Stellar Cartography

Size of the Federation

The writers of Star Trek have kept the size of the Federation and the approximate dates of the adventures of the crew of the USS Enterprise deliberately vague. While this is fine as a storytelling device it is a real headache if you want to use the Star Trek universe as a basis for a war-gaming or role-playing setting. Star Fleet Battles, the first major attempt to define the Star Trek universe as a game setting, simply tossed caution to the wind and decided that the federation was a sphere about 10,000 parsecs across. Unfortunately this is ludicrous. The center of the galaxy is a 'mere' 7600 parsecs (about 25,000 light years) away from Earth and no existing Star Trek lore holds that the galactic center is within Federation space. With all respect to Mr. Cole, he is plain wrong about the scale of the Star Trek universe. In the Next Generation movie First Contact, we are told the Federation is about 8000 light years (~2450 parsecs) across. This is about 25% of Steve Cole's estimate and even this a bit much to settle in a period of 200-400 years, even with 150 member systems. There are real problems with a 'large' Federation.

The official size of the Federation

According to dialogue in Star Trek: First Contact the size of the Federation is established at 8000 light years. This is about 2455 parsecs (a parsec is the Parallax of one Second or about 3.258 light years)

If the Federation were a sphere some 8000 light years in diameter, it would take a ship equipped with the most advanced warp drive years to travel across it.

Yet the established canon has the Enterprise moving rather quickly between the Klingon and Cardassian frontiers, even though it is also established that the those powers are on opposite sides of the Federation. Consequently, even at maximum warp, a patrol ship would need several years to travel through the giant empire only once - not to mention the fact that the vessels of everyday traffic like freighters and personal transporters mostly can only attain the cruising speed of warp 6 and furthermore have to stop at a starbase after some weeks of flight for maintenance, repair or fuelling (typically, Federation-designed ships need tons of deuterium and a antimatter replacement every 3 years). These circumstances increase the already decades-long travel time by many years. Clearly the Federation can't be 8000+ light years in diameter.

Size determined from the episodes

Most dialogue in the episodes and movies, however, seems to favor a Federation a few hundred light years in diameter.

Although the official extension of the Federation given by the official publications is fixed too often and too definitely not to be regarded as an affirmed basis figure in the Star Trek universe, amazingly in most episodes and movies, which finally have established the dimensions of the Star Trek Galaxy, the size of the Federation appears to fluctuate.

This is especially in The Next Generation episodes, the shown maps of the galaxy, which are usually based on the official Federation size or even depict larger space regions, contradict completely with the shown travels of the Enterprise within very limited time (usually hours or days at maximum). But also in the other Star Trek series, maps or given distances don't match with the longest possible duration for the journeys (e.g. the time between two episodes). In Star Trek: Deep Space Nine, however, first attempt at consistency for the distances in the Star Trek universe occur, because detailed localized maps are used instead of maps of the entire Milky Way, and the mentioned distances to important planets (Cardassia, Ferenginar, Trill) are all within 30 parsecs (about 100 light years) of DS9.

With its three-dimensional astrometric maps, Voyager hasn't gone into the size of the Federation yet, but the permanent disregard of the Beta Quadrant (the most obvious error was in "Barge of the Dead": "the Borg have assimilated a Klingon Bird of Prey in the Alpha Quadrant") and doubtful ideas like the Jankata Accords, which actually shouldn't apply to the Federation as a inter-quadrant power, doesn't bode well for the future.

Nevertheless, using what evidence there is from the dialogue one can begin to get a handle on the size and dimensions of the Federation. Generally speaking, the established facts from the films support a "theory of a small Federation" rather than official "large Federation theory".

Map from Star Trek: The Next Generation - [019] Conspiracy

The map in the Next Generation episode 'Conspiracy' shows a Federation about 200  light years (about 60 parsecs) in diameter. Additionally, Prof. Galen proposes to travel from DS5 in the upper b quadrant to Indri VIII in the lower a quadrant within a few weeks via SHUTTLE!  Clearly the Federation can't be thousands of light years across if such a journey is feasible. In the DS9 episode "The Way of the Warrior" we hear the quote "At maximum warp, Cestus III is almost 8 weeks away from the station."

It is a rather unexpected case of luck that the distance to a planet at the border of the Federation in the Beta Quadrant is mentioned. On the basis of the statement that Cestus III (which is fixed as a point at the "Eastern" border of the Federation) we can guesstimate the distance between the Gorn and Cardassian frontiers (and, by extension, the 'east-west' axis of the Federation). Although we don't know exactly what the "maximum speed" is considered to be, we can assume a speed between warp 9 and warp 9.9 - what results in a small Federation diameter of 200-800 light years.

