3D map of Federation space WHEN???!!!

A few thoughts. Voyager's 70kly journey is alluded to requiring 70 years to complete, suggesting the best Federation ships have a maximum sustainable speed of about 1000c, whatever their dash speed might be. DS9 suggests that certain destinations within the Federation take six months or so to travel between, when Sisko and Kassidy are talking about her brother's baseball games. Ergo the major axis of the Federation can be supposed to be about 500 light years. The minor axes are probably much smaller, perhaps as small as 100 light years based on the distances to DS9 and the various Neutral Zones, so the total area of the Federation is probably in the neighborhood of 5 million cubic light years. Average galactic density is 0.4 stars per cubic light year so this would give the Federation territorial claim over some two million systems, only a tiny fraction of which could possibly have been actually visited by crewed ships over the Federation's two-hundred-year lifespan. If one-tenth of those systems have habitable planets, and one-tenth of those habitable planets have life, and one-tenth of those have intelligent life, and one-tenth of *those* are warp-capable, this suggests two hundred warp-capable species in Federation territory, which is a surprisingly close estimate to the 154 member species quoted in TNG.

I’ve said it a thousand times and I’ll say it a million more, Star Trek federation would be a great docuseries, a look into the federation as a whole and how it works, see the worlds, see the federation in all its glory.

154 members doesn't mean 154 worlds, each world colonized a few planets nearby that didn't have sentient life on them. The UN analogy is very accurate, each member would have 1- perhaps up to a dozen colony worlds that are under their 'banner'. This would be especially true for the founding members of the Federation that had 'proto-empires' that were merged into the original Federation border. The show Enterprise suggests Earth had at least Alpha Centauri, and Vulcan, Andor and Tellar each had many colonies each before the founding of the Federation.

8000 light years could be the circumference, just drawing a line on a 2d version of a starchart and measuring how long it is.

The best explanation I've heard for the Federation's inconsistent size is that the UFP is NOT one continquous area, as with the US, but is instead broken up into pockets, small regions of Fed territory, with empty space between them.

I don’t think most colonies don’t have federation council status until they reach a certain size. Take for example Jurrae IV, the colony the Borg wiped out right before Best of Both Worlds. The crater the cube left appears to be the size of a town, probably with a bunch of individual houses on the outskirts or scattered around the planet. I think that’s a pretty standard federation colony. A few thousand people mostly living on one continent all by themselves. They’re federation citizens and get to vote for President or whatever, but Jurrae IV never had a seat on the council

32 ambassadors were on the Enterprise, but some may have already been on Babel. Each member might consist of many worlds, which they're finding all the time. 8,000 light years might be the furthest extents of the Federation from one extreme end to the other. I would imagine it's a big sphere centered on Earth.

I still choke laughing that in the first episode of star trek enterprise Kronos the Klingon homeworld was less than one week's travel in a warp 4-star ship...

A few members of the Federation may be groups of planets or systems rather than single planets. Some of the species pre-Federation had their own alliances and territories that existed under one government. We also have the TOS First Federation from The Corbomite Maneuver in some canons have joined the Federation or have alliances and consider themselves part of The Federation but govern themselves independently. Of course there is at least one story that The First Federation is waiting for the UFP to catch up before it joins.

in addition to open space and pre-warp planetary systems Federation space would likely have a number of contact-level planetary systems that for whatever reason have not decided to join the Federation. A number of these might have treaties making them "Protectorates" of the Federation, independent but under Federation protection in regards to trade with treaties to allow for visitation and commerce with Federation worlds. A number of the Orion colonies would likely be such protectorates as would some of the worlds visited by TOS and NG Enterprise

Really good video! although the real answer is just that writers don’t feel like doing the math while writing the script, I also like to think that the discrepancy between travel times has to do with warp factors. Warp 9 is exponentially faster than even warp 8 and is typically only used in emergencies if the ship is even capable so there’s not a consistent speed for the ships

You’ve mentioned Romans in the video. They actually never said “millions of sestertii/denarii etc” when speaking about currency; they just said 3 thousand, meaning 3,000,000. So maybe when Picard talks about 8,000 LY, he actually means something bigger (several orders of magnitude), just like the Romans. I am Russian, and many Russians dealing with a thousand rubles name it just “one ruble”, omitting the thousand. So perhaps something like this exists in Trekverse. Thanks for the video!

