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Stellar CartographyIntroduction The United Federation of Planets extends some 2500 parsecs (about 8000 light years along the galactic plane as well as 300 parsecs (about 1000 light years) above and below it. Mapping this volume of space is a Herculean task. In order to assist Starfleet in carrying out its task of exploring and charting the galaxy, the Stellar Cartography Office has created certain standards for mapping large volumes of space.
Fig 1.0 The Federation straddles a and b quadrants, with most UFP territory in the a quadrant. Of more interest to cartographers on a local scale is the sector quad. A sector quad is an area 300 parsecs x 300 parsecs x 300 parsecs (about 1000 light years x 1000 light years x 1000 light years). Each quad is broken into sector blocs of 30 parsecs x 30 parsecs x 30 parsecs (about 100 light years x 100 light years x 100 light years). Each bloc is divided into sectors of 6 parsecs x 6 parsecs x 6 parsecs (about 20 light years x 20 light years x 20 light years). Each Quad is numbered (001-999), in the order it was explored by the Federation. Federation territory covers 12 quads (numbered, creatively enough, 001-012) Blocs are likewise numbered 0001-1000. Sectors within a Bloc are numbered 001-125. A Starbase typically is assigned to a single bloc, while a Star Station is assigned an individual sector. Stellar co-ordinates are then given as quadrant-quad-bloc-sector-hex mark z value (in parsecs). Therefore, the co-ordinates b 004 555 095 303 mark 0 refer to Archanis, a Federation outpost along the galactic plane on the Klingon Frontier. The mapping system is loosely based on the hex map system pioneered by the Traveller � system. This cartography system is, however, system independent and would work with any system by any publisher. The size of each unit of volume is established by existing Star Trek canon. Size and Structure of the United Federation of Planets The United Federation of Planets is located - and that is accepted by all official sources - in the heart of the known Star Trek universe, about 24000 light years away from the Galactic center in the Local Arm of the Milky Way. The Federation is the largest of the six known empires in local space and the sole power to extend over two quadrants - the Alpha- and the Beta Quadrant, therefore the Federation takes a special position concerning the Jankata Accords signed by all powers. Although the quadrant border, the position of the most important planet: Earth, with the Federation Council, the Federation President's Office and Starfleet Headquarters, is situated nearly in the center of the territory of the Federation, the share of the total area that is located in the Alpha Quadrant is nevertheless larger than the part in the Beta Quadrant.
Surrounded by the 5 other larger alliances and empires, and a dozen smaller ones like the Talarians, the Tzenkethi, the Gorn and the Trill, the Federation is a typical "middle power" - it is the "connecting piece" between the classical empires of the Klingons and Romulans at the Eastern border in the Beta Quadrant and the territories of the Cardassian Union, Bajor, Ferenginar and the Breen at the Western border in the Alpha Quadrant, regions that were not discovered until the 24th century. Undoubtedly the United Federation of Planets is the strongest power in the Alpha and Beta Quadrant, however, the officially fixed extension of the Federation (8000 light years) is so large that the resulting problems can't be simply ignored. Adding to the confusion, the dialogue (primarily in DS9, but also in Enterprise and TNG) set the diameter of the Federation much smaller than the �official� source material suggests. While not particularly important for the purposes of writing any individual story, it does make mapping the Federation and its environs for war gaming and role-playing purposes more difficult. The purpose of this document is to reconcile (so far as it is possible to do so) the various guesstimates of the size of the Federation and the surrounding powers. 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 100 light years from DS9. 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 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 200-500 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 diameter of the Federation, we can indeed say something about the size of the Federation by analyzing the given distance. Undoubtedly, the Federation must have a horizontal 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 200-500 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, Rigel Kentaurus, also known as Alpha Centauri. Alpha Centauri is a binary star system, Rigel Kentaurus a is a G2V subdwarf (a star identical to our sun) and it is orbited at a distance of 11 au by Rigel 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, Rigel Kentaurus is very close to the main traffic corridors of the Federation as well. In all likelihood Rigel 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 freetraders 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. 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 π 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. Turning to 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 much larger (c. 800+ light years diameter) Federation 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. Perhaps the Antares yards orbit a much closer, more stable red giant star that was named "New Antares" or "β Antares" by its discoverers. The only other 'problem' star is Canopus (α Carinae), an F-class super-giant star 100-350 light-years from Earth, in the constellation Carina. It is the second-brightest star in the sky (second only to Sirius). Notice the extreme range of distances given for Canopus. This is because we aren't 100% sure if Canopus is a class I or class II giant and at a certain point stellar distances are guesses. If Canopus is only 100 light years away (source; Columbia University) it poses no real problem. If it is 313 light years away, as calculated by NASA and the University of Illinois (among others), it is a little more problematic but not extremely so. If the radius of the Federation fluctuates between 65-200 (q.q.v.) light years, then Canopus is only a few parsecs