# The Length of the Bajoran Year in Stardate Units

Discussion in 'Star Trek: Deep Space Nine' started by MAGolding, Apr 23, 2021.

1. ### MAGoldingFleet CaptainFleet Captain

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Dec 11, 2015
Short Version:

My calculations indicate that there should between 717.6 to 721.1 stardate units (SU) in the Bajoran year. It is also possible that the length of the Bajoran year should have an even narrower possible range, from 717.1 to 719.9375 stardate unites (SU).

Long version:

If there is a constant unchanging relationship between TNG era stardate units and the rate at which time passes on a planet, it should be possible to calculate the length of the year of a planet in stardate units (SU), if ther eis enough information given.

Assuming that there X number of stardate units always equals Y number of years on a planet, it is theoretically possible to calculated the length of a planet's year in TNG era SU.

Of course this calculation depends on the Bajran Gratitude Festival always happening on the same date each Bajoran year, being a fixed holiday like Christmas instead of a moveable holiday like Easter. It also assumes that the Bajor calendar year is always about the same length, instead of sometimes being a lot longer than other times, like lunisolar calendars on Earth that add a leap month every few years.

Part One: The Bajoran Gratitude Festival & Maximum Possible Length of Bajoran Year..

"Fascination" has no stardate, but immediately follos "Defiant" which begins on stardate 48437.3 and is immediately followed by "Past tense Part 1" with a beginning stardate of 48481.2 and should happen on a stardate between those two.

"Fascination" happens during the Bajoran Gratitude Festival:

http://www.chakoteya.net/DS9/456.htm

If the first time Jadzia helped set up the Renewal scrolls was exactly two years earlier, Jadzia and Kira should have come to DS9 longer than exactly two years ago. It is possible they set up the decorations for the first time off screen sometime during "Emissary", but that would still have to be after Dax arrives at the station in"Emissary":

http://www.chakoteya.net/DS9/401.htm

48481.2 minus 46390.1 equals 2091.1. Divided by two that makes the maximum length of the Bajoran year 1,045.55 SU.

Part Two: The Bajoran Gratitude Festival From "The Nagus" to "Fascination".

However, there probably wasn't a Gratitude Festival during "Emissary", since a Gratitude Festival happens in "The Nagus".

http://www.chakoteya.net/DS9/411.htm

There is no stardate in "The Nagus" , but if it happens sometime during the first season and thus after stardate 46393.1, the latest stardate in "Emissary" and before, the earliest stardate in the 2nd season, 47182.1 in "Invasive Proceedures" , there should be about 1,285.2 to 2,088.1 SU in the interval, making a Bajoran year equal to 642.6 to 1,044.05 SU.

Part Three: The Bajoran Gratitude Festival From "Fascination" to "Tears of the Prophets".

In "Tears of the Prophets":

http://www.chakoteya.net/DS9/550.htm

So it seems like another Gratitude Festival has just ended.

"Tears of the Prophets" has no stardate, but the episode before it, "The Sound of her Voice" has stardate 51948.3, and "Shadows and Symbols" two episodes later has stardate 52152.6. Stardate 51948.3 minus 48481.2 is 3,467.1 SU. Stardate 52152.6 minus 48467.3 is 3,685.3 SU.

3,467.1 to 3,685.3 divided by 3 is 1,155.7 to 1,228.4333.

3,467.1 to 3,685.3 dvided by 4 is 866.775 to 921.325 SU.;

3,467.1 to 3,685.3 divided by 5 is 693.42 to 737.06 SU.

3,467.1 to 3,685.3 divided by 6 is 577.85 to 614.2166 SU.

Part Four: The Bajoran Gratitude Festival From "The Nagus" to "Tears of the Prophets".

Since "The Nagus" should be two years before "Fascination", "Tears of the Prophets" should be about 5 to 8 years before "The Nagus".

There should be abou 4,766.2 to 5759.5 SU between "The Nagus" and "Tears of the Prophets".

4766.2 to 5759.5 divided by 4 is 1,191.55 to 1,439.879 SU.

4766.2 to 5759.5 divided by 5 is 956.24 to 1,151.9 SU.

4766.2 to 5759.5 divided by 6 is 794.3666 to 959.91666 SU.

4766.2 to 5759.5 divided by 7 is 680.88571 to 822.78571 SU.

4766.2 to 5759.5 divided by 8 is 595.775 to 719.9375

4766.2 to 5759.5 divided by 9 is 529.5777 to 639.94444 SU.