 This is backed up by the DS9 episode "Trials and Tribble-ations"

"The distance to our previous location [near Cardassia] is almost 200 light years [...] We're orbiting K-7, one of the old deep space stations near the Klingon border."

This quote does not directly deal with the size of the Federation, but because the Cardassian and Klingon Empires directly adjoin the Federation in the "West" / "East" and therefore the distance between these two empires defines the distance across the Federation at least between the Cardassian and Klingon interfaces, we can indeed say something about the size of the Federation by analyzing the given distance.

Assuming that the Cardassians and Klingons are not diametrically opposite one another across the Federation (most maps, including the semi-official  Star Trek Star Charts support this assumption). Undoubtedly, the Federation must have a z-axis diameter of less than 200 light years according to the statement. We can even specify this assumption: according to the map of the Bajor Sector in the ST:DS9, Starbase 375 (which is located at the border of the Federation in the Alpha Quadrant) is located approximately 30 light years away from DS9, whose distance to the Defiant is merely a few light years at the moment of the time travel. Hence, a Federation diameter of about 170 light years is used in this episode, what again supports the "theory of a small federation".  

However, on the other hand, the figure is a bit too low in comparison with other DS9 episodes. Nevertheless, we can still argue that Dax roughly rounded the distance and that K-7 is located in the "lower part" of the Federation-Klingon border, what would considerably boost the distance to DS9.

Federation diameters of 400-800 light years are backed up in several other DS9 episodes as well.

The size of the Federation in view of real stars

Although most real stars that were mentioned in Star Trek as Federation outposts or outposts close to the Federation are located within 200 light years from Earth and therefore seem to clearly fix the core region of the Federation, there are four stars which, at first blush, are very far away from Earth and are nonetheless within or near Federation space. These three stars - Deneb, Antares, Canopus and Rigel - are therefore often called "boundary stones" of the Federation. They mark the outmost borders in the West, North and South of the sphere of influence of the Federation, and they consequently restrict its region to a certain size, because at the sole "open" side - the East - the empires of the Romulans and Klingons limit the extension of the Federation.

The star Deneb, which is about 2600 light years away from Earth, marks the Western border of the Federation, because Farpoint Station on Deneb IV is regarded as the last outpost before "the great unknown that starts beyond" ([TNG] Encounter at Farpoint). This assumes that we mean Deneb itself and not the much closer Deneb Kaitos, a dying supergiant star similar to Arcturus. Deneb Kaitos is only 96 light years from Earth. A frontier being about 100 light years from Earth is more in keeping with the idea of a Federation some 200 light years in diameter.

The next problem star is Rigel. Rigel is difficult for several reasons. Firstly, it has to be a star system that can support multiple inhabitable planets. Furthermore, it has to be proximate to the main traffic corridors of the Federation.

These twin requirements make Beta Orionis (Rigel) a poor candidate for the "Rigel System". We have Rigel XII which is nowhere near the main traffic corridors of the Federation, we know this because, the mining colony on Rigel XII "would never get help this far out" ([TOS] Mudd's Women).  It is unlikely that a camp so far out that it would not likely get a response to its distress calls is located in the "most heavily populated system in the Federation'. On the other hand it is entirely possible that the mining camp doesn't orbit "Rigel" at all, but is something like Camp XII of the Rigel Mining Co. The Rigel Mining Co. could be based in Ft. Worth for all we know.

On the other hand the "Rigel system" is called the most heavily populated system in Federation space, with 7 inhabited planets. If this is the system orbiting Beta Orion (Rigel), then it would be over 770 light years from Earth, but there are good reasons why it may not be. Rigel is a blue super-giant, an O class star that is very large and very hot. Such a star is deemed unlikely to support a planetary system as it is too hot to allow rocky planetary masses to coalesce around it.

"Rigel" could be another star, namely, Rigil Kentaurus, also known as Alpha Centauri. Alpha Centauri is a binary star system, Rigil Kentaurus a is a G2V subdwarf (a star identical to our sun) and it is orbited at a distance of 11 au by Rigil Kentaurus b, a K2V subdwarf. Both Rigel Kentaurus stars could support earth-like planets under the right conditions making Rigel Kentaurus a good candidate for "the most populated star system in the Federation". At an average distance from Earth of 4.4 light years, Rigil Kentaurus is very close to the main traffic corridors of the Federation as well. In all likelihood Rigil Kentaurus is the "Rigel System" of Star Trek lore.

