This post is incomplete. I lost much of my work. Since it is now 2:33 AM I am going to bed and will finish later.
The Romulans must have left Vulcan a hell of a long time ago for the Vulcans not to have known where they went or that they now called themselves Romulans, even if both races still kept similar traditions, language and hand gestures!
I mean Spock is as surprised as the rest of the crew when the Romulan Commander appears on screen in Balance of Terror!
JB
Short Post:
I agree. Chronologically, there is strong evidence that the Romulans left Vuclan many thousands of years ago, before the hypothetical fall of the hypothetical first Vulcan civilization, and long before the era of Surak when some sources claim that they left Vulcan.
Long Post:
The branch of astronomy called astrometry is relevant here:
Astrometry is the branch of
astronomy that involves precise measurements of the positions and movements of
stars and other
celestial bodies. The information obtained by astrometric measurements provides information on the
kinematics and physical origin of the
Solar System and our
galaxy, the
Milky Way.
https://en.wikipedia.org/wiki/Astrometry
The directions between various stars change very slowly as they orbit the center of the galaxy.
Proper motion is the
astronomical measure of the observed changes in the
apparent places of
stars or other celestial objects in the sky, as seen from the
center of mass of the
Solar System, compared to the abstract background of the more
distant stars.
[1]
For the majority of stars seen in the sky, the observed proper motions are usually small and unremarkable. Such stars are often either faint or are significantly distant, have changes of below 10 milliarcseconds per year, and do not appear to move appreciably over many millennia. A few do have significant motions, and are usually called
high-proper motion stars. Motions can also be in almost seemingly random directions. Two or more stars,
double stars or
open star clusters, which are moving in similar directions, exhibit so-called shared or
common proper motion (or cpm.), suggesting they may be gravitationally attached or share similar motion in space.
https://en.wikipedia.org/wiki/Proper_motion
There are 360 degrees of arc in a full circle, and 60 arc minutes in a degree, or 21,600 arc minutes in a full circle, and 60 arc seconds in a arc minute or 1,296,000 arc seconds in a full circle.
Milli- (symbol m) is a unit prefix in the metric system denoting a factor of one thousandth (10−3). Proposed in 1793 and adopted in 1795, the prefix comes from the Latin mille, meaning "one thousand" (the Latin plural is milia). Since 1960, the prefix is part of the International System of Units (SI).
https://en.wikipedia.org/wiki/Milli-
So there are 1,296,000,000 milliarcseconds in a full circle, and the majority of stars observed by astronomers change their apparent position in the sky by less than 10 of them per year. To repeat, the majority of stars observed by astronomers change their apparent positions in the sky by less than 0.000000007 of a full circle each year.
So if the Romulan home world had last been in contact with Vulcan 100,000 years earlier, its apparent position in the sky of Vulcan would have changed only 0.000771604 of a full circle or less in those 100,000 years. That would be total position change of only 1.75 minutes.
If the time elapsed had been 2,000 years, the position of Romulus's star in the sky of Vulcan would have changed by 2 arc seconds or less in those 2,000 years.
That is if the star of Romulus has a typiclaamount of proper motion as seen in the sky of Vulcan.
The second nearest star system to the Sun is Barnard's Star, sometimes called Barnard's Runaway Star.
The star is named after the American
astronomer E. E. Barnard.
[18] He was not the first to observe the star (it appeared on Harvard University plates in 1888 and 1890), but in 1916 he measured its
proper motion as 10.3
arcseconds per year relative to the Sun, the highest known for any star.
[19]
So the proper motion of Barnard's star is more than 1,030 times as much as the majority of stars whose proper motions have been measured by astronomers. If the last contact between Vulcan and the Romulan star system was 100,000 years earlier, the apparent position of the Romulan star in the sky of Vulcan would have changed by 1,030,000 arc seconds,or close to a full circle, in those 100,000 years. Except that the proper motion would have been the highest when the two stars were passing closest to each other and fall off before and after their closest pass.
In about 2,000 years, the direction between Vulcan and that star would have changed by about 20,600 arc seconds, or about 343.3333 arc minutes, or about 5.722221 degrees.
Of course, stars are not all at the same distance from Earth or Vulcan. Two stars that appear next to each other in the sky of planet could vary greatly in their actual distances from that planet.
Assume that the star of Romulus had no detectable proper motion in the sky of Vulcan, because the two star systems were travelling directly toward or away from each other. Suppose that the combined velocity difference between the two stars was 500 kilometers per second, or 60,000 kilometers per minute, or 1,800,000 kilometers per hour, or 43,200,000. kilometers per day.