Part Five: The Anniversary of the Emissaary"

In 'Starship Down":

and:

http://www.chakoteya.net/DS9/479.htm

Obviously the arrival of the Emissary happened during the episode "Emissary", sometime between the earliest stardate 46379.1 and the latest stardate, 46393.1, in that episode.

So there should be about 2,2870.4 to 2,884.4 SU in a period which should be evenly divided into an unspecifie number of Bajoran years (unless the Bajorans have given up using Bajoran years, of course).

2,2870.4 to 2,884.4 SU divided by 2 equals.1,435.2 to 1,442.2 SU.

2,2870.4 to 2,884.4 SU divided by 3 equals 956.8 to 961.46666 SU.

2,2870.4 to 2,884.4 SU divided by 4 equals 717.6 to 721.1 SU.

2,2870.4 to 2,884.4 SU divided by 5 equals 574.08 to 576.88 SU.

2,2870.4 to 2,884.4 SU divided by 6 equals 478.4 to 480.7333 SU.

2,2870.4 to 2,884.4 SU divided by 7 equals 410.05714 to 412.05714

2,2870.4 to 2,884.4 SU divided by 8 equals 358.8 to 360.55.

This calulation produces much narrower ranges tha others.

Part Six: Conclusion.

574.08 to 576.88 SU is consistent with 529.5777 to 639.94444 SU calculated from "The Nagus" to "Tears of the Prophets".

574.08 to 576.88 SU is also consistent withand with 577.85 to 614.2166 SU calculated from "Fascination" to "Tears of the Prophets".

717.6 to 721.1 SU is consistent with 595.775 to 719.9375 calculated from "The Nagus" to "Tears of the Prophets",

717.6 to 721.1 SU is also consistent with with 680.88571 to 822.78571 SU calculated from "The Nagus" to "Tears of the Prophets".

717.6 to 721.1 SU is also consistent with 693.42 to 737.06 SU calculated from "Fascination" to "Tears of the Prophets"

956.8 to 961.46666 SU is consistent with 794.3666 to 959.91666 SU calculated from "The Nagus" to "Tears of the Prophets",

956.8 to 961.46666 SU is also consistent with with 956.24 to 1,151.9 SU.calculated from "The Nagus" to "Tears of the Prophets", but not with any range calculated from "Fascination" to "Tears of the Prophets".

1,435.2 to 1,442.2 SU is not consistent with the maximum possible length of the Bajoran year calculated from "Emissary" or "The Nagus" to "Fascination".

Since "The Nagus" to "Fascinaton" also establishes tihe minimum possible length of the Bajoran year as 642.6, a range of 574.08 to 576.88 SU also seems to be eliminated, thus leaving 717.6 to 721.1 SU as the possible range for the bajoran Year.

In my following calculations I assume that the Bajoran year is between717.6 and 721.1 stardate units (SU) long, though there is a chance that the possible length range could be even narrower, from 717.6 to 719.9375 stardate units (SU)

Calculating from stardate 49263.5 in "Starship Down", the previous anniversaries of the coming of the Emissary were:

in 48542.4 to 48545.9,

in 47821.3 to 47828.3

in 47100.2 to 47110.3,

And the previous one was "Emissary" when the Emissary arrived.

Calculating from "Fascination" sometime between stardates 48437.3 and 48481.2, the previous Bajoran Gratitude festivals were:

in 47716.2 to 17763.6

and in 46995.1 to 47146.0, the one during "the Nagus".

Calculating from "Fascination" sometime between stardates 48437.3 and 48481.2, the following Bajoran Gratitude fstivals were:

between 49154.9 and 49202.3

between 49872.5 and 49923.4

between 50590.1 and 50644.5

between 51307.7 and 51365.6

and between 52025.3 and 52086.7.

This last one between 52025.3 and 52086.7 is during the period between 51948.3 and 52152.6, and thus in the possible range for "Tears of the Prophets".

The next Bajoran Gratitude festival would be held sometime between stardates 52742.4 and 52807.8, which should be sometime after the highest DS9 stardate I could dig up today, 52576.2 in "Penumbra". Thus it is uncertain whether that festival happened before or after the last DS9 episode "What You Leave Behind".

Anyway, these are my calculations about the possible length of the Bajoran year in Stardate Units (SU).

Last edited: Apr 23, 2021
2. ### NewHeavensNewEarthFleet CaptainFleet Captain

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Indeed.

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Location:
Bajor was the eleventh planet in its star system. It's revolution likely is more like a Martian year.

