Passing thought; Spock was originally supposed to be half-Martian, and of course Mars's year is longer than Earth's. A hangover of the early ideas making its way to screen?
I doubt it. Plus I'm pretty sure the length of the Vulcan year never made it on-screen, it's from the novelization. And considering that iirc that's the same novelization that claims that humanity outside Star Fleet is evolving into espers that gather in mass minds and junk like that, I don't even know why wlthis thread takes any part of it seriously.
In regards to the classification of white dwarfs, doesn't have anything to do with their former spectral class: "It classifies a spectrum by a symbol which consists of an initial D, a letter describing the primary feature of the spectrum followed by an optional sequence of letters describing secondary features of the spectrum (as shown in the adjacent table), and a temperature index number, computed by dividing 50,400 K by the effective temperature." "White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority, approximately 80%, of all observed white dwarfs" Source:https://en.wikipedia.org/wiki/White_dwarf#Atmosphere_and_spectra
Part One: Summary: This post seems to prove that if all the information about the location and year length of Vulcan is correct, the Vulcan calendar year must be longer than the Vulcan year as defined as Vulcan's orbital period, or else Vulcan orbits much farther from its star than the distance where it would receive the necessary radiaiton to be as warm as it is, but some factor enambles Vulcan to be as warm as it is.. Part Two: Discussion. Is Vulcan "really: ( use "really" loosely) a planet of 40 Eridani A? Probably, although there is no direct canon evidence to that effect. In the TOS episode "Metamorphosis", 11 Nov. 1967, They meet Zefram Cochrane, discoverer of the space warp, who has been lost in space for 150 years: Warp drive was probably a lot slower in Cochrane's time, but he managed to travel far enough to see Vulcans, or at least learn what they looked like. So possibly the star of Vulcan is one that is very close to Earth. http://www.chakoteya.net/StarTrek/31.htm In Star Trek: The Motion Picture,1979, at the end, when the Enterprise is back at Earth: http://www.chakoteya.net/movies/movie1.html If Vulcan is about 16.0 to 17.0 light years from Earth and it would take 3.0 to 5.0 Earth days to reach Vulcan, the speed would be between 1,168.8 and 2,069.25 times the speed of light. According to the alleged TOS warp speed formula, the speed of a warp factor would equal the speed of light times the warp factor number cubed. Warp factor 1 would be 1 times the speed of light. Warp factor 2 would be 8 times the speed of light. Warp factor 3 would be 24 times the speed of light. Warp factor 4 would be 64 times the speed of light. Warp factor 5 would be 125 times the speed of light. Warp factor 6 would be 216 times the speed of light. Warp factor 7 would be 343 times the speed of light. Warp factor 8 would be 512 times the speed of light. Warp factor 9 would be 729 times the speed of light. Warp factor 10 would be 1,000 times the speed of light. Warp factor 11 would be 1,331 times the speed of light. Warp factor 12 would be 1,728 times the speed of light. Warp factor 13 would be 2,197 times the speed of light. And so on. So a voyage to Vulcan could be made in 3 to 5 days using a TOS warp factor somewhere between warp 10 and warp 13. I believe it was said the new engines in Star Trek: The Motion Picture could reach warp factor 12, although I don't know whether that was said in the movie and thus is canonical. And of course the TOS warp scale was never specified in any canon production. Of course, nobody said that Vulcan was 16 light years from Earth in Star Trek: The Motion Picture When Star Trek: The Motion Picture was made Vulcan might have been considered to be much farther from Earth, or possibly much closer to Earth, than 16 light years. Since Proxima Centauri, the closest star to Earth, is about 4.2466 light years from Earth, and is the nearest possible location of Vulcan, being able to travel to Proxima Centaauri or farther in 3.0 to 5.0 days indicates a speed of at least about 309.732 (three hundred nine point seven three two) to 517.4375 (five hundred seventeen point four three seven five) times the speed of light. In the StarTrek:Enterprise episode "Home", 22 Oct. 2004, Tucker and T'Pol travel from Earth to her home on Vulcan. While there Tucker says: http://www.chakoteya.net/Enterprise/79.htm In the Star Trek:Enterprise episode "Daedalus", 14 Jan. 2005, there is a duscusison of the possibility of sub-quantum teleportation: http://www.chakoteya.net/Enterprise/86.htm So Tucker's statements seem to prove that the dsistance between Earth and Vulcan is between 16.0 and 17.0 light years - and 40 Eridania the long time favorite to be the star of Vulcan, is about 16.42 (sixteen point four two) light years from Earth. However, some other stars are also between 16.0 and 17.0 lightyears from Earth, and any of them could theoretically be the star of Vulcan according to canonical information. Could any of them have a habitable planet with a year close to the lengths indicated by Yesteryear" and the novelization of Star Trek: The Motion Picture? according to this list: https://en.wikipedia.org/wiki/List_of_star_systems_within_16–20_light-years There are 16 stars and brown dwarfs (not