How long is the year of the planet Vulcan in Star Trek?

Does anyone know any other information about the length of the Vulcan year in various Star Trek productions to add to the information about the length of the Vulcan year that I state in this question? I have a problem with the length of the Vulcan year, so any additional data related to it would be useful.

As far as I know, there is very little totally canon data about the length of the year of the planet Vulcan in Star Trek.

Part One: "Yesteryear"

One episode of TAS, which some peopel do not consider to be canon, gives a bit of data about the lengthof the Vulcan year.

In "Yesteryear" Kirk and Spock return from a journey to the past to find that Spock has been erased from history.

KIRK: I don’t know what’s going on, but the first officer of this ship will be treated with respect.

(An Andorian enters)

THELIN: Captain, I assure you no one has ever treated me otherwise.

KIRK: Who are you?

MCCOY: Oh, I thought sure you’d know Thelin by now, Jim. He’s been your first officer for five years.

If Thelin became first officer to Kirk at the same time as Spock did in the "prime" universe, Spock should have done so about five years, more or less, before "Yesteryear".

Later Kirk learns that while He and Spock were in the past, someone else was using the Guardian of Forever:

KIRK: If we didn’t change anything while we were in the time vortex, someone else must have. Was the Guardian in use while we were gone?

GREY: Yes, but it was nothing unusual. We were scanning recent Vulcan history.

SPOCK: What time period?

GREY: Twenty to thirty Vulcan years past.

So the change in the timeline happened twenty to thirty Vulcan years in the past.

And in another scene:

BATES [on monitor]: Yes, sir. I can relay that to your screen. (showing relevant images) Sarek of Vulcan. Ambassador to seventeen Federation planets in the past thirty years.

SPOCK: That is not correct.

So the change in history should have been thirty or more years earlier.

If the change was both twenty to thirty Vulcan years earlier, and at least thirty years earlier, it should have been thirty years earlier. If years of the same type were used every time.

And:

SPOCK: My mother. The son, what was his name and age when he died?

BATES [on monitor]: Spock. Age seven.

And Spock tells the Guardian of Time"

Blockquote

SPOCK: I wish to visit the planet Vulcan, thirty years past, the month of Tasmeen. Location, near the city of ShirKahr.

So this establishes that Spock was probably aged about thirty seven in "Yesteryear" and probably about thirty two when he became Kirk’s first officer about five years earlier.

Of course there is the problem that some of or all of the data is given in Vulcan years, which may be noticably longer or shorter than Earth years.

https://en.wikipedia.org/wiki/40_Eridani[1]

Part Two: A Digression Which You Can skip:

When asking the Guardian of Time to send him to the past to try to restore the timeline, Spock says:

SPOCK: I wish to visit the planet Vulcan, thirty years past, the month of Tasmeen. Location, near the city of ShirKahr.

I note that it seems rather illogical for Spock to specify the Vulcan month of Tasmeen, but not the specific day in Tasmeen, thirty years earlier while asking the Guardian of Forever to go back in time. What if the Guardian sent Spock back to the day after young Spock died?

Of course, if Spock was certain how the Guardian of Forever would interpret "thirty years", maybe he xpected that only one day in Tasmeen would fall withing the chronological period.

Some Earth societies began the year in the middle of a month. For example The Feast of the Annunciation, or Lady Day, March 25, was the new year’s day in England for for almost 600 years from 1155 to 1752.

https://en.wikipedia.org/wiki/Lady_Day[2]

Or if the Gauardian would interpret "thirty years" not as referring to a specific complete calendar year, but to the period between thirty point zero years and thirty one point zero years earlier, perhaps Spock knew that only one day in Tasmeen, the first or the last day, would come within the time period.

But the date of Spock’s death in the altered timeline was:

SPOCK: The twentieth day of Tasmeen.

iN the past Spock asks:

SPOCK: The boy goes through the kahs-wan ordeal soon, does he not?

AMANDA: Next month.

SPOCK: But tomorrow is the twentieth day of Tasmeen.

So Spock arrived on the 19th day of Tasmeen. The 19th of Tasmeen cannot be the first day of Tasmeen, since there were 18 earlier days in Tasmeen, nor can it be the last day of Tasmeen, since tomorrow will be the 20th day of tasmeen. And if it is not either the first or the last day of Tasmeen, it cannot the the only day in Tasmeen that is thirty years earlier.

So Spock took a terrible risk of ending up too late to save himself by not being more specific in his request to the Guardian of Forever.

Part Three: The Relative Length of Earth and Vulcan Years in "Yesteryear"

Whether the years are Earth, Vulcan, or other years are not specified during this episode, except once.