An Astronomical Unit or AU is now defined as 149,597, 870.7 kilometers. So if the relative speed of two stars was 500 kilometers per second, or 43,200,000 kilometers per day, it would take them 3.462913674 days to change their distance by 1 AU. A light year is 63,241.077 AU. So in one year of 365.25 days the two stars would change their relative distance by 105.47476 AU. In 1,000 year the two stars would change their relative distance by 105,474.76 AU, or 1.6678204 light years, and in 100,000 years the two stars would change their relative distance by 10,547,476 AU, or 166.478204 light years.
This post is incomplete. I lost much of my work. Since it is now 2:33 AM I am going to bed and will finish later.
03-26-2020. I am finishing this post.
Most stars would not change their distance from Vulcan more than a fraction of a percent that fast, anymore than most stars would change their direction from Vulcan more than a fraction of a percent as fast as Barnard's Star changes its direction as seen from Earth.
For centuries astronomers have been developing better and more precise astrometric techniques to measure the apparent positions, distances, and changes in both, of more and more stars more and more precisely, and developing better and better mathematics and computer programs to calculate those factors farther and farther into the past and the future.
As a result of such efforts, this table:
https://en.wikipedia.org/wiki/List_...own_dwarfs#Distant_future_and_past_encounters
lists stars passing within 5 light years of Earth within three million years in the past and the future.
So if Vulcan colonized the planet Romulus thousands, or tens of thousands, or hundreds of thousands, or millions of years ago, records of the location of that colony should still be preserved by Vulcan civilization, and when the Romulan Star Empire was discovered it would be easy for Vulcans to check where the star of Romulus would have been all those millennia previously, and note that Romulus would have been colonized by ancient Vulcans.
In TOS episode "Balance of Terror", in the conference room after it has been discovered that Romulans look like Vulcans:
MCCOY: Based on what? Memories of a war over a century ago? On theories about a people we've never even met face to face?
STILES: We know what they look like.
SPOCK: Yes, indeed we do, Mister Stiles. And if Romulans are an offshoot of my Vulcan blood, and I think this likely, then attack becomes even more imperative.
MCCOY: War is never imperative, Mister Spock.
SPOCK: It is for them, Doctor. Vulcan, like Earth, had its aggressive colonising period. Savage, even by Earth standards. And if Romulans retain this martial philosophy, then weakness is something we dare not show.
So Spock decides that the Romulans, based on their looks, are probably descended from a lost Vulcan colony from the more advanced part of Vulcan's "aggressive colonizing period".
In "The Enterprise Incident":
KIRK: What earns Spock your special interest?
COMMANDER: He is a Vulcan. Our forebears had the same roots and origins. Something you wouldn't understand, Captain. We can appreciate the Vulcans, our distant brothers. I have heard of Vulcan integrity and personal honour. There's a well-known saying, or is it a myth, that Vulcans are incapable of lying?
So Romulans believe that they are related to Vulcans, and might have believed that before "Balance of Terror".
In "The Paradise Syndrome":
MCCOY: I prescribed sleep.
SPOCK: You prescribed rest, Doctor. The symbols on the obelisk are not words. They are musical notes.
MCCOY: Musical notes? You mean it's nothing but a song?
SPOCK: In a way, yes. Other cultures, among them certain Vulcan offshoots, use musical notes as words. The tones correspond roughly to an alphabet.
So Spock knows of some Vulcan offshoots, including some that use musical notes as words. Romulans are certainly not the only known Vulcan offshoots.
But how could it be possible for the Vulcans not to know where every planet they colonized once was and now is?
Therefore, long ago I deduced that some event similar to "The Fall of the Vulcan Space Empire" happened many thousands of years ago, and resulted in the collapse of civilization on Vulcan and all planets colonized by Vulcans. On every planet where some Vulcans survived, they reverted to barbarism and didn't rebuild their civilization for many thousands of years, if ever.
And thus all the records from the the ancient Vulcan civilization of Vulcan and other Vulcan planets were gradually lost due to weathering over the decades, centuries, or millennia, and it is quite possible that Vulcans forgot all about their travel to other stars. But when Vulcans rebuilt their civilization enough to explore their solar system again, they would have discovered space probes and space ships, space stations and space habitats, and domed or underground colonies on airless planets and moons, and would have discovered that they once traveled to other stars.
