Part One:
In my post number 106 in the thread:
https://www.trekbbs.com/threads/tos-science-tech-changes.302191/page-6#post-13189776 I discussed the stars Gamma Canaris and Epsilon Canaris in "Methamorposis",
I described the Bayer designations of stars and said that Gamma Canaris and Epsilon Canaris sound like Bayer designations of stars in the constellation Canaris. Except that there is no constellation Canaris in Earth astronomy. I discussed two possible solutions to that. One solution was:
Another theory could be that an Earth colony far from Earth created new constellations in its sky and gave the stars in those constellations Bayer type designations. Thus there could be a constellation Canaris, possibly named after Canary birds or the Canary Islands, or someone named Canaris, like Admiral Wilhelm Canaris, (1877-1945), for example.
https://en.wikipedia.org/wiki/Domestic_canary
https://en.wikipedia.org/wiki/Canary_Islands
https://en.wikipedia.org/wiki/Wilhelm_Canaris
Beta Niobe in "All Our Yesterdays" is another example of a star with a Bayer type designation without being in any constellation in Earth astronomy. So, like Gamma Canaris and Epsilon Canaris, Beta Niobe might possibly be a designation of a star seen in the sky of some Earth colony planet.
So how far from Earth might Beta Niobe be? Presumably Beta Niobe would be close enough to that hypothetical Earth colony to be seen with the naked eye from there. Thus it might be only tens of light years, or possibly hundreds of light years, or possibly a few thousand light years, from that hypothetical Earth colony, depending on how luminous Beta Niobe may be.
Assuming that like all other stars visited in TOS, Beta Niobe must be within the disc of the Milky War Galaxy, it should be less than about 75,000 light years from Earth. The galactic disc probably has a diameter of about 100,000 light years, and Earth is about 26,490 light years, plus or minus about 100 light years, from the center of the galaxy.
There are many problems with time, distance, and speed of various voyages in
Star Trek. One common explanation is that different regions of space have different characteristics which multiply or divide the basic speed of a warp factor by various amounts, thus enabling various voyages to take longer, about the same time, or much less time, than would be calculated from the TOS warp speed formula.
But another possible explanation is that there are a number of space warps that starshps can use to disappear from one star system and instantly reappear in another star system, that might be tens, or hundreds, or thousands, of light years away.
So the hypothetical Earth colony that named Beta Niobe might be tens of thousands of light years from Earth, reached through a space warp which spans tens of thousands of light years from a star near Earth to one tens of thousands of light years away.
And maybe the Enterprise was traveling though several space warps right before "All Our Yesterdays", to see where they went to, and appeared somewhere beyond the hypothetical Earth colony mentioned above. And someone working in stellar cartography or astrometrics would have informed Kirk that they were just a few light years from the position of Beta Niobe, a star that is due to go nova soon. Furthermore, Beta Niobe was known to have an inhabited planet Sarpedon, so the Enterprise would then scan Sarpeidon from a distance many light years closer than Sarpeidon had ever been scanned before, and they would discover that there was no trace of the inhabitants of Sarpeidon in the scans, a puzzle that was worth investigating.
So when they arrived at Sarpeidon at the beginning of "All Our Yesterdays" Kirk would make the log entry:
Captain's log, Stardate 5943.7. We have calculated that Beta Niobe will go nova in approximately three and a half hours. Its only satellite, Sarpeidon, is a Class M planet, which at last report was inhabited by a civilised humanoid species. Now our instruments show that no intelligent life remains on the planet.
http://www.chakoteya.net/StarTrek/78.htm
Of course a star that is about to go nova is not likely to have any habitable planets left, if it ever did have any. The star is likely to have killed off any life on any habitable planets while undergoing various changes leading up to going nova.
So maybe Beta Niobe is a binary star, and the brighter star, Beta Niobe A, is the one that is about to go nova, and Sarpeidon might orbit the dimmer star, Beta Niobe B, which might still be shining steadily during its main sequence phase. Beta Nioba B might be far enough from Beta Niobe A that Sarpeidon has been protected so far from the previous changes of Beta Niobe A, but close enough that Sarpeidon will be vaporized when Beta Niobe A woes nova.
Or possibly Sarpeidon might have been moved to the Beta Niobe system comparatively recently by astronomical and geological standards, though possibly many thousands of Earth years ago, and put into orbit by a super advanced civilization.
A star system that is about to go nova should contain a close binary star including a white dwarf star and a more massive star that are orbiting closely together. Close enough together for the white dwarf star to siphon hydrogen off the surface of the other star. This hydrogen piles up on the surface of the white dwarf and eventually undergoes fusion and explodes.
So possibly the bright star in the system is Beta Niobe Aa, closely orbited by a dim white Dwarf Beta Niobe Ab, and orbited at a greater distance by Beta Niobe B, which should probably be a dim red class M star, with the planet Sarpeidon orbiting the red star Beta Niobe B at a very close distance.
Astronomers have now discovered over four thousand exoplanets orbiting various stars. And a few of them are calculated to orbit in the habitable zones of their stars, and thus be potentially habitable planets. The potentially habitable exoplanet with the shortest orbital period and year known so far is TRAPPIST-1 d which orbits the time red star TRAPPIST-1.