counting the Sun) between 16.0 and 17.0 light years from Earth, arranged in 12 star systems. The answer by user177107 to the question: https://astronomy.stackexchange.com/questions/40746/how-would-the-characteristics-of-a-habitable-planet-change-with-stars-of-differe[2] Has a table showing main sequence stars of various spectral trypes and masses with data about hypotheticla planets orbiting them at the distance to receive exactly the same amount of radiation of that star as Earth receives from the Sun. I call such an orbit the exact Earth equivalent radiation orbit, or EEERO. And for each star type included in the hart, it gives the distance of the EEERO and the length of The planet's year in Earth days. The lest massive and luminous star type listed is a class M8V, which would have an EEERO with a year of only 3.82 Earth days. But three of the "stars" listed between 16.0 and 17.0 light years from Earth, WISE J 63940.83-684738.6, WISE J 052126.29+102528.4, and WISE J150649.97+702736.1, are actually sub stars, brown dwarfs, less massive and less luminous than even the faintest stars. Any hypothetical habitable planets orbiting them would have to orbit even closer and have even shorter years than planets orbiting a closs M8V star. the next more luminous class of star listed in the chart is M5V, which would have an EEERO year of 11.68 days. One star on the list, El Cancerii A, is a M5.5V star, and so would have EEERO with a year between 3.82 and 11.68 days. the next more luminous class of star listed in the chart is M2V, which would have an EEERO year of 36.51 days. Five stars on the list are between M2V and M5V and have EEERO years between 11.68 and 36.51 days - ADLeonis, 40 Eridani C, Gliese 682, EV Lacertae, and GJ3379. One other star, El Cancerii B, is a clss M and thus should have an EEERO year less than 70.95 days. the next more luminous class of star listed in the chart is K8V, which would have an EEERO year of 70.95 days. The only star of the list between M2V and K8V is Gliese 832, which thus has a EEERO year between 36.51 and 70.95 days. the next more luminous class of star listed in the chart is K5V, which would have an EEERO year of 114.84 days. One star of tne list, 70 Ophiuchi B, is a K5V star and thus should have an EEERO of 114.84 days. the next more luminous class of star listed in the chart is K2V, which would have an EEERO year of 182.93 days. the next more luminous class of star listed in the chart is G8V, which would have an EEERO year of 280.06 days. Two stars on the list, 40 Eridani A and 70 Ophiuchi A, are between K2V and G8v, and so have EEERO years between 182.93 and 280.06 days. the next more luminous class of star listed in the chart is G5V, which would have an EEERO year of 337.48 days. the next more luminous class of star listed in the chart is G2V, which would have an EEERO year of 365.56 days. the next more luminous class of star listed in the chart is F8V, which would have an EEERO year of 572.18 days. the next more luminous class of star listed in the chart is F5V, which would have an EEERO year of 799.11 days. the next more luminous class of star listed in the chart is F2V, which would have an EEERO year of 1,018.01 days. the next more luminous class of star listed in the chart is A8V, which would have an EEERO year of 1,505.21 days. The only star on the list between A8V and A5V is Altair, an A7 star, which thus should have an EEERO year of between 1.505.21 and 1,984.21 days. the next more luminous class of star listed in the chart is A5V, which would have an EEERO year of 1,984.21 days. the next more luminous class of star listed in the chart is A2V, which would have an EEERO year of 2,526.01 days. The only other star on the list is 40 Eridani B, which is a white dwarf star. which has a low luminosity.and would have a short year. Since Vulcanis hotter than Earth, a Vulcan like planet orbiting any of those stars would probably orbit signifiantly closer than the EEERO distance and thus have a years signficantly shorter than the EEERO year of that star. So none of the stars listed here should be able to have a Vuclan like planet with a year length near the the lengths indicated by "Yesteryear" and the novelization of Star Trek: The Motion Picture. Their years would all be too short, except for a habitable planet orbiting Altair, which would be too long. And "Amok Tinme" seems to prove that Altair isnot Vulcan's star. However, if research in the coming years, decades, centuries, or millennia proves that 40 Eridani can not have a planet like Vulcan, it might be that one or more of the other stars on this list will be discovered to have a planet o fthe right mass and orbit to potentially be Vulcan like. This post seems to prove that if all the information about the location and year length of Vulcan is correct, the Vulcan calendar year must be longer than the Vulcan year as defined as Vulcan's orbital period, or else Vulcan orbits much farther from its star than the distance where it would receive the necessary radiaiton to be as warm as it is, but some factor enambles Vulcan to be as warm as it is.. So the problem for fans who want to make everything iin Star Trek as plausible as possible, should be to find a way to make a Vulcan year longer than a Vulcan year would be expected to be. The problem is to justify why Vulcans woud use a calendar year longer than the oribital period of Vulcan around its s star.