And when Vulcans rediscovered methods of interstellar travel, they would have discovered planets with extinct or surviving populations of Vulcan colonists, but apparently the records surviving in space were not complete enough to show every planet which had been colonized by Vulcans, and many were discovered whose locations were not mentioned in surviving records.
In the
Star Trek: Enterprise episode "the Andorian Incident, the Vulcan sanctuary at P'Jem is not in the Vulcan star system but in a different one. When they arrive:
TUCKER: You say this is a place to purge emotions? Looks like somebody had to purge pretty bad. He bashed the door in.
T'POL: The temple is almost three thousand years old, Commander. You can't expect it to be in pristine condition.
(She pulls on a big bell rope. After a few moments, Archer pushes the doors open anyway and they enter.)
I guess that "almost three thousand years" is about 2,500 to 3,000 years. "The Andorian Incident" is in the first season, and various episodes are dated to 2151 and 2152. Both the Wikipedia episode list:
https://en.wikipedia.org/wiki/List_of_Star_Trek:_Enterprise_episodes
and Memory Alpha:
give the date as June 19, 2151. And of course most fans naively assume that the year 2151 is AD 2151, even though it is not explicitly specified that it is
Anno Domini dating.
Since AD 2151 is 12151 HE (Holocene Era), the sanctuary at P'Jem would have been built between about 9151 HE and 9651 HE, which corresponds to between about 849 BC and 349 BC if my calculations are correct.
https://en.wikipedia.org/wiki/Holocene_calendar
If P'Jem was built by Vulcans who traveled from Vulcan to another star system using slower than light or faster than light spaceships, the planet Vulcan would have recovered from the fall of the ancient Vulcan civilization and developed methods of interstellar travel sometime during the first millennium BC or even earlier.
The
Star trek:The Next Generation episode "Gambit Part 1" is in the 6th Season, and thus happens in AD 2370 according to the official chronology, which is not necessarily canonical or correct.
At the planet Barradas III:
DATA: Barradas Three is the only class M planet in this system, and it is listed as unpopulated. However, sensors have detected intermittent energy signals emanating from its surface.
RIKER: What's the source?
LAFORGE: The signals are difficult to localise, but they could be emissions from some kind of power converter.
WORF: Which could indicate a base or a ship.
RIKER: What else do we know about Barradas Three?
DATA: The planet was used as an outpost for the Debrune approximately two thousand years ago. The Federation's Archaeological survey has catalogued numerous ruins on the surface.
Since Data is rather precise, his "approximately three thousand years ago" might be between 1,900 and 2,100 years. Thus the Debrune should have built an outpost on Barradas Three about AD 270 to 470. or 10270 to 10470 HE.
And:
WORF: The search teams have reported in. They found several archaeological sites. Each one has been looted.
LAFORGE: It's possible that the microcrystalline damage I found in these indentations was the result of some kind of high energy transporter beam but I still don't understand. There's nothing here that's particularly valuable. Why would anyone want to steal any of these things?
DATA: Perhaps these artefacts have a special value to the Romulans.
WORF: The Romulans?
DATA: These structures were built by the Debrune. That race is an ancient offshoot of the Romulans. The ruins on the planet where Captain Picard was killed were also Romulan in origin.
So the Debrune race was travelling to various star systems around about AD 270 to 470. or 10270 to 10470 HE - and possibly earlier - and was an offshoot of the Romulans.
When did Surak live and teach Vulcans to adopt logic and non violence?
In the TOS episode "Let that Be Your Last Battlefield":
SPOCK: Commissioner, perhaps the experience of my own planet Vulcan may set an example of some value to you. Vulcan was in danger of being destroyed by the same conditions and characteristics which threaten to destroy Cheron. We were once a people like yourselves, wildly emotional, often committed to irrationally opposing points of view, leading, of course, to death and destruction. Only the discipline of logic saved my planet from extinction.
In the TOS episode "The Savage Curtain":
SURAK: Just as I am whom I appear to be.
SPOCK: Surak.
KIRK: Who?
SPOCK: The greatest of all who ever lived on our planet, Captain. The father of all we became.
SURAK: The cause was more than sufficient. Let us speak no further of it. In my time, we knew not of Earth men. I am pleased to see that we have differences. May we together become greater than the sum of both of us.