over the 'border'. However, we also have several references to Canopus as being part of the Federation. α Carinae II is mentioned as the location of the M-5 tests in TOS episode The Ultimate Computer. α Carinae V is mentioned as the home of the Drella, a creature that derives sustenance from the emotion of love in the TOS episode The Wolf in the Fold. It is also mentioned as the home of the New California colony in the fan publication The Starfleet Officer's Manual. The poet Phineas Tarbolde, a resident of the Canopus planet, wrote "Nightingale Woman" there in 1996, considered to be one of the most passionate love sonnets of the last couple of centuries. Here, the dialogue clearly establishes that we are talking about the real Canopus. Canopus is such a galactic landmark that current space probes such as Pioneer, Voyager, and Galileo use it as a reference point. However, the M-5 was a super-secret project. Perhaps the Federation chose Canopus, a remote star far from normal Starfleet proving grounds, to test the system so as to keep it from the prying eyes of foreign intelligence agents. Does this extend the diameter of the Federation out to 300 light years? Perhaps, or perhaps Canopus is a non-contiguous part of the Federation, sort of a Guam-in-space. Either answer works, you will have to decide for yourself. On the other hand there is a large number of near real stars which undoubtedly belong to the Federation, for example Tau Ceti, Vulcan (40 Eridani-A), Gamma Hydrae etc., supports a quite small Federation (<200 light years), while the also often mentioned. While there are rather distant 'boundary stars' mentioned, it is entirely possible that we are referring to stars much closer to Earth than the generally accepted 'boundaries'. Given this, the dialogue support for a 'small Federation' seems particularly strong. 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 100 light years (or a radius from Earth about 50 light years) we'd have 1400 star systems containing over 2000 stars including over 125 likely to support life as we know it. Expand your diameter to 200 light years and according to NASA estimates, you'd have 14,000 stars. Within 250 light years of Earth there are over 260,000 stars again according to NASA estimates. In any of these cases there is plenty of room to support the requisite number of home worlds and colonial worlds for our Federation. Solving the problem 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 series dialogue seems to support the idea of a Federation that is about 200 light years or less in diameter. But doesn't Picard's statement to Lily in "Star Trek: First Contact" seem to support the idea of a large 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 200 light years (an area of about 31915 square light years along the galactic plane). It does appear that the UFP is not a sphere and its radius measured from Earth to its frontiers varies between 65 and 250 light years with 100 light years being the median distance. There is some official support for these conclusions. According to the 2002 publication Star Trek Star Charts by Geoffrey Mandel, the Federation has a core diameter that fluctuates between 65 light years (distance to the Romulan Neutral Zone from Earth) and 100 light years (distance to the Klingon Neutral Zone). Other borders are between these two figures. The Cardassian/Bajoran interface is about 75 light years from Earth. More obscure borders are somewhat farther away, Cestus III is 215 light years and the Tholian interface is about 250 light years from Earth. All of these measurements are reasonable, since the Gorn and Tholian frontiers are touched only by "fingers" or "corridors" of Federation space and not be the contiguous mass of the UFP. Furthermore, they are remote frontiers that don't often enter the storyline. Mandel "fills in" the rest of the alleged 10,000 light years diameter of the Federation with non-contiguous territory between and around the other powers of the Star Trek Universe. While one can understand his reasoning on this, it makes little real sense. If I am a culture 5000 light years from Earth, why would I bother to join the Federation and send a set of representatives to Earth and receive Federal bureaucrats in return to join a system I can only get the most limited benefit from? Wouldn't it make more sense to simply exchange ambassadors and conduct friendly diplomatic relations with the Feds while maintaining my independence perhaps forming a confederacy with more proximate, like-minded societies? Nevertheless, one can ignore the non-contiguous regions of the Federation on the Star Charts and be left with a reasonable representation of the size and extension of the UFP. While the Star Charts are useful for mapping the core of Federation space. It would have been nice if a set of xyz co-ordinates were included as they were in the original Star Trek Maps folio to facilitate calculating distances between stars. There is an excellent Windows program called ChView (download it here) which was originally developed to view the worlds of C.J. Cherryh in a 3-D format. You can use the 150 ly or 250 ly datafile to view the area of space occupied by the Federation. In the alternative, one could use a system of mapping similar to the one pioneered by the Traveller game by Far Future Enterprises (Mark Miller's new company). A Federation sector is 6 parsecs by 6 parsecs. This would approximate a subsector in the classic Traveller mapping system. A sector bloc would be 5 sectors by 5 sectors (approximating a sector in the Traveller mapping system). If one assumed the Federation to be about 500-600 light years in diameter (big enough to include Canopus and Antares) then it would be broken into about 30 sector blocs. A smaller Federation, say one about 250 light years in diameter, then only 9-12 sector blocs would be required to map all of Charted Space. If one used the classic Traveller mapping and planetary notation system, literally dozens of programs are available to chart and map space. The best are Galactic 2.4 and Heaven & Earth. You will have to make some modifications to the datafiles in either program to make it 'Trek-friendly' but the results are worth it. | |||||||||||||||
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