actually broadcast form (
The Menagerie) this dialogue was cut, so maybe the Enterprise isn't really that fast?
Good work.
Approximately 18 light years in about 24 hours is about 0.75 light years per hour, 18 light years per day, or about 6,574.5 light years per Earth year, at time warp factor seven. Later, in TOS, warp factor seven was allegedly 343 times the speed of light, only 0.052 of 6,574.5 times the speed of light, and warp factor seven and warp factor eight were only used in emergencies. This indicates that time warp factors are not the same as TOS warp factors, and that there was some unspecified type of problem with the superfast engines of Pike's Enterprise which caused them to be replaced with much slower engines in a later refit in order to avoid those unspecified problems.
Thus must be canon In any fictional universe that includes "The Cage".
In a fictional universe which includes "The Menagerie" and not "The Cage", there isn't such a precise indication of how long it took the Enterprise to reach Talos IV.
In the Rigel VII illusion in "The Menagerie, Part 2" Pike says:
PIKE: It's starting just as it happened two weeks ago, except for you.
One one hand, they could have received the distress call from Talos IV right as they were leaving the Rigel system. Then the full two weeks of travel would have been the 18 light year voyage from the Rigel system to the Talos Star Group. If the distance was 18.00 to 18.99 light years and the two weeks was between 11.00 days and 17.00 days, the speed of the Enterprise would would been between 1.058 light years per day - about 386.43 times the speed of light - and 1.726 light years per day, about 630.55 times the speed of light.
Uniderth's original post in this thread says:
Rigel is about 860 light years from earth. Vega is about 25 light years from earth. Running some basic calculations based on the positions of Rigel, Sol, and Vega, that puts Vega at about 881 light years from Rigel. That means Earth is about 21 light years closer.
At speeds of 386.43 to 630.55 times the sped of light, it should take about 1.317 to 2.409 years to travel about 831 to 931 light years from Rigel to Vega.
Note that the lower speed for time warp factor seven would be a little more than the 343 times the speed of light for the official TOS warp factor seven.
On the other hand, it could have taken them two weeks to travel the entire distance from Rigel VII to the Vega Colony, and then they zipped 18 light years to the Talos Star Group too fast to add much time to the journey.
So if the Enterprise travels about 881 light years - about 831 to 931 light years - in two weeks - between 11.00 days and 17.00 days - it's speed would be about 48.882 light years per day - about 17,854.279 times the sped of light - to about 84.63 light years per day, - about 30,913.431 times the speed of light.
Travelling 18 light years to Talos at that speed range would take about 0.00058 days - 0.838 minutes - to 0.001 days - or 1.45 minutes. Not worth counting.
So if the spot where the Enterprise picked up the distress call from Talos IV was somewhere between Rigel and Vega, the speed of the Enterprise making the trip would be somewhere between about 386.43 to 30,913.431 times the speed of light.
And it would be possible to chose a position for the spot where the Enterprise picked up the distress call from Talos IV so that the speed of the Enterprise from Rigel to there was consistent with time warp factor seven being 6,574.5 times the speed of light, as indicated by Pike's comment in the Cage" that was not included in "Menagerie".
If the journey from Rigel VII to where they picked up the distress call from Talos IV took two weeks minus one day, or about 10.00 to 16.00 days, at 6,574.5 times the speed of light, the Enterprise would have traveled about 180.00 to 306.00 light years from Rigel VII to where they picked up the distress call from Talos IV. And the total journey of 831 to 931 light years from Rigel VII to Vega would take about 0.126 to 0.141 years at 6,574.5 times the speed of light.
At 343 times the speed of light, the official TOS warp factor seven, it would take about two weeks, or about 10.0 to 18.00 days, to travel a distance of about 3,430 to 6,174 light days, or 9.390 to 16.903 light years. At the official TOS warp factor seven, it would take 18.102 days to travel 17.00 light years. So it would take about 18.113 days to travel 17.01 light years at 343 times the speed of light.
So it is possible that "time warp factor seven" in "The Cage" could equal the official TOS warp factor seven, though that would make the "two weeks" to travel to Talos closer to three weeks. And of course that would make the 831 to 931 light year voyage from Rigel (Beta Orionis) to Vega (Alpha Lyrae) take between 2.422 and 2.714 years.
So according to the data in "Menagerie", it would take the Enterprise sometime between 11.00 days and 2.714 years to travel from Rigel to Vega, and the longer trip time would be more consistent with the official TOS warp scale. So Pike was not heading from Rigel to Vega to get his injured crew members emergency medical treatment. Instead he was probably planning to leave crew members too badly wounded to perform their duties in the hospitals there for recovery, rehabilitation, and possibly receiving artificial limbs or regeneration of limbs.
Spock describes what the Enterprise was doing when they received the message from Talos IV:
SPOCK: As I stated, gentlemen, this was thirteen years ago. We were on routine patrol when the ship's sensors detected something ahead. At first we were not certain what it was.
So that would seem to indicate that they were making a routine patrol with stops at places as far apart as Rigel and Vega and Pike decided to leave his injured crew members at Vega when he made his scheduled stop there. And that opens the possibility that the Enterprise was not heading straight from Rigel to Vega but was zig-zagging between various destination stars, making the problem of how long it would take to travel from Rigel to Vega even worse.