4. ### kktCommodoreCommodore

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Seattle
The extra-solar planets we've discovered have been from an enormous range of distances from their sun. Some solar systems have all the planets packed in closer than Mercury. Others have them spread out more than our system does.

5. ### MAGoldingFleet CaptainFleet Captain

Joined:
Dec 11, 2015
Memory Alpha also says Bajor is the 11th planet in the system.

https://memory-alpha.fandom.com/wiki/Bajor

But I don't know which episodes or movies mention that.

If the spacing of planets in the Bajor system is is like that in the Solary System, Bajor would have a year many centuries or even millennia long.

In our solar system, the orbit of Neptune, the eighth planet, is about 19.78 times as far from the Sun as the orbit of Mars, the fourth planet. The year of Neptune is 164.79 Earth years long, 87.654 times the year of Mars. So obviously any hypothetical eleventh planet in our Solar System would have a year centuries or millennia long.

So if the planets in the Bajor System are spaced the same way as the palnets in the solar System, the year of Bajor would probably be hundreds of times as long as you claim.

But astronomers have now discovered over four thousand exoplanets orbiting other stars, and sometimes they have discovered two or more planets within a star system. Astronomers now know that the spacing of planets in star systems can vary greatly.

The star TRAPPIST-1 has seven exoplanets.

The seventh and outermost planet, TRAPPIST-1 h, orbits at a distance of about 0.06189±0.00053 Astronomical Units (AU).

Assuming that the seventh planet in the Bajor system orbited at a distance of about 0.06189 AU, and that the planets farther out each orbited at twice the distance of the next inner planet:

Bajor VIII would orbit at about 0.12378 AU.

Bajor IX would orbit at about 0.24756 AU,

Bajor X would orbit at about 0.49512 AU ,

Bajor XI would orbit at about 0.99024 AU,

The smallest known ratio between the orbits of successive planets in a system is 1.1127493. Exoplanet Kepler-36 c has an orbit with a semi-major axis which is 1.1127493 times the semi-major axis of the orbit of Kepler-36 b.

So if we make the ratio between planetary orbits of the outer planets in the hypthetical Bajoran ssystem have an orbital ratio of 1.2, then:

Bajor VIII would orbit at about 0.074268 AU.

Bajor IX would orbit at about 0.0891216 AU,

Bajor X would orbit at about 0.1069459 AU ,

Bajor XI would orbit at about 0.128335 AU,

Mercury orbits at about 0.39AU, Venus at about 0.62 AU, and Earth at 1.000 AU. So it is perfectlypossible for a planetary system to have an eleventh planet orbiting much closer to the star than Earth orbits the Sun, and even more close compared to the orbit of Mars.

This blog post https://planetplanet.net/2017/05/03/the-ultimate-engineered-solar-system/ Says that a number of moons or planets could share the same orbit, if between seven and forty two worlds of the same mass were equally spaced within the orbit. So seven to ten planets could share a single orbit, and there could be only one to four planetary orbits within the orbit of Bajor.

For Bajor to have the right temperature range for life, it should beceive about the same amount of radiation from its star as Earth Gets from the Sun.

An answer by user 177107 at the question: https://astronomy.stackexchange.com...anet-change-with-stars-of-differe/40758#40758

Has a table listing the masses and luminosities of various spectral types of main sequence stars. The table also lists the disances at which a planet would receive the exact same amount of radiation from its star as Earth receives from the Sun for each type of star, and the length of the year of a planet orbiting at that distance.

Thus it can be seen that it is possible for a habitable planet, even if it is the eleventh planet in the star system, to
orbit its star at a distance which gives it a year much shorter than Martian year or even an Earth year.

Joined:
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It's noteworthy that the distance from DS9 to Bajor, as measured in runabout-at-impulse-hours, varies between exactly two figures: 2 hours and 6 hours. Those are travel hours at top speed, too, since both get quoted in cases of hurry.

The obvious setup would be for the distance between the two orbits to be 2 such hours, and the distance between the planet and the star to also be 2 such hours - meaning A-to-B would be either the difference between the orbits when A and B are at the closest, or the difference plus the full diameter of the inner orbit when they are at the farthest. Simple, eh!

If we nail down the orbital radius of Bajor, we have the orbital radius of DS9 down pat as well, then...

We could well go with a radius derived directly from a 720-SD year (that is, some 260 Earth days). Or then we could take into account the prominent and numerous moons of Bajor and assume their festivals depend on those more than anything else. This could be made to fit the "anniversary" datapoints above, at total random rather than systematically. But tying it all with a single neat bow sounds more satisfactory.