TRAPPIST-1 d has an orbital period or planetary year of only 4.05 Earth days, which is only 0.0110881 of earth's orbital period of 365.256 Earth days.
https://en.wikipedia.org/wiki/List_...exoplanets_in_the_conservative_habitable_zone
To be continued:
Part Two:
December 28 2019:
Spock reverts to his primitive self from 5000 years earlier but McCoy stays exactly exactly the same. The phaser doesn't work because they're in the past but the medical scanner works no problem. The entire episode is pretty much the first example of fanfiction. Written by a woman who finds a technicality so that Spock can be a passionate character and literally have his hands around the throat of anybody who might get between him and his woman.
But Spock hasn't been prepared so why does he revert to his time appropriate ancient Vulcan self?
It is my belief that the subconscious telepathic influence of millions or billions of highly emotional Vulcan on Vulcan influenced Spock to become more emotional when he was 5,000 years in the past, even across interstellar space.
In part one it was demonstrated that a planet in the habitable zone of its star could have a year as short as 4.05 Earth days. Thus it is possible that Sarpeidon could have a year as short as 4.05 Earth days, which is 0.0110882 Earth years. Thus there could be as many as 90.185185 Sarpeidon years in one Earth year.
Spock says Earth was millions of light years away.
I like to think the system was out in the far reaches of known space and that's why the Federation didn't try an evacuation. Some probe picked up the civilisation there and it was too late when Starfleet realised.
OK maybe in the future they can predict a supernova blast to the minute but would you send your top 3 people down to just investigate not to rescue. I mean communicators get broken. Natives capture you.
And what was Kirk doing jumping in to rescue someone with just 3 1/2 hours to spare. If I were Starfleet command I'd have Kirk court-martialled for incompetence for this mission. Maybe Spock too,
Nothing justified the risk/
You mean the planet Vulcan.

But that distinction doesn't matter in the scale of things. Earth or Vulcan, it adds up the same: Spock had to be speaking poetically, in-universe, while in-production it was a flat-out mistake.
In fact Spock does tell Zarabeth how far away Vulcan is:
ZARABETH: The atavachron is far away, but I think you come from someplace farther than that.
SPOCK: That is true. I am not from the world you know at all. My home is a planet millions of light years away.
http://www.chakoteya.net/StarTrek/78.htm
So possibly Spock told Zarabeth said that Vulcan was millions of Sarpeidon light years away, though it was only thousands of Earth light years away.
If Spock would say "millions of light years" if Sarpeidon was at least 1,000,000 Sarpeidon light years from Vulcan, the distance would be at least 11,088.295 Earth light years.
If Spock would say "millions of light years" only if Sarpeidon was at least 2,000,000 Sarpeidon light years from Vulcan, the distance would be at least 22,176.591 Earth light years.
If Earth is about 26,390 to 26,590 light years from the center of the galaxy, and the galactic disc is about 100,000 light years in diameter, Sarpeidon should not be more than about 73,410 to 73,610 light years from Earth and Vulcan.
If Spock could feel the death of 400 Vulcans on the Intrepid over a distance of light years in "the Immunity Syndrome", and we assume the distance was between 10 and 100 light years, the distance between Vulcan and Sarpeidon should be about 110.88295 to 7,361 times as far.
If the strength of telepathy diminishes with the square of the distance, which seems reasonable, the strength of the telepathic links between Vuclan and Spock on Sarpeidon should be only 1 over 12,295.028 to 1 over 54,184,321 as strong as the link between the Intrepid and Spock. If there were only 400 Vulcans on Vulcan 5,000 years earlier.
But if there were 100,000,000 to 10,000,000,000 Vulcans on Vulcan 5,000 years earlier, their telepathic influence on Spock would thus be between 1.845 and 81,333.69 times as strong as the telepathic influence of the 400 Vulcans on the Intrepid.
So it certainly seems plausible that the subconscious telepathic influence of the emotional Vulcans on Vulcan 5,000 years earlier might have influenced Spock and made him more emotional and less rational.
Sarpeidon's star Beta NIobe is marked on space maps in the TAS episode "The Counter-Clock Incident" and in
Star trek VI: The Undiscovered Country (1991).that apparently show it in the Milky Way Galaxy.
https://memory-alpha.fandom.com/wiki/Beta_Niobe
So Beta Niobe and Sarpeidon are probably in our own Milky Way Galaxy. But a theory that Sarpeidon and Beta NIobe could be in another galaxy millions of light years from Vulcan is also possible.
It is possible that a space warp was discovered that enabled instant travel between a star in our galaxy and a distant galaxy, and so a part of that distant galaxy was explored. An Earth colony could have been settled in that distant galaxy, and settlers could have named new constellations in their sky, such as a constellation Niobe, and named a star in it Beta Niobe.
If Spock would say "millions of light years" if Sarpeidon was at least 1,000,000 Earth light years from Vulcan, the nearest galaxy that Sarpeidon could be in would be the Leo T Dwarf Galaxy, 1,370,000 light years from Earth and Vulcan.
If Spock would say "millions of light years" only if Sarpeidon was at least 2,000,000 Earth light years from Vulcan, the nearest galaxy that Sarpeidon could be in would be NGC 185, 2,050,000 light years from Earth and Vulcan.
And of course there are many other galaxies that are millions of light years from Earth.