I think one thing not discussed here, is that there is on the order of magnitudes, differences in the speed of ships from the original series to the later ones. The Enterprise E can go 21,000 times the speed of light, so 8000 light years is not that far. Plus you do not have an empire with all your ships at the home world. Fleets would be set up across the Federation to defend sectors. While it will take you time to get a backup fleet there, it will also take the same time for an enemy to invade your space as well.

People tend to forget how big space actually is. Especially in Star Trek. The shows and films only depict highlights of the crew's adventures. It diesn't cover the day-to-day humdrum of a typical workday on a Starfleet vessel. Each episode of Trek covers an important event of note to the narrative, but one episode in a sense of time might take place weeks or even months after the previous episode. To put this into some perspective; it can take eleven days at warp 9 to travel from Earth to Vulcan. That's just short of two weeks. This is an issue I think Enterprise handled better than most. As it tended to regard distances more heavily than other series, since the writers had to emphasize that this was a much older and slower vessel than what we were used to seeing.

When dealing with galaxies shaped as ours is, I generally take any such measurement of territory to be according to a top-down view. In this context, the 8000 ly number makes sense, especially given our galaxy's 1000 ly thickness (10,000 at the central bulge).

Not too forget that not all system might contain habitable planets, or even live, Or most live is just some mono cellular lifeforms.

I once heard someone say (in regards to 2d cartography) that "across" can go 'across' several axis.... So 8,000ly across can mean the maximum distance between coreward and rimward + maximum distance spinward and counter-spinward + the maximum distance between galactic-north and galactic-south...

The true size of the Federation? It is 8 1/2 " x 11" ...exactly the size of a page of television script.

Keep in mind Picard doesn't say its 8,000 light years wide. He says the number of Federation planets is "over 150...spread across 8,000 light years". 'Spread' can mean any number of things and not necessarily adjacent to each other. Just as the 50 United States of America includes the land masses of Alaska and Hawaii but not the vast stretches of Canada and the Pacific Ocean between them and the continental other 48. Any member planet likely controls the cubical volume of space immediately surrounding their system. Think our system's bounderies of the Oort Cloud (2 to 4 light years across or 8 to 64 cubical L/Y). Of various sizes depending on the size of each star system, collectively they could add up to 8,000 NONcontiguous light years scattered within a 3D volume of space of any diameter but probably only hundreds of light years across in any direction. Lastly, by 'light years'.....who's years? Its one thing to have Earth be a location of government and institutions but highly unlikely its solar revolutionary time duration is to be the universal unit for interstellar distance measurements above, and used by, all other planets and their inhabitants own measuring units. Some standardized 'year', calculated by some metric other than planetary solar revolution, is more likely. Which means 8,000 light years in Star Trek context could be anything.

Just awesome, u mention Alpha Centauri. U are the first person that I remember to state so. As I remember Centauri was a colony of Earth, at some point it got it’s independent. I know this because I have the Star Trek: Star Fleet Technical Manual from 1976, my most prize possessions.

I like the idea of the territory not been a continuous thing occupying all space between member worlds but something more like every planet (or star system) is sort of an island and some space arround it, lets say one light year, is considered its space and anything that is more than one light year away from any planet is considered "international" space. Sort of the territorial waters and international waters we have in the real world.

Great video. Loved the way you walked through things and your voice is well-suited to these types of videos.

Awesome video and awesome info! Thank you! Look forward to more videos!

Just recently found your page when I saw the video Klingon anatomy is weird. Sir you are the David Attenborough of Star Trek . It’s a pleasure listening to your videos and being entertained and informed.

actually, we can describe our galaxy as being just a diameter across using only one dimension it is now recently accepted that our galaxy is about 150, 000 light-years across. yes technically we are dealing with a volume but the size of the ratio of the galaxy's diameter to its thickness is so large the diameter usually the only measurement considering when talking about distances and size in the galaxy. so it would be reasonable for the federation to speak only of the distance across the federation

Simple solution: Picard likes to brag. No 8,000 ly straight line. Below someone suggests and ellipsoid 500 ly x 100 ly. x 100 ly. This feels right even though in many plots even that distance seems outside of events (kind of like the transporter that must exist in the world of Game of Thrones). A half year to cover the major axis (assuming max ship speed of 1000c) or a year if 500 c (Warp 8). This would be approximately 35,000 solar masses (0.059 solar masses/parsec3).