Timo Saloniemi

7. ### Boris SkrbicFleet CaptainFleet Captain

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Stardate units often suggest that the Earth year is about as short, eg. with the fourth anniversary of Jennifer’s death being the day before stardate 47329.1, or when the opening of the pilot rounds the time between ~44002 and 46379.1 to three instead of two years.

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The dialogue describing the Bajoran system comes from The Nagus. Jake helps Nog read a text that describes Bajor as the largest planet of the 14. As the terrestrial planet was the largest, there would be no gas giants to space out the planets in the system. Habitable zones is more of a means of designating good candidates for livable planets from bad from the perspective of thousands of light years away. There is no need for a planet to be in our habitable zone if (1) the star emits more radiation than our Sun or (2) the planet is more massive. The second caveat is important, because a larger terrestrial planet would hold onto atmosphere more easily, produce more internal heat, and be seismically active, all of which would make it more likely the planet would have liquid water. Moreover, the higher gravity would probably reduce the number of extreme geographical features (mountain ranges) that would limit the spread of early life.

Joined:
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Bajor of course is physically exactly like Earth, for obvious reasons. But she probably would be, quite regardless of how nature made her: the galaxy has been the sandbox of terraforming cultures for billions of years, and it only makes sense that in all that time, life here would have standardized on a single type of habitable world. Any culture compatible with that would start off with the terraforming heritage of the preceding dominant cultures, and any culture at odds with that would need to re-terraform those worlds more to its liking and suffer in the process.

The deeper inside the system we put Bajor, the deeper we can put DS9 which, as said, is probably at twice the distance. The station ain't out there with the local Pluto, not with the amount of starlight falling on it. Since "Emissary" gives us the distance from Bajor to Denorios at 160 million klicks or roughly 1 AU, we really should assume Bajor's own orbit is also of 1 AU radius, give or take ten or perhaps twenty percent.

"Take" helps with the 260-day year (although that's less in local days, apparently, if a Bajoran hour is the same as the Earth hour). It doesn't get us quite there, but it's what we have to live with; essentially, Bajor is at alightly more than the distance of Venus from the local star (which thus is probably dimmer rather than brighter, although not necessarily by all that much).

But Bajor isn't the eleventh planet out, not on those Okudagrams that show nine planets inward of DS9 and the Denorios Belt and thus suggest Bajor is around the fifth or so. I don't really know where this "Bajor XI" nonsense started, but it's not in the dialogue and not in those Okudagrams that actually show things.

(Whether Bajor is the largest of the fourteen is debatable. Nog reads this out of a book that says the planet has three moons, which we know is false from the episode taking place on the fifth moon. So we get to pick and choose what to believe and what to dismiss as an error in Nog's substandard reading, or perhaps in a book whose "facts" were pulled out of the non-Bajoran writer's ass. Perhaps the largest planet in the Bajoran system has three moons, but is not Bajor? Of course, we could also say the Cardassians imported a couple of moons, but "Progress" doesn't really play out that way...)

But that's exclusive to DS9. Probably Ben has simply gone native and is living by Bajoran years, this being the most convenient for him anyway.

Timo Saloniemi

Last edited: Apr 24, 2021
10. ### MAGoldingFleet CaptainFleet Captain

Joined:
Dec 11, 2015
Part One of Five:

The stardate when Jennifer Sisko was killed.

In TNG "The best of Borth Worlds Part 2" :

44001.4

So it looks like the battle of Wolf 359 will start only one stardate units (SU) after stardate 44001.4, or a tmost only afew sU after stardate 44001.4.

Later, still a few hours before the Enterprise can begin following the Borg cube:

So the Battle at Wolf 359 begins les than the 8 to 12 hourse that LaForge estimated after stardate 44001.4, unles it takes longer than LaForge estimates to get the ship ready. IThe Battle of Wolf 359 should probably begin less than 24 hourss after stardate 44001.4 if Hanen's estiimate is correct.

Later:

So the Battle at Wolf 359 began after stardate 44001.4 and before stardate 44002.3. The battle may have ended before stardate 44002.3 or continued after that stardate.

Later Riker and Guinan talk:

Since Riker tried to kill Locutus/Picard before stardate 44001.3, so the 0.9 SU betweem 44001.4 and 4402.3 hshoud equal less than 2 days.

That scene ends as Riker is called to the bridge and they enter the Wolf system and find the wreckage of the fleet.

So we can guess that Jennifer Sisko waskilld at the Battle of Wolf 359 sometime between stardates 44001.4 and 44002.3, or possibly just a little bit after 44002.3. So to be certain, we can assume that she was killed sometime beteen stardates 44001.4 and 44003.3.