In post number 25 I discussed thee vidence for the location of Vulcan, and decided that orbiting 40 Eridania A was not good for having a years as long as there is some evidence the Vulcan year is. But the other stars which are between sixteen and seventeen light years from Earth are no better and usually worse to justificy the length of the Vulcan year. So I concluded: Part One: The Problem Restated Differently. Remember that in "Amok Time" the heat of Vulcan was mentioned a few times. And in "the Deadly Yesrs", when Spock is rapidly aging and loosing his ability to tolerate a non Vulcan environment: Ao this indicates that Vulcan should be significantly hotter than Earth, and thus should receive more radiation from it star than Earth gets from the Sun. Thus it should orbit its star signficantly closer than the distance at which it would receive exactly as much radiation as Earth gets from the Sun, and thus Vulcan should have a much shorter orbital period than it would have if it received exactly as much energy as Earth gets from the Sun. I call an orbit where a planet receives exactly as much radiation from its star as Earth receives from the Sun an exact Earth equivalent radiation orbit, or EEERO. 40 Eridania A is a spectral type K1V star. https://en.wikipedia.org/wiki/40_Eridani So according to the Wikipedia calculations, the EEERO of Vulcan should have an orbital period of 223 Earth days, and the orbital period of Vulcan would have to be shorter than 233 Earth days for Vulcan to be ashot as it is. According to the answer by Conner Garcia to this question: https://astronomy.stackexchange.com...-length-of-a-habitable-planet-of-40-eridani-a A planet in an EEERO around 40 Eridani A would have an orbital period of 193 Earth days. If that is correct Vulcan would have to have an orbital period shorter than 193 Earth days to be as hot as it is. The answer to the question: https://astronomy.stackexchange.com/questions/40746/how-would-the-characteristics-of-a-habitable-planet-change-with-stars-of-differe[2] by User177107 gives the lengths of years of planets in the EEEROs of stars of various spectral types. Since 40 Eridani A is a K1V type star, its orbital period at the EEERO should between between those of planets in the EEEROs of K2V and G8V stars, and thus between 182.93 and 280.06 Earth days. So those sources do not agree with each other very closely, but they are not very different. They put the EEERO of a planet of 40 Eridani A at 223, or 193, or 182.93 to 280.06 Earth days. And since Vulcan is so much hotter than Earth, it shoudl orbit 40 Eridani A closer than the EEERO distance and have a year significantly shorter than the orbital period in the EEERO. But "Yesteryear" indicates that the Vulcan calendar year should be either close to an Earth year of 365.25 Earth days, and thus significantly longer than the orbital period in the EEERO of 40 Eridani A, or else possibly significantly longer than Earth's year, possibly up to about 1.5 Earth years long. That is directly p opposite to the orbital period of a planet orbiting 40 Eridania A at a distance significantly less than the EEERO distance. And one solution which I suggested is that possibly the Vulcan calendar year is significantly longer than the orbital period of Vulcan around its star. Part Two: Making the Vulcan Year Longer Than its Orbital Period. Why would the Vulcan calendar have a "year" which is longer than the orbital period of Vulcan around its star? On Earth the inclination of the axis of the Earth's rotation causes various latitudes to have longer and shorter periods of daylight, and thus be warmer or colder, during different parts of the year, which causes the changing seasons including the seasons for food to grow. So the length of Earth's orbital period around the Sun determines the length of the astronomical seasons, which strongly influence the growing seasons in the temperate latitudes. Thus it is important for Earth calendars to have years equal ito Earth's orbital period around the sun. So calendars used in places where temperatures were much the same in every season didn't bother to make their years equal Earth orbital period. Instead those lunar calendars usually had 12 lunar months in a year, with a 13th leap month every few years. The axial tilt of Earth is 23.44 degrees, but