Nice work. Thank you for making this.

Another comment for the KZfaq Algorithm gods

Good presentation, although I'm partial to a smaller Federation myself, to help make sense of the otherwise very local "Deep" Space Nine...

Some of the additional un-named Federation members could be independent autonomous former colonies of other Federation races. This would increase the Federation membership worlds without increasing the number of races.

The real answer to this age old question is. That the writers never sat down with some one who actually understood the vast distances of deep space. So they just grabbed a random number that sounded cool and threw it in the script. I don't think any of the writers ever really grasped the thought multiple dimensional movement in space. Take space combat as an example it wasn't until wraith of khan we saw the Enterprise use vertical movement in combat when it rose up through the nebula gas behind the Reliant. Granted before that the series had been limited by budget constraints. But it wasn't until six or seven years later during TNG's Klingon Civil War story that we actually saw ships fight in a three dimensional way. Before that it was all horizontal movement based on a solar systems elliptical plan. But the Klingons were actually dog fighting in ships like they were old WW2 fighter planes. 8000 light years is vast but small in relative size at the same time. I mean seriously think about it, Our solar system is considered a light year in diameter. It takes the light from our sun to travel one year in all directions to the farthest ends of the Oort cloud. So does that mean the Federation consists of 8000 solar systems. Or is it just made up of the member worlds and their colonies and the protectorates and all the empty space between those worlds. Just sitting like a lumpy blob of mashed potatoes inside the galaxy.

The first time Riker is offered a command in TNG involved a mission to an area on the edge of federation space and would require "months at high warp" just to get there. We're not really given any details but we know the federation has launched long-range unmannered probes and has subspace telescopes so they could reasonably say they've "explored" and area 8000 light years across.

I love your work dudemas prime

The size and population of the federation (or any galactic civilization) was a topic I went on a binge about after the destruction of Vulcan in that film, I shall not name. It was a tragic event, but should not have been nearly the death of the Vulcan race. Logically for the survival of the species, they or any race, would spread out to colonize other worlds. There can be lots of debate over many factors, but if we limit the colonies to uninhabited worlds that are close enough to home environment, and we see in universe generally an abundance of "class M" planets, then we can start to make some educated guesses. The lowest value being an average of 1 colony established per year. Say over a 100 year time span. This means a minimum of 100 sizable colony worlds, excluding small outposts and mining or science stations. This means the early colonies have had nearly a century of growth and development. Now if we take Vulcan as an example, population numbers may still be low, as they dont seem to have large families. But according to something I recall reading, Vulcan had warp drive fore several centuries not just one, before meeting the Earthers. Having said all that, consider a race like Humans and how fast we have expanded here on Earth. Some of the Federation member races could and should have expanded to inhabit dozens of worlds if not 100s. The often encountered warp capable alien race that only lives on its home planet should be an oddity rather than the norm. An old race, that is good at terraforming or building space habitats could simply inhabit ALL the stars near its home system including the inhospitable ones. Even a supernova that came as a surprise is unlikely to destroy all their colonies. sorry for being a long post have a nice day

the roma empire could take month to be crossed, even by the legion (who moves on foot way faster than people walking around)

so in First Contact they are patrolling the neutral zone and then suddenly they make the trip to Earth in presumably a few moments, but in actuality it would have taken them a couple of years. I think the battle would have been over by then.

If anyone is interested, Google star trek mal's maps. He has done a really good job of mapping the area. Many sector maps that uses real stars.

Very interesting thanks,! Always wonder about this subject.

You forget that Cestus III is 3 weeks travel from DS-9

An 8000 light year estimate does make since when you think that its probably not continuous. It even makes since when you think about the number of ships Starfleet SHOULD have. Even some of the maps seem to show this. Bajor borders Cardassian space, which the Federation has been at war with for it seems like years by the time we meet them in TNG. We also know that the Klingon and Romulans are that far away in the Beta Quadrant. So its probably on the diagonal. Also, we know that between Star Trek III and the end of Voyager, starfleet some how managed to obtain (ether built or through merger) 73,000 starships, yet they cry over losing 34 and that requires rebuilding the fleet. Its a problem because they are in fact to spread out and it is becoming a problem. So 8000lys makes a bit of since.