If Spock goes back thirty years, to when he was seven years old, then his present age should be about thirty seven. To be precise 30.0 (thirty point zero) to 31.0 (thirty one point zero) years years plus 7.0 (seven point zero) to 8.0 (eight point zero) years should equal 307.0 (thirty seven point zero) to 39.0 (thiry nine point zero) years, giving Spock’s possible age range – if the same years are used all though the episode.

Doctor MCCoy says:

MCCOY: Oh, I thought sure you’d know Thelin by now, Jim. He’s been your first officer for five years.

If McCoy means 5.0 (five point zero) to 6.0 (six point zero) years, Thelin became Kirk’s first officer when Spock was aged 31.0 (thirty one point zero) to 31.0 (thirty four point zero) years, and that should be Spock’s age when he became Kirk’s first officer in the "prime" timeline – if years of the same length were always used in "Yesteryear".

However, McCoy probably used Earth years when he said Thelin had been the first officer for five years, while Grey said the time period being recorded was "twenty to Thirty Vulcan years past". The other ages and time spans mentioned in the episode could have been Earth years, Vulcan years, Time Guardian planet years, etc., or some mix of years of various types.

Suppose that Spock used Earth years or Time Guardian planet years when he asked the Time Guardian to send him thirty years into the past. In that case there would be 30.0 (thirty point zero) to 31.0 (thirty one point zero) Earth or Time Guardian planet years in a span between 20.0 (twenty point zero) and 31.0 (thirty one point zero) Vulcan years.

Thus a Vulcan year could equal somewhere between about 0.967 (zero point nine six seven) to 1.55 (one point five five) Earth or Time Guardian planet years.

So if Spock went back in time thirty Earth years to save himself, a Vulcan year could be anywhere from about 0.967 (zero point nine six seven) to 1.55 (one point five five) Earth years long.

So if a Vulcan year is about 0.967 (zero point nine six seven) to 1.55 (one point five five) Earth years long and if young Spock was seven Vulcan years old in the past, adult Spock was about 36.769 (thirty six point seven six nine) to 43.4 (forty three point four) Earth years old in "Yesteryear".

And if Spock went back in time thirty time Guardian planet years to when he was seven Vulcan years old, without an indication of the relative length of Time Guardian planet years and Earth years there would be no way of knowing how long Vulcan years are relative to Earth years.

And if Spock went back in time thirty Vulcan years to when he was seven Vulcan years old there would be no way to tell how long Vulcan years are relative to Earth years.

Part Four: Spock’s Possible Age Range in TOS.

Some episodes in TOS give hints to Spock’s age in them.

In "The Menagerie" Spock twice says the Talos IV incident was thirteen years earlier, and Kirk also says it was thirteen years earlier. The natural presumption is they were Earth years. So if, repeat if, that is true, the Talos IV incident was 13.0 (thirteen point zero) to 14.0 (fourteen point zero) earth years before "The Menagerie". Spock was apparently third in command of the Enteprise, and so should have graduated from Starfleet Academy a few years earlier. If Spock graduated at the typical and usual age of twenty two, Spock would have been aged about 35.0 (thirty five point zero) to 37.0 (thirty seven point zero) Earth years in "The Menagerie", plus the unknown number of years between Spock’s graduation and the voyage to Talos IV.

Spock decided to apply to Starfleet Academy, applied, was accepted, entered the Academy, spent presumably years there, graduated, and was commissioned, presumably as an ensign, in Starfleet.

in "Journey to Babel":

AMANDA: You don’t understand the Vulcan way, Captain. It’s logical. It’s a better way than ours. But it’s not easy. It has kept Spock and Sarek from speaking as father and son for eighteen years.

So if Amanda used Earth years, and the various stages of Spock entering Starfleet happened at about the same ages as is typical for contemporary US officers, Spock should be aged about 35.0 (thirty five point zero) to 42.0 forty two point zero) Earth years in "Journey to Babel".

In "The Enterprsie Incident":

COMMANDER: How long have you been a Starfleet officer, Spock?

SPOCK: Eighteen years.

I think that it is the rule in the US armed forces to count the years of membership from being commissioned, and not from entering the service academy. So it is probable that Spock was commissioned in Starfleet 18.0 (eighteen point zero) to 19.0 (ninteen point zero) years before the Enterprise Incident". If Spock was commissioned at the typical age for USA service academy graduates, Spock would be aged 40.0 (forty point zero) to 42.0 (Forty two point zero) Earth years in "The Enterprise Incident".