the axialtilts of other planets in the solar system vary widely, from 0.10 degrees for Mercury to 97.86 degrees for Uranus and even 177.30 degrees for Venus. https://en.wikipedia.org/wiki/Planet#Planetary_attributes If Vulcan has a very slight axial tilt, like the 3.12 degrees of Jupiter or the 0.10 degrees of Mercury, there would be very little season variation on Vulcan, and the length of Vulcan astronomical seasons,a nd thus the length of the Vulcan orbital period around its star, would be rather unimportant to Vulcans. Vulcans would still notice how long it took for the stars visible at night to cycle thorugh a full circle and thus know that the duration of their orbital period was astronomically significant, but ithe orbital period might not be important enough to Vulcans to become the period of the Vulcan year. The thought has occurred to me that possibly the length of the Vulcan calendar year might be based on the synodic period of Vulcan and another planet orbiting 40 Eridania A. The synodic period of two planets orbiting the same star is the length of time it takes them to return to the same posiitons relative to each other and to the star. The synodic period of Vulcan and another plandet in the system could possibly be important enough for some reason to Vulcans that their only known calendar (out of doubtless many calendars) uses the synodic period as the length of its "year". Looking up a table of the synodic periods of the planets in the solar system relative to Earth, you will see that the closer the orbit of another planet is the orbit of Earth, and the more similar their year length's are, the longer the synodic period of that planet will be. Mercury orbits the Sun in 87.97 days and has a synodic period of 113.88 days. Venus orbits the Sun in 224.70 days and has a synodic period of 583.92 days. Mars orbits the Sun in 686.98 days and has a synodic period of 779.94 days. Ceres orbits the Sun in 4.604 Earth years and has a synodic period of 466.6 days. jupter orbits the Sun in 11.86223 Earth years and has a synodic period of 398.88 days. And so on. The only planet discovered so far in the 40 Eridani A system, 40 Eridani Ab, orbits with a semi major axis of 0.224 AU and an orbital period of 42.378 Earth days. Since 40 Eridani Ab receives far too much radiation from 40 Eridani A and is far too hot for Earth life, Vulcan would have to orbit at several times its distance to be cool enough for life, and also to have a year length long enough. And with that great a difference betweem the orbits of Vulcan and 40 ERidani Ab, the synotic period should be only slightly longer than the year of 40 ERidani Ab and shorter than the orbital period of Vulcan. So the Vulcan year, longer than the orbital period of Vulcan, should not be the synodic period of Vulcan and 40 Eridani Ab. For a synodic period to be be long enough to solve the problem of the Vulcan year, it should be the synodic period of a planet which either orbits slightly closer to 40 Eridani A than Vuclan or else orbits slightly farther than Vulcan And it has to be a planet small enough to not have been discovered yet, just as Vulcan itself has to e small enough noto have been discovered yet. It is my hope that a Star Trek fan interested in orbital mechanics will be able to design a solar system where Vulcan could have a "year " within the proper length range (as deduced inpaost number on of this thread) which is equal to the synodic period of Vulcan and another planet orbiting 40 Eridani A..
Or something else compensates for the difference, say greenhouse gases maybe. After all: "Without greenhouse gases, the average temperature of Earth's surface would be about −18 °C (0 °F)*...rather than the present average of 15 °C (59 °F)." ---Greenhouse gas *(some apparently rounding here:-18 °C = -0.4 °F and -17.777 °C = 0 °F )
I try not to get too much reality in my fiction. Especially scientific facts that were unknown to the original writers. In 1966 exactly NO exoplanets were known. It is all pulled from whole cloth, and they had nothing factual to hang Vulcan on. I leave it there. The Vulcan year is what it is stated. The air is hot and thin and the gravity a touch heavier. It is a fictional universe with fictional physics. Trying to rectify old fiction with modern discoveries? That Way Lies Madness.