We know from First Contact that the UFP comprised about 150 members. Earth during TOS had around thousand colonies and is among the youngest memeber in the Federation. But if we assume Earth was avarage member the Federation would have around 150 capitals with 150 000 colonies.

lots of fun! I'd like to see more of the local group - 20-30 light years out - and how they fit into or around canon... Where are the Tellarites relative to Vulcan, etc... I remember the battle at Wolf 359 and had to look up where it was/is on a real star map... all of that would be a kick to check out.

I love this. Thank you!

As far as the 32 ambassadors I don't think every federation planet was present in person because the universe is a big place and everyone getting together in one place isn't likely to happen. It would make more sense to have multiple meeting locations that are in communication with each other. This would make it more convenient and manageable and would reduce risk of something happening and then all of a sudden all the people in power in the galaxy suddenly dies leaving a massive power vacuum.

My guess for the 8k ly “across” stat is that it represents a lower bound estimate for the total distance you’d have to travel to visit every Federation member world.

Commenting for the algorithm. All hail the almighty algorithm, may it bless our humble creator with trending and adsense, amen.

Very Informative.

Might take a while to clarify. Starships can travel vast distances in very short periods of time; but this quickly depletes a ship's supply of anti-matter. Intrepid class vessels Can travel 1000 l y in one minute, warp 8 is something like 800-1000 l y in an hour. The Federation could be 8000 l y across, probably meaning the distance between its two furthest outposts. Voyager's problem was they can only produce a limited supply of anti-matter and there are no Starbases in the Delta Quadrant

"Federation space" probably looks like a giant sponge. The holes in the sponge are areas that haven't been explored, they're too hazardous, or they are claimed by another species that the Federation either bypassed or couldn't get to join. In other words, "Federation space" is not contiguous. We should not assume when we hear things like "the edge of Federation space" that it is the farthest point away. It could simply be a region that the Feds haven't been to yet for whatever reason.

I think it's safe to say that the writers are better at story lines than they are at physical realities of space and time. Seth Shostak, in one of his talks, gives an anecdote where he asks one of the writers about how fast warp is. Their answer was less than impressive.

Here's a point to consider: Stellar Kinematics. (Note: I first read this term 3 days ago) - As the various stars move around the Galactic Centre, some travelling X fast, some Z fast, some are barely moving at all; some are literally shooting almost straight out across the disc, from the centre, across the paths (sort of) of most other stars, and some do all sorts of other different things (or not). How would we define territory across these shifting regions of stars, where some planets (albeit in terms of thousands of years, perhaps longer) would begin in one territory/empire/federation/association, and end up in another? I'm trying to visualise this by imagining coarse salt dissolving in stirred water. Some of the larger grains will be the last to dissolve, and often appear to travel at a different speed compared to the smaller, inner grains, and all of this at different depths in the water. Is it even possible to define, or describe, a territory for more than a relatively brief period of overall time? Yeah I don't sleep much *Additional: I didn't scroll the comments to see if this had already been posited.

Just found your channel. Great stuff.

StarTrek writers couldnt possibly comprehend the vast scale and density of stars in our galaxy which is approx 150 million LY across (latest data indicates it may be quite a bit bigger than previous estimates). All of startrek could take place in a 100ly cubic volume of space and there would still be millions of stars to explore, billions of planetary bodies, trillions of stellar phenomena to investigate across 3D space just in that tiny sector alone...