SURAK: In my time on Vulcan, we also faced these same alternatives. We'd suffered devastating wars which nearly destroyed our planet. Another was about to begin. We were torn. But out of our suffering some of us found the discipline to act. We sent emissaries to our opponents to propose peace. The first were killed, but others followed. Ultimately we achieved peace, which has lasted since then.
Obviously Vulcan science and technology was advanced enough in Surak's time to build weapons of mass destruction which might have wiped out the Vulcans. Whether Vulcan was advanced enough to explore other star systems is not certain from this.
The
Star Trek: Enterprise episode "The Forge" happens in the fourth season and thus in 2154.
FORREST: Ambassador. Are Vulcans afraid of humans? Why?
SOVAL: Because there is one species you remind us of.
FORREST: Vulcans.
SOVAL: We had our wars, Admiral, just as humans did. Our planet was devastated, our civilisation nearly destroyed. Logic saved us. But it took almost fifteen hundred years for us to rebuild our world and travel to the stars. You humans did the same in less than a century. There are those on the High Command who wonder what humans would achieve in the century to come, and they don't like the answer.
If 2154 is AD 2154, then subtracting "almost fifteen hundred years" (about 1,450 to 1,500 yeas) from AD 2154 gives a date of 654 to 704 for the wars that devastated Vulcan.
But a Vulcan ship landed on Earth in "2063" in
Star Trek: First Contact. If 2063 is AD 2063, the wars that devastated Vulcan should have been sometime between AD 563 and AD 613.
The
Star Trek: Enterprise episode "Carbon Creek" supposedly happens on April 12, 2152 T'Pol tells how her great grandmother visited Earth, allegedly in October 1957 to January 1958.
T'POL [OC]: They'd gone to Earth to investigate the launch of its first artificial satellite, called Sputnik.
[Captain's mess]
T'POL: During their third week of gathering information about humanity their impulse manifold began to malfunction. They had no choice but to attempt an emergency landing.
Since Sputnik 1 was launched October 4, 1957 in our history, that seems to show that Vulcans were observing Earth in AD 1957. So the wars that devastated Vulcan would have had to have happened sometime between AD 457 and AD 507. Or sooner if Vulcans had star travel before 1957.
The
Star Trek: Deep Space Nine episode "Little Green Men" has an alien spaceship crash at Roswell, New Mexico.
(We pan over to a calendar with a picture of Rita Hayworth for July 1947.)
ROM: Maybe their universal translators are broken too.
NOG: No. They don't have universal translators. I recognise those uniforms from my guidebook. They're from the twentieth century.
ROM: The twentieth century? You mean we travelled back through time?
NOG: More than four hundred years. Those are military uniforms from one of the old nation states. Australia or something.
NOG: But Uncle, what about the timeline?
QUARK: Forget this timeline. The one we're going to create will be better. Once we get things in order here, we'll contact the Ferengi homeworld and sell them our ship. The Ferengi will have warp drive technology centuries before humans or Klingons or even the Vulcans. We'll establish an economic empire beyond even Grand Nagus Zek's wildest dreams. And I'll control it all.
So apparently Quark thinks that Vulcans didn't have warp drive in 1947.
The
Star Trek: Enterprise episode "The Forge" happens in the fourth season and thus in 2154.
STEL: Syrrannites.
ARCHER: I've never heard of that species.
T'POL: Actually, they're a small group of Vulcans. They follow a corrupted form of Surak's teachings.
ARCHER: Surak I've heard of. He's the father of Vulcan logic.
V'LAS: Even after eighteen hundred years, we consider him the most important Vulcan who ever lived.
So if 2154 is AD 2154, Surak would have flourished "eighteen hundred years" earlier. If that is about 1,700 to 1,800 years, Surak would have been active sometime during the period of about AD 254 to AD 454, If the last of the wars which devastated Vulcan was sometime during that period, Vulcan would have developed interstellar travel, for the second or third time in Vulcan history, about AD 1704 to AD 1954.
So if the Debrune race was travelling to various star systems around about AD 270 to 470. or 10270 to 10470 HE - and possibly earlier - and was an offshoot of the Romulans, and if Surak was active on Vulcan sometime during the period of about AD 254 to 454, 10254 to 10454 HE, it seems chronologically very improbable that there would have been enough time for the Romulans to reject Surak's teachings and leave Vulcan and form an offshoot group called the Debrune.
Thus it seems very probable that the ancestors of the Romulans left Vulcan centuries, or more likely many millennia, before Surak taught logic and nonviolence.
Also, "offshoot" implies some sort of biological changes, too. 