Good idea about Vulcan's low tilt and possible synodic planets. Maybe the synodic planet is just slightly farther out than Vulcan (perhaps smaller and an ice planet a la ST2009 with a synodic period close to an Earth year. Once a year, the planet looms in the sky like a moon (keeps the fact that Vulcan has no moon)! It's closest approach signifies a Vulcan year. Due to the gravitational pull, Vulcan may experience heightened vulcanism and tidal action in its oceans during this period. Things that early Vulcans may find important to keep track as early humans keep track of seasons on Earth. Keeping fictional, Vulcan has active vulcanism which puts gases into its atmosphere. These gases/dust could be affecting the planet's average surface temperature (up or down; who knows?). How constant or periodic are these gas levels is unknown? Active vulcanism also implies its planet core is molten which is key to projecting a protective magnetic field over the planet against solar radiation. So, how stable is Vulcan to support life? Return To Tomorrow hints that Vulcans may have been deposited on Vulcan a little over 500,000 years ago. In geological terms, that's actual a fairly modest time when it comes to supporting a species. Vulcanism wouldn't reshape the planet's surface that much. It may involve plate tectonics, too, but reorganizing continents is unlikely. Like Earth, they could have had several ice or heat ages. Sargon's people wouldn't seed a planet unless they knew it would stable for long enough time to support the seeded species.
@Henoch Vulcanism would help with the goal being that such mechanisms allow the orbit to be larger and the year longer. If Vulcan has a higher surface gravity that could mean the planet itself is larger than Earth, thereby increasing the amount of radiation hitting it (bigger target.) Cumulatively one might be able to construct a Vulcan that matches more and more of the stated criteria.
It seems probable that if all the information about the location and year length of Vulcan is correct, the Vulcan calendar year must be longer than the Vulcan year as defined as Vulcan's orbital period, or else Vulcan orbits much farther from its star than the distance where it would receive the necessary radiation to be as warm as it is, but some factor enables Vulcan to be as warm as it is. In post number 26 above I discussed way to make the Vulcan calendar year longer than Vulcan's orbital period around its star, suggesting that it might be the synodic period between consecutive times when Vulcan and another planet were in the same position realtive to Vulcan's star. In this post I will duscuss the possibility that Vulcan might orbit its star at a distance where it would receive much less radiation from the star than Earth receives from the Sun. Thus Vulcan should have a year about as long as a Earth year, or even longer, but it would be much colder than Earth, not hotter than Earth. Unless some other factor caused Vulcan to be much hotter than the amount of radiation it receives from its star could make it. Vulcan would have to have lo have some other source of heat. And tidal heating by tidal interactions with companion worlds could be a source of significant heat that could make Vulcan "hot as Vulcan" despite the much smaller and inadequte amount of radiation Vuclan received from its star. So possibly Vulcan has companion worlds which share its orbit around its star, and is heated up by tidal interactions with those companion worlds. There are three categories of companion worlds which Vulcan could have: One) Moons. Natural satellites which orbit around Vulcan and are significantly less massive than Vulcan. Two) Companion planets that orbit around a barycenter of a double planet with Vulcan, a barycenter which is outside the surface of the planet Vuclan. if Vulcan is part of a double planet, the other planet would have a mass fairly similar to that of Vulcan. Three) A companion planet which is many times as massive as Vulcan. The barycenter of fhe system would be within the body of the companion planet, and Vulcan would revovle around the barycenter and thus around the companion planet. So Vulcan would be a moon or natural satellite of the companion planet. And it is possible that the one or more companion worlds of Vulcan might belong to one, two, or three of the above categories. In the TOS episode "The Man Trap", september 8, 1966, Uhura and Spock have a conversation: So Vulcan has no moon, according to a direct statement by a scientists from Vulcan. That would seem to elimiate all possibiity of a companion world of type one, a natural stellite. In the later episodes "Amok Time", September 15, 1967, and "Journey to Babel", November 17, 1967, the Enterprise is seen at Vulcan, and only