Good comments on this video and I'll add mine. Yes that is a good point that 150 members or 350 it isn't just that amount of planets, it' essentially the amount of polities that agreed to membership of the Federation. And each one could have one or two planets/colonies or maybe even a hundred. And also its a possibility that in that 8,000 light year border of the federation that there are protectorates, pre-warp civilizations and also polities that have been contacted or know of the federation but decided not to be a member or the federation doesn't think they should. But as I have said in other trek forums if the federation from one end ot the other is 8,000 light years, it's to damn big to govern. It would take years to get to one end of the federation to the other. It takes weeks for communication (remember when Cassidy Yates on DS9 said to Sisko that her brother played baseball and that it will take weeks for the sub-space communication to get to her about his team). Even i f we had consul offices in or on those planets far away, they where essentially hostages to any situation that happens if even they could get communication out in the first place. Do you know how much mischief a burgeoning power in that area inside the federation or the other major powers outside the federation could do on the borders and deeper inside the federation if it takes the years to get to said incident in their borders? I'm so surprised that the Romulans who are known for doing this has never went deep into federation territory to gin up support for them and make the federation look bad. And if not that just do damage where the federation is looked at s bad and when they come to said planet they are attacked by the natives etc. etc.. There is just so much you could do to a power that is to overextended that I'll leave it at that. But one economic way that they could keep it together is to look into research building artificial stargates/wormholes that could connect one section of the federation to another and then once they transverse it the federation could use it's warp engines to get to the handful of sectors in that area that are a week or two away. They wouldn't need a bunch of these maybe 100 gates.

The thing about space is that it's not really possible to map it in a way that most people in 2023 would think of. The UFP can have hundreds of member worlds, colonies, outposts, et cetera. But there could also be local powers or even regional powers that exist between member worlds, holes in UFP controlled space. What about independent colonies? Unsettled worlds. You'd have to use a 3D map showing the extent of UFP controlled space, but it would be more useful to just color stars based off of their allegiance rather than a bubble filled in like a traditional political map.

The federation is eight thousand light years across the galactic plane, vertically. If you took the federation outpost the furthest below the plane of the galactic disk, and the outpost that was the furthest above the galactic disk the difference between them would measure eight thousand light years, though it may be substantially thinner at some points. It is possible that this eight thousand number represents the point at which the galactic barrier cuts off travel, making it a natural barrier to expansion. An empire which spanned the full eight thousand light years would be able to obstruct travel through their space, where as one that controlled only say, four thousand light years would see spaceships simply pass above or below them and thereby circumvent their territorial control. This matters because the ability to regulate travel in an area allows you to act as a middle-man in trades between the empires on either side of you, and allows you to tax cargo running through your space, enriching your empire beyond what a smaller empire that couldn’t project “vertical” force would be able to. It also allows you to obstruct fleet movements and thereby protect your smaller allies from attacks by simply blocking access to their space. That would explain why the Romulans have such a chip on their shoulder, as the Federation would be essentially boxing them in and limiting their ability to expand in other regions by not allowing them to pass through their space. And the cloaking technology would allow them to circumvent territorial blocks and pass through federation space to reach other areas, even with the full eight thousand lightyear blockade. If the federation acquired enough understanding of cloaking technology themselves they would be able to detect those ships, the Romulans would be cut off, and they would lose any leverage or negotiating power they might otherwise have had because the federation would be their only option for trade with the outside galaxy. Thus the federations vertical height may gave a lot more impact on how they interact with their neighbors than one would expect.

The Federation can have empire's worth of non member space enclosed within their volume of influence. The voyager returned with slipstream technology. Starfleet starting to build slipstream vessels would help them control their huge territory.

Maybe 8000 light years across was a diagonal measurement of its two furthest points. Like a TV screen lol

This is a good video 👍🏼

Thank this is good stuff. Always curious about the Federation facts, even with a grain of salt.

There's multiple times on the show where character request support and the nearest federation ship is weeks away. So I really doubt you'd be able to cross it in weeks. I've always assumed it would be months at least

I would love to see a video of under developed and pre-warp worlds and how far or close are those planets from earth.

It's an 8,000ly x 8,000ly x8000ly block of Swiss cheese. The negative space representing undeveloped species and species that just haven't joined or are hostile towards them.

in discovery we know that the number of federation worlds numbered at arround 350 by the 31st century so i think that would mean at its Hight the federation was the dominant alpha quadrant power and possibly the dominant power in the beta quadrant as well depending on the state of the Klingons and if they ever nutted up and joined the UFP or not

154 member worlds//thousand worlds and spreading out... star systems have multiple worlds 154 member worlds could = systems with dozens of planetoids and moons.

8 years old? perfect! Untouched by the Kurtzman plague

Who says it has to be earth years? Many planets in the Federation may have shorter years, or maybe there is some interstellar standard year calculated very differently. Every world would therefore envision a different distance when talking about "lightyears".