Of course, that leaves the problem of the Orion Colonies. The Orions are an independent bunch. They are free traders and freebooters by turns (sort of like green skinned Space Vikings). Orions practice slavery and are known to traffic in Orion women (whose erotic skills are famous across the galaxy). Obviously, such a libertine and stratified society would be unlikely to exist in the core regions of the Federation or in a system that is home to a founding member of the UFP. Most fan wisdom, and a fair amount of logic, suggests the Orion colonies are near the Federation frontier. Captain Pike mused about retiring from Star Fleet to pursue a life as a merchant captain in one of the Orion colonies ([TOS] Menagerie). The implication was that the Orion colonies are along the frontier. Also, it would make sense for whatever star system we choose to be in the constellation Orion (hence the name "Orions" for its denizens). Fortunately, there is a star that fits the bill nicely. A G4 class IV-V star called HR 1988 Orionis. It is only 138 light years from Earth and is known to support at least 2 Jovian planets. HR 1988 Orionis is a G4 IV (sub giant) or V (main sequence dwarf) star, similar to our sun (a G2 V main sequence dwarf) it is visually close to Rigel in the night sky and it is an "Orion" star. This neatly places the Orion colonies out on the frontier and explains the association between Orions and Rigel.

Another possible location for the Orion colonies comes from the Star Trek Star Charts which places Orion at  π3 Orionis α, an F6V main sequence dwarf about 26.18 light years from Sol. Like HR1988 Orionis, π Orionis α is an "Orion" star. It isn't as 'far out' but is is closer to the core of the Federation and it orbits a star that might support life in the real world, making it an attractive choice as well and one with better cannon support. In either case, if the Orion Colonies aren't at  β Orionis (Rigel) and there is a Rigel system much closer to Earth (Rigel Kentaurus), there is no reason to believe that β Orionis which is over 770 light years away is actually part of the Federation.

Having dealt with the two most distant stars from the classic Trek canon, we are left with Canopus and Antares. These bright stars are unmistakable, Canopus (Alpha Carinae) is used as navigational referent for real world spacecraft and Antares is one of the brightest objects in the sky and it lies within 5º of Sol's elliptic. Like Canopus, Antares is also used as a navigational referent for real spacecraft. No other stars currently discovered could be confused with either Canopus or Antares.

Let's begin with Antares, which is firmly established as the boundary of explored space (In the TOS episode "The Changeling" Uhura's song "Beyond Antares" is about having one's heart in exploration, and "beyond Antares" lays the unknown). Of course, being the limit of explored space doesn't mean there is any permanent Federation presence at Antares, only that Starfleet vessels have visited Antares. Antares is a real star. It is a giant red binary star, the brightest in the constellation Scorpio (its formal name is α Scorpii), about 424 light-years from Earth. Many consider it to be the "boundary stone" of the coreward extension of the Federation. Indeed, Antares can be used to argue for a Federation at the high end of our range (c. 800+ light years diameter) because it seems illogical to place one of the most important yards of the Federation (the Antares IV Starfleet Yards) at the border of totally unknown space. Once again this assumes that the Antares IV yards actually orbit Antares and not some other star. There are good reasons to doubt that Starfleet would place such a critical asset in orbit around Antares. As was pointed out, Antares is a real star; it is also a very old and unstable star. Scientists believe that it has started to form iron in its core, meaning its fuel is nearly depleted. Within the next million or so years, Antares is expected to explode in a supernova (becoming the brightest object in the galaxy for several years) and while a million years is a long time, there is no way to know exactly when the detonation will occur. It could be anytime from 400 years ago to a million years from now. It seems illogical to put a major starship yard so close to what is quite literally a ticking bomb. Antares does have an unseen companion (a star normally obscured by light from Antares), A B2v (very hot, blue main sequence star) called β Antares that orbits Antares at an average distance of 550 AU (or about the distance from our sun to the inner most part of the Oort Cloud). β Antares was discovered in 1813 during a lunar occulation of Antares. The Antares IV yards are most likely in a planetoid belt orbiting this companion star. However, if Antares is a contiguous part of the Federation, we are looking at a diameter of about 800 light years.

Canopus (Alpha Carinae) is an F0 Ia yellow-white super giant, and while it is unlikely to host planets, if it did and such a planet orbited at sufficient distance, it is just possible it could be a colonization candidate (as Star Trek assumes it will be and will eventually be home to the famous poet Phineas Tarbolde according to Kirk in City on the Edge of Forever). However, Canopus is a mere 98 parsecs (about 320 light years) distant so it's inclusion in the Federation isn't a huge problem assuming a diameter of about 800 light years centered more or less on Sol.

The minimum size and the growth aspect

Despite all speculations and assumptions about the "theory of a small Federation", it should be taken into consideration that a too small Federation is as problematic as a too large one. It is an official fact that there are at least 150 Federation members, which all have their own home planet and possibly several dozen colonies, therefore for all these planets, a certain space is needed.