the planet Vulcan is seen. It has no visible moons or other companion worlds. But if a spaceship approached Earth the Moon from the plane of the Moon's orbit around Earth, the chances of seeing the Moon would depend on how close the spaceship was. After the spaceship got closer to Earth than the moon, the Moon would be behind the spaceship and thus invisible if the space ship was coming from a direction which passed close to the Moon. There is a scene in the TOS-R version of "Tomorrow is Yesterday" when the Enterprsie passes the Moon and leaves it behind and out of frame as it heads toward Earth, for example.. As a general rule, if a spaceship approached the Earth and Moon in the plane of the Moon's orbit, whether the Moon was visible would depend on the distance to the spaceship and the angles between the Earth, the Moon, and the Space. And the closer the spaceship got to the Earth, the more likely the Moon would not be visible at th e same time as the Earth. In "Amok Time" and "Journey to Babel" The Enterprise seems to be only a few hundred or thosund miles above Vulcan, a distance which would make viewing any moon of Vulcan in the same shot as Vuclan rather unlikely. What if a spaceship approached the Earth and the Moon from a direction 90 degress perpendicular to the plane where the Moon orbited the Earth. From a distance the Earth and Moon would appear to be two bright stars which grew brighter and brighter and farther apart as the spaceship got closer. Eventually the Earth and Moon would appear as tiny circles, or tiny half circles since half of their surfaces would be in shadow. And how large would the surfaces of Earth and Luna appear compared to the distance between them? Earth has an average radius of 6,371.0 kilometers and thus an average diameter of 12,742 kilometers. The Moon has an average radius of 1,737.4 kilometers and thus an average diameter of 3,474.8 kilometers. The perigee of the Moon's oribit around the Earth is 362,600 kilometers and the apogee of the orbit is 405,400 kilometers. Thus the separation between the Earth and the Moon would be about 28.45 to 31.81 times the diameter of the Earth, and about 104.35 to 116.66 times the diameter of the Moon. As the spaceship headed toward the Earth, its view ahead would show mostly black space studded with stars, and two tiny half discs, the Earth and the Moon, separated by many times their diameter. By the time Earth was close enough to look large in the view ahead, the Moon would be out of sight to the side. So "Amok Time" and "Journey to Babel" don't prove that Vulcan has no companion world(s), since it would be quite probable that those companion world(s) would be out of sight during such close approaches to Vulcan as were seen. And that was all the information about hypthetical companion worlds of Vulcan in TOS. In the TAS episode "Yesteryear", September 15, 1973, Roddenberry and Fontana put notes in the script saying not to draw any moon of Vulcan. However, they included lines in the script mentioning the Vulcan month of Tasmeen. Earth calendar months are divisions of Earth years that are based on the Moon's orbit around the Earth. If Vulcan has no moon, what are Vulcan "months" based on? Possibly on cycles related to other types of of companion worlds of Vulcan. Anyway, the animaters drew a moon-like object in "Yesteryear" A view of Spock's home city of Shikahr showed a semicircle a the horizon, at least as wide as Shikahr, This is usually considered to be a moon or other sister world of Vulcan. I think that there is a possibility that the semicircle could be a giant dome, at least as wide as Shikahr, on the horizon. Or possibly it could be the rising or setting sun on the horizon. When a rising or setting sun is low in the sky, or actually at the horizon, it turns orange and even red, and gets dim enough to look at without hurting your eyes. The orb at the horizon, or millions of miles beyond it, looks red, so it could be a star reddened by shining thorugh atmospheric layers near the horizon. It is hard to draw a bright light, so the dimness of that orb, if it is a star, is easy to explain by the that difficulting in drawing bright lights as well as it being dimmed by the atmosphere near the horizon. But Gene Roddenberry and D.C. Fontana didn't think about such possibilities, or else rejected them. Their explanation for a "moon" which shouldn't have been there was that it was a sister planet. https://memory-alpha.fandom.com/wiki/Ni'Var#Sister_planet So if that object was a sister planet of Vulcan, maybe it had a different orbit and it would appear largest in the sky of Vulcan when it was at its closest, once a synodic period. In that case it would have to be in an orbit outside that of Vulcan if it was illuminated by the star