To me, those 8,000 light-years are simply the two furthest points in the Federation. Depending on the measurement, Deneb is up to 6000 light-years away from Earth and the "real" star Mintaka is almost 3000 light-years in the other direction. So 8000 ly makes sense.

Interesting video! :)

Would “circumference” be what they meant with the 8k “across” statement?

it's an interesting question to consider the rights of non-warp capable or otherwise unaware planets to suddenly become aware that you are surrounded on all sides and with no claim the resources of the surrounding region of space unless they joined the Federation.

"Member worlds" would also include a number of Earth colony worlds, of which many would be de facto members. Also, some mini-empires may have joined the Federation, such that one ambassador may represent a group of planets or even a group of allied worlds. So there may be many more worlds than there are species.

I think if you covered each era seperately explored memberships and just the general era's politiics with cannon nations like klingon's war might have alot more references with border's and romulan dmz draws clear line too

Them: size doesn't matter Me: thats what people with small federations say

For any discussions about speed and distance to work in ST, you need to ignore Voyager.

Great video

Never thought about until now. United Federation of Planets can be shortened as "UFOP"

asked chatGPT for a list of federation members year by year.. def not complete but a cool result 2161: The Federation is founded with the signing of the United Federation of Planets Charter by Earth, Vulcan, Andor, Tellar, and Alpha Centauri. 2164: Coridan joins the Federation. 2165: Terra Nova joins the Federation. 2175: Deneva joins the Federation. 2191: Efros joins the Federation. 2196: Axanar joins the Federation. 2218: Cait joins the Federation. 2223: Betazed joins the Federation. 2234: Rigel joins the Federation. 2239: Trill joins the Federation. 2248: Altair joins the Federation. 2261: Bolarus joins the Federation. 2263: Troyius joins the Federation. 2264: Ardana joins the Federation. 2265: Benzar joins the Federation. 2266: Delta Vega joins the Federation. 2270: Efrosian joins the Federation. 2286: Alpha III joins the Federation. 2323: Cheron joins the Federation. 2324: Efros Delta joins the Federation. 2336: Ktaris joins the Federation. 2344: Zakdorn joins the Federation. 2354: Betazed secedes from the Federation. 2379: Romulus is destroyed in a supernova, leading to the formation of the Romulan Free State, which does not join the Federation.

What if the 8k light years is means the total sum of lengths of individual travel corridors between member worlds and colonies rather than distance from the furthest point of a bubble to the other furthest point on the opposite side. Like if you measured a spider web by counting individual threads between points where they intersect and added them up to get a length of virtual single long thread if that web untangled into a single straight line. This space "web" would be rather compact in galactic scale yet very dense with many intersections (worlds and colonies) which makes traveling across it several times like enterprise did in the show.

I need to get that big book i love looking at maps

The UFP is basically, just huge. The Federation is probably about 20% into becoming a Galactic Empire? It just have to get the other 80%.

I feel like despite the fact that it doesn't make much sense to measure it that way, square light years (presumably from a "top down" view of the galaxy) is the only thing that works. That could put it at roughly 150 or so light years "long" by 50 or so "wide", with the "vertical" depth being ambiguous. Travel from DS9 (supposedly on the frontier of the federation) to earth takes only a few days, and even for the NX01 Qo'nos was a short journey away. Of course with 3d territory there are all sorts of ways to make that work. Borders can fold over and under one another, empires need not be a coherent shape, nor their capitals be at their center. Many countries have capitals directly on their borders or close to. It's also possible that the main body of the federation is fairly small, but there are far flung members who are officially part of the federation but so far away they are functionally independent. Think the many small island nations in the british commonwealth. Anyway the reason the federation CANT be a blob 8KLY across is that the Valiant was supposed to circumnavigate the federation as part of red squad's training before graduation. A defiant class is a fairly slow ship, maxing out at warp 8 or 9 I believe, probably closer to warp 6 sustainable. In one ep they got warp 9.5 out of it but only after extensive modifications, and if I recall it was quite risky. Certainly not normal operation. But even for an intrepid class, fastest ship in the fleet before the sovereign, a roughly spherical area of space 8KLY in diameter would take a quarter of a century to circumnavigate. For a defiant probably 30-35. Those cadets would be getting back in their late 40s or early 50s to graduate and become ensigns or lieutenants. Clearly that doesn't work, but equally as clearly the extent of the federations borders was never very well defined.