Of course, having 150 members does not mean that 150 discreet star systems are needed to support those members. In the Sol system alone we have three different Federation members, namely; the United Earth Republic, the Republic of Luna and the United Martian Colonies. Rigel boasts 7 inhabited planets, five of which are Federation members. In the entire film series, over 500 different planets are mentioned. Assuming that each Federation member sponsors or maintains about 5-6 colonial dependencies on average, we would expect about 750-1000 or so inhabited worlds within the Federation. Obviously this requires some space. Of course, not all stars have planetary systems and not all planetary systems contain "class M" planets.

If we assume a Federation with an average diameter of 650 light years (or a radius from Earth of about 100 parsecs) we'd have almost two million star systems containing over four million stars including over 15,625 that might be able to support life as we know it. In any of these cases there is plenty of room to support the requisite number of home worlds and colonial worlds for our Federation as well as allow for lots of unexplored space, pre-warp civilizations and other available room for growth.

Putting is all together

This leaves us a Federation that is 250 parsecs across (or about 800 light years) - on the high side of our small Federation but within a reasonable margin of error considering the inconsistencies in the cannon itself and leaving plenty of room to account for growth. The core settled regions are probably in that central 100 – 200 parsec sphere while the region reaching out towards Antares is the 'Outback' of the Federation. Interestingly enough, the Next Generation films did refer to such a region on more than one occasion.

On the Star Fleet Battles/Federation and Empire maps, The Federation is 10 hexes in radius, given the calculations above, that means each hex should be 40 light years or about 12 parsecs across (not the 500 parsecs given in the official Star Fleet Battles materials) representing a 'sector quad' of four 20x20x20 light year sectors. However, since this correction has no impact on SFB or F&E game play, it isn't a major issue but it does bring the mathematical model of the Star Trek universe into sharper focus.

Speed of Warp Starships

Having established the approximate size of the Federation, we can further assume the Romulan and Klingon Empires are adjacent since they obviously had diplomatic contacts and technology sharing agreements with each other and therefore borders of each are about 400 light years distant from Earth. This number is important since it establishes the relative speed of Subspace radio. In the classic Trek episode The Balance of Terror Lt. Uhura tells us that it will take about 3 weeks to receive a reply from Earth. Looking at the tables below, a subspace radio message would go from the frontier to Earth and back in about 27 days - or 'about three weeks' just as Lt. Uhura predicted.

The only fly in the ointment is the two trips the Enterprise took to the galactic rim. If the "rim" in question was along the z-axis it would take Enterprise over 2 years to reach it under normal operating conditions. If the rim in question is along the y-axis, it would take over 30 years. Of course, we are not stuck with plodding through space to get to the rim, Star Trek lore provides us with a loophole - or more accurately a wormhole. If there is a stable wormhole leading from some point inside the Federation to a point near the galactic rim, those missions are easily explained. We have an example of a stable wormhole in Star Trek: Deep Space Nine. Of course, the Bajoran wormhole is mentioned regularly and often but no mention is made of the wormhole to the rim.

Of course, in Deep Space 9 we have a wormhole which stretches halfway across the galaxy, so a much shorter wormhole between some point in the Federation and the galactic rim isn't too far fetched given the existing canon. This renders the trip to the galactic rim plausible while still explaining why the Bajoran wormhole is so valuable – it is much larger and leads to populated regions of the galaxy rather than a desolate frontier like the galactic rim.

Warp Speed Tables

For FASA ships, simply use the warp speeds derived from the Starship Construction Tables.

Some Final Thoughts

We have the quote from 'Star Trek: First Contact' that says "The Federation consists of 150 planets, spread over 8000 light years". The Star Trek Encyclopedia says that the distance 'across the Federation' is 10,000 light years. However, dialogue takes precedence over even 'official' publications and just about all the TNG series dialogue seems to support the idea of a Federation that is about 200 light years or less in diameter. Of the Boundary Stone stars, it seems only Antares and Canopus must be within the Federation. Taking the more distant of the two (namely, Antares) this gives us a Federation about 800 light years in diameter rather than 8000.

But doesn't Picard's statement to Lily in 'Star Trek: First Contact' seem to support the idea of a huge Federation? Not exactly. He said the Federation was 'spread' over 8000 light years, not that it had an 8000 light years diameter. A circular area of 8000 square light years along the galactic plane requires a diameter of a mere 100 light years. Consider the geometry, the area of a circle is a=πr², so the diameter is d=2√(a/π).  Plugging in Picard's area figure of 8000 light years we get 2√(8000/π) ≈ 100.925. If we assume an area of 10,000 light years, the diameter is about the same, roughly 113 light years.

Thus the smallest practical diameter of the Federation is about 100 light years or about 31 parsecs. A roughly spherical Federation about 100 light years across is a 1,000,000 cubic light year volume of space. The largest practical diameter according to established dialogue is about 800 light years.

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