Part Two:

The length in stardate units (SU) of the "three" years between The Battle of Wolf 359 and "Emissary".

"Emissary", the first episode of DS9, begins with a flashback to the Battle of Wolf 359 and the death of Jennifer Sisko.

Then a title card says"

Stardate 46379.1 minus 44001.4 to 44003.3 is about 2,375.8 to 2,377.7 SU.

If the "three years" means a time span between 2.000 and 4.000 years, the length of the type of year mentioned in the tile card should be about 593.95 to 1,188.85 SU long. Since the title card was written for 20th century Earth audiences the type of years mentioned should be an Earth year, but might possibly be another type of year.

Part Three:

The relationship between time and stardate units (SU) in TNG era shows.

The creators of the TNG era shows considered 1,000 stardate units to equal one year. Assuming the year that was 1,000 SU long was an Earth year aproximately 365.25 Earth days long, a SU would be approximately 0.36525 Earth days long, and there should be about 2.73785 SU in an Earth day.

The creators of the TNG era shows also considered one SU to equal one Earth day. Thus a year 1,000 SU long would be 1,000 Earth days long, or about 2.7378507 Earth years long.

And creators of the TNG era programs never explained that seeming paradox.

I suggest that sometimes the "days" mentioned in TNG era programs were the days of planets featured in the episodes, and sometimes the daily cycle aboard the ships, which should be approxaimately 24 Earth hours long for the comfort of the humans in the crews, but possibly a little longer or shorter,and sometimes the period that someone would normally work each day - a "day's work" period.

Assuming that there were 2 to 4 work periods or shifts or watches or "work days" on a starship each day or daily period, and there was 1 SU per work day", a year 1,000 stardate units long would be about 250 to 500 of such work periods or shifts or watches or "work days" long. If the daily period or "day" was about 24 Earth hours long, and there were 2 to 4 work periods or "days" in one "day of work", 1,000 SU, a 'Stardate year", would equal about 250 Earth days to 500 Earth days, or about 0.6844 to 1.3689 Earth years.

And possibly some references to "years" in TNG era shows may be references to "stardate years" which are 1,000 SU long, and which might not be the same length as the years of any specific planet.

Part Four:

The time in stardate units (SU) between The Battle of Wolf 359 and "Second Sight":

"Second Sight" begins with:

Since Jennifer Sisko was killed at the Battle of Worl 359 sometime between stardates 44001.4 and 44003.3,and since "yesterday" befor e stardate 47329.4 was probably sometime between.stardates 47319.4 and 47329.4, we can calculate there were approximately 3,316.1 to 3,328 SU between the two events.

There seems to be a slight possibiity that Benjamin Sisko counted the actucal day of Jennifer's death as the first anniversary, and thus that the Battle of Worlf 359 was exactly 3 years before the 4th nniversary. Thus the years used in that log would be approximately 1,105.3666 to 1,109.3333 SU long.

But it seems almost certain that Benjamin Sisko considered the first anniversary to be exactly one year after Jennifer's death, and thus that he considered the fourth anniversary to be exactly four years after Jennifer's death. Thus the years used in that log would be approximately 829.025 to 832 SU long.

And it seeems to me that the type of year which benjamin Sisko would naturally use to mark the anniversary of Jennifer's death would be Earth calendar years approximately 365.28 Earth days long.

Most of the numbers of years mentioned as elapsing between episodes with stardates during the TNG era are consistent with the characters using either stardate years"1,000 sU long, or Earth years whch might be
1,105.3666 to 1,109.3333 SU long but are very probably 829.025 to 832 SU long.

Part Five:

The relative lengths of Bajoran and Earth years.

Since my post number one calculates that there should be about 717.6 to 721.1 stardate units (SU) in a Bajoran year, we can calculate the possible relationships between a Bajoran year and an Earth year.

If an Earth year is 1,105.3666 to 1,109.3333 SU long, a Bajoran year 717.6 to 721.1 SU long would be about 0.646875 to 0.6523627 Earth years, or about 236.27109 to 238.27547 Earth days.

If an Earth year is 1,000 SU long, a Bajoran year 717.6 to 721.1 SU long would be about 0.7176 to 0.7211 Earth years, or about 262.1034 to 263.38177 Earth days.

If an Earth year is 829.025 to 832 SU long, a Bajoran year 717.6 to 721.1 SU long would be about 0.8625 to 0.8698169 Earth years, or about 315.02812 to 317.70062 Earth days.