Ronald Held said:
I recently watch that episode. The Enterprise was displaced 990.7 LY. At Warp 8.4 it would take 11.33 hours to return to the planet. I assumed a Cochrane factor was needed and computed it to be about 1332. Is that high for TOS travel? I did not try to estimate how much time passed from the time the ship accelerated past 8.4 until they orbited the planet.
Actually a light year is defined as the distance traveled by light in a vacuum during 365.25 Earth days, or 8766 hours. 990.7 light years equals 8,684,476.2 light hours.
The Enterprise started at warp factor eight:
SPOCK: Good. Then prepare to come to warp eight.
And later increased the speed to warp 8.4:
RAHDA: We're holding warp eight point four, sir. If we can maintain it, our estimated time of arrival is eleven and one half solar hours.
SPOCK: Eleven point three three seven hours, Lieutenant. I wish you would be more precise.
Ignoring the distance traveled before this statement, the Enterprise would need a speed of 766,029.47 times the speed of light to travel 8,684,476.2 light hours in 11.337 hours. warp factor 8.4 is equal to 592.704 times the speed of light according to the official TOS warp formula. Thus they traveled 1292.4317 times as fast as the official warp formula, as has been pointed out in various sources before.
Thus 1292.4317 should be the number that constantly shows up in Star Trek, instead of 47.
A Cochrane factor is one of many proposed solutions to various problems in Star Trek galactogrphy.
That's the default assumption. But since we really don't know what "Our new ships can-" because Tyler never finishes his boast, and since we get no hints of a speed barrier in any meaningful brackets (Earth ships can do warp 5 in 2151 already, and Vulcan ships can do at least warp 6.5, while Kirk's engineer a century later thinks warp 8 is a lot), we might just as well consider a more physical Barrier.
Perhaps Tyme was a dress rehearsal for the daring attempt to have Our New Ships brave the Galactic Barrier, and perhaps ultimately the Great Barrier as well...
Having Talos be cut off from Earth by a Barrier is attractive also in the sense that mere distance, defeated by speed, is a highly dissatisfactory obstacle. After all, Talos sits somewhere between Rigel and Vega, both stars well within the reach of earlier generations of starships (heck, a famous earlier starship did visit Rigel, or at least a Rigel, right off the bat!).
Timo Saloniemi
Why not expand your theory to explain that the Thyme Barrier was broken after the Parsley Barrier, the Sage Barrier, and the Rosemary Barrier.

As you may remember, Pike said the Time Warp Factor to Talos IV would be seven. And Tyler didn't say that breaking the Time Barrier made the new ships faster, he said that they wouldn't believe how fast they would get to Earth. The time warp need not make the ships travel faster according to the outside world, it might make the trip seem much shorter to those aboard the ship - days instead of years or weeks instead of millennia.
Samuel said:
I don't take the names of solar systems in the Star Trek universe to be the same as the ones in ours. I mean most of recent history (1970s to 2018) in the Trek universe is radically different from our own. Why would we expect the names of stars to be accurate.
It wouldn't be hard by the way if anyone was interested in doing some modern day retconning to changing dialogue in Star Trek to accurately reflect what has happened historically, star names, and travel distances.
Actually, the Star Trek universe diverged from ours earlier, before Star Trek was first produced. That is the only possible explaination for the many historical errors that careless writers made.
But no divergence during historical times could change the locations of the stars. The stars would have the same locations in 3-D space and the same luminosities and would look the same in Earth's skies. So in such a similar alternate universe as that of star trek they should be given the same names.
If you want to make the stars different, you should make the Earth different. Perhaps the Earth of Star Trek and our Earth are both decoy copies of the real Earth. Perhaps it is prophesized across the universe that on the real Earth Humans will release the Spawn of Cthulhu, who will spread out from Earth and spread death and destruction across the universe. Beings aware of the prophecies are on the alert to find the real Earth and destroy it to prevent the spread of the Cthulhu Spawn.
And maybe the Cthulhu Spawn created many millions of fake Earths across the universe. Those who destroy one of the decoy Earths will stop looking for the real Earth. And those different decoy Earth's will have different stars visible in their skies, which will all be given the names of stars visible from the real Earth. With this theory one can rearrange the Star Trek stars to avoid many problems of Galactography.
I have had a lot of problems writing this since the Trek BBS page kept closing on me.