Assuming it's 8kly across the Galaxy from a top down perspective. We live in the Spiral, which remains disk shaped. From a top down, 8kly across makes a bit more sense.

I would like to know what federation members contribute to the technology used in starfleet.

The Federation is a multi species organization, however most of their main rivals are not(or if they are, we really don't hear about their other members). The Klingons, Romulans and Cardasians all control enough space to field fleets that seem to put them on roughly equal footing with the Federation in terms of power. And those are just the main players in the shows. I roughly recall one TNG episode where the ship's computer is hijacked and sends them toward another race. Picard is quite worried about this, not bc of breaking Fed. law, but because the last war with them was brutal and fought to a stalemate. There is also the Shelliac(however it is spelled) Corporate who seem powerful enough to require a treaty of such complexity that understanding it is damn near impossible. Picard solves the problem by requiring outside arbitration, from a list of potential species(each who by definition could not be Federation or Shelliac members) who are currently in their hibernation cycle, so it stands to reason that there are potentially dozens of species both the Federation and the Shelliac view as impartial/fair enough to decide the outcome(which by extension would likely mean there are a vast number more that both sides could not agree on).

The federation can be so big thanks to his political system, a free association of previously indipendent worlds, so the superstructure don't need a strong control the territory

In the prime time line Kirk's ship visited the edge of the galactic core at least once and the edge of the galaxy at least twice withing five years. I've somehow missed where the Kelvin time line has better propusion systems.

Your vids are great but damn cut back on the LCARS sfx!

The sphere of influence of the Federation would likely be far larger than the volume containing the core worlds. It's highly likely that many worlds would have affiliate status or even be trading partners rather than full fledged UFP membership. If your world happens to be in a region dominated by affiliates or UFP members you're going to reap the benefits even without being a UFP member. Indeed you may not wish to be bound by many of the more stringent UFP membership rules. Many non UFP members have crew members serving in Star Fleet so they gain knowledge and experience and interact with UFP members. Also many colonies of UFP members might become independent in time (or from the beginning) such as Mars or Terra Prime even though they have apparently initially largely human settlers and inhabitants. Other species might have the same or similar structures for their colony worlds. Large numbers of UFP members may not be a stretch 😀🖖

32 Ambassadors on the Enterprise. I remember nothing to indicate that no other ships carried parties of Ambassadors from other parts of the Federation.

Cool Info.

Maybe the answer to the 8000 light-year "problem" is that some writer just thought it sounded good.

"Wake up babe, Star Trek cartography video just dropped"

Seems to me the simplest way to give the Federation size would take the volume of all the contiguous space of the member worlds.

You mentioned that, in "Journey To Babel", from Star Trek TOS, that "only" 32 Ambassadors were aboard the USS Enterprise. Well, that's just one of the ships headed to the conference. What if many ships are carrying Ambassadors to the conference, each carrying about 30 guests? So, possibly, there are about four other starships enroute, which would make 150 members counting all five. Five times 30 equals 150. It isn't rocket science.

The Klingon and Romulan empires are huge as well. There must be a lot of other species within their borders. I wonder what the political situation is there and why it was never mentioned in canon.

I always assumed it was just implied that 8000 ly included stellar space, that is, essentially "2.5-D" as the Milky Way is disc shaped and, while you could keep going 'up' or 'down' into dark space, there's virtually no reason to and so it's not really considered (sort of like the arctic waters for Canada, the US, and Russia largely-strategic, sure, but not really what you'd consider part of their 'nation'.

I think it's just a "general" crosssection of where the federation has influence. It doesn't incorporate non-member planets that happen to be located "in" the federation for instance. Nor all the planets with sentient life that has not invented warpdrive technology yet, eventhough they may technically be "in" federation space too. The Romulans, Klingons etc might see a simpler "federation border", while the federation itself might only view memberworlds and other planets etc with resources, as "theirs" and the rest as others.

I think the idea of inconsistent growth rates makes sense. There could have been a relatively peaceful era of expansion in the early-mid 24th century that eventually led to the wars in the 2340s/2350s. Cardassians being the biggest, but also Tholians, Tzenkethi, Talarians...