of Vulcan instead of being in shadow during "Yesteryear". Many people think that this sister planet would have to be very large and/or very close to appear as large in the sky of Vulcan as it seems to. But objects photographed with a telephoto lens can appear much larger in angular diameter than they appear to the unaided eye, so there really is very little evidence about the angular diameter of any objects seen in the Vulcan sky. If the sister planet was a constant companion of Vulcan, sharing the same orbit, then it would have to be either: Two) a double planet with Vulcan, roughly similar in size to Vulcan, or Three) a much larger planet that Vulcan was a moon of, since: One), a moon of Vulcan, had been declared to not exist. In Star Trek: The Motion Picture (1979) there is a scene where Spock is at Gol, presumably on Vulcan, and in bright sunlight squinting as he looks up to the sky. This scene is intercut with several shots showing the surface of a planet, presumably Vulcan, and presumably at night, since the sky is black. In one shot, two circular bodies are seen, a red one about twice the angular diameter of the other one. In another shot, the horizon of that planet is seen, with a vast orb at the horizon, and a smaller red orb passing in front of it. It is uncertain whether the two red orbs in Star Trek: The Motion Picture (1979) are the same one or different ones, and uncertain if either is the same as the one in "Yesteryear". There is a minimum diameter, several hundred kilometers, for an object to be compressed into a spheroidal shape by its gravity. There is also a maximum possible diameter for a giant planet, or even for a brown dwarf intermediate in mass between a planet and a star. The ratio between the apparante diameters of the various objects seen in Vulcan's sky, combined with the ratio between the minimum and maximum possible diameters of spheroidal non stellar objects, can be used to find maximum and minimum possible sizes for the objects in Vulcan's sky. Since the scene with Spock is in daylight, and the scenes with objects in the sky seem to be at night, they should not happen at the same place at the same time. If they happen at the same place, they should happen at different times. If they happen at the same time, they should happen in different places. Thus the scenes with objects in the sky could happen on a different part of Vulcan, or on another planet in the Vulcan system, or even in another star system. The scenes with objects in the sky of - presumably - Vulcan, are in the theatrical and television versions of Star Trek: The Motion Picture (1979), but not in the director's cut, which they were removed from for various reasons. https://memory-alpha.fandom.com/wiki/Vulcan_system Vulcan was visited In the TNG episodes "Unification Part 1", November 4 1991, and "Gambit Part 2", October 18, 1993, and no companion worlds were seen. Vulcan was also visited in the ENT episodes "Home", October 22, 2004, and "The Forge", November 19, 2004, "Awakening", November 26, 2004, and "Kir'Shara", December 3, 2004, and again no companion worlds were seen. In the movie Star Trek (2009) the Enterprise leaves the Vulcan system using warp drive. Later, Young Spock drops off Kirk in an escape pod. Kirk lands on a planet, meets, Old Spock, and is told the planet is Delta Vega. Old Spock tells Kirk of witnessing the destruction of Vulcan. If Spock saw that with his eyes, instead of telepathically, Delta Vega should have been a sister world of Vulcan. But if the Enterprise was warping away from the Vulcan system before dropping Kirk off at Delta Vega, Delta Vega should be far from Vulcan. And in "Where No Man Has Gone Before", September 22, 1966, Delta Vega is the name of a planet near the edge of the galaxy, and so hundreds or thousands of light years from Vulcan. So the location of Delta Vega in Star Trek (2009) is rather uncertain. https://memory-alpha.fandom.com/wiki/Delta_Vega_(Vulcan_system) https://memory-alpha.fandom.com/wiki/Vulcan_system "Lethe" was released October 22, 2017, "If Memory Serves" was released March 7, 2019, "Such Sweet Sorrow " was released April 11 & 18, 2019, and "Unification III" was released November 26, 2019. So that is a list of the available information about objects seen in the sky of Vulcan, objects which might possibly be sister worlds of Vulcan, sister worlds which might possibly cause enough tidal heating to make Vulcan far hotter than it should be at its distance from its star. The problem or task for Star Trek fans who like that concept is thus to design a Vulcan system where the orbits and masses of the various bodies are such that Vulcan would have as long a year as it seems to have, while also plausibly being hotter than the Earth due to tidal heating..