Jane wyatt was 57 years old when she filmed her scenes in "Journey to Babel".

https://memory-alpha.fandom.com/wiki/Jane_Wyatt[3]

And of course a ficitonal character can be older or younger than the actor hired to portray them in a production. However, I believe the script of "Journey to Babel" and the chapter on Spock in "The Making of Star Trek" both describe Amanda as being 58 years old. And I think that the script for "Yesteryear" describes Amanda in the past on Vulcan as being thirty.

So given the canon evidence for Spock’s age, and the non canon but strong evidence for Amanda’s age, one might estimate that Amanda was aged about 14.0 (fourteen point zero) to 26.0 (twenty siz point zero) when Spock was born.

Thus there seem to be three possibilities:

One) That the evidence for Amanda’s age is not canon and doesn’t count.

Two) Somthing science fictional happened to Amanda after Spock was born, so she did not age as many years as elapsed during that period. Perhaps Amanda went into suspended animation or some type of time warp, only emerging to live and age during Spock’s rare visits to his parents.

Three) Amnada and/or spock was precocious and advanced for their age.

And I prefer to use all the evidence, and believe that Spock was a precocius student and Starfleet officer rather than that Amanda was a teenaged teacher who decided to maarry an alien from other space and had a child.

So the approximate age of spock, estimated from data in various TOS episodes, indicates that his age in Earth years should be fairly close to his age in Vulcan years calculated from "Yesteryear". Thus the evidence indicates that the length of Vulcan years should be fairly close to the length of Earth years.

Part Five: The Problem

The canon evidence written in scripts for the location of Vulcan is slight.

At the end of Star Trek: The Motion Picture:

SCOTT: I would say it’s time for that, sir, aye. We can have you back on Vulcan in fo[u]r days, Mister Spock.

So if the warp factor of the proposed voyage, and the speed of that warp factor, was known, the distance from Earth to Vulcan could be estimated.

In the ENT episode "Home", T’Pol and Tucker travel from earth to Vulcan:

TUCKER: You’re sorry. You brought me sixteen light years just to watch you get married to someone you barely know.

In the ENT episode "Daedalus" a theoretical long range transporter is discussed.

EMORY: Sub-quantum teleportation. You step on to a transporter on Earth, a few seconds later, you’re on Vulcan.

TUCKER: That’s over sixteen light years.

So according to Tucker, Vulcan should be between 16.0 (sixteen point zero) and 17.0 (seventeen point zero) light years from Earth.

According to this list:

https://en.wikipedia.org/wiki/List_of_star_systems_within_16%E2%80%9320_light-years[1]

There are sixteen stars in systems between 16.0 (sixteen point zero) and 17.0 (seventeen point zero) light years from Earth. They include eight class M stars unlikely to have habitable planets, three brown dwarfs more unlikely to have habitable planets, one white dwarf that probably destroyed any habitable planets it once had, one class A star too massive and short lived to have habitable planets (Altair – which is also eliminated by "Amok time" putting Altair VI and Vulcan in different star systems), and three class K stars which could have habitable planets.

The three class K stars which could have habitable planets include 70 Ohiuchi A, 70 Ophiuchi B, and Keid, also known as Omicron 2 Eridani A or 40 Eridania A.

And 40 Eridani A happens to be the favorite choice for the star that Vulcan orbits.

https://memory-alpha.fandom.com/wiki/Vulcan_system#:~:text=The%20Vulcan%20system%20was%20an%20inhabited%20star%20system,located%20sixteen%20light%20years%20from%20the%20Sol%20system.[4]

The habitable zone of 40 Eridani A, where a planet could exist with liquid water, is near 0.68 AU from A. At this distance a planet would complete a revolution in 223 Earth days (according to the third of Kepler’s laws) and 40 Eridani A would appear nearly 20%[note 3] wider than the Sun does on Earth.

https://en.wikipedia.org/wiki/40_Eridani[5]

An orbital period 255 Earth days long would be about 0.698 (zero point six nine eight) as long as an Earth year. If a Vulcan year is the same length as its orbital period, Spock would be about 25 in "Yesteryear" and extremely young when he entered Starfleet if he served for eighteen earthyears before "The Enteprise Incident". Spock should be precocious, but not that precocious.

So if Vulcan is a planet of 40 Eridani A, and if "Yesteryear" is canon, either Vulcan orbits a lot farther from its star than it should, and has to have some other major source of heat the keep from freezing, or else for some reason a Vulcan calendar "year" is a lot longer than one orbital period of Vulcan around its star.

Does anyone know any other information about the length of the Vulcan year in various Star Trek productions to add to the information about the length of the Vulcan year that I state in this question?