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The Universe is a big place. There are over one hundred billion galaxies in the observable universe. Of these 100,000,000,000 galaxies, only one falls under the domain of the Imperium: a barred spiral galaxy some 100,000 light years across, known in antiquity as the 'Milky Way'. At the centre of Milky Way is a super massive black hole (more), it's immense gradational power orchestrating the heavens, binding all the stars orbit around it. Over four hundred billion stars orbit this black hole and of these 400,000,000,000 stars (it is thought that) around thirty billion (30,000,000,000) are similar to the star (the Sun) of our Solar System, that shines it's light upon holy Terra. Nearly all of these stars are orbited by planets of various sizes, the largest the size of Jupiter which are so massive they nearly became stars themselves, all the way down to dwarf planets (but they are not the only stars to be orbited by planets.)
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Of these planets that orbit stars that are similar to our sun, very few in number can support life naturally. In Battlefleet Gothic is is stated that on average there are 75 inhabited worlds per light year sector (200 light year cube). This works out at 70 million inhabited worlds in the milky way galaxy. This is statistically impossible (highly improbable), and it seems logical that most habitable worlds are not natural but instead are artificial, perhaps created in bygone era by ancient and arcane ghods, or more recently by the artifice of the machines of the Dark Age of Technology in alliance with humanity. Either way, I imagine very few would actually be like our Earth, though it the Slann were messing about with worlds I suppose many could be like Earth.

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The number of inhabited worlds in the galaxy seems to be as large or small as the story/ background/ setting needs it to be. In material published by GW over the years there seems to be are between a few million to 70 million (BFG) inhabited worlds in the Milky Way. For the purposes of this fan material of mine, I have plumbed for the later 70 million figure.
In official background the number of worlds that make up the Imperium is a mere fraction of this, and seems to have consistently been a 'million worlds' ever since the ye olde Rogue Trader (first edition) days. However, this seems to he a poetic 'million', a fancy 40K way of saying 'lots and lots' rather than an actual figure, which may be much larger.
If only a fraction of these habitable planets have humans on them, and even less are governed by the Imperium, even a small fraction of such a huge pie will yield incredible numbers. I guesstimate that the Imperium hold around 1-2 of every 7 inhabited worlds, giving a 'true' figure of 10-20 Million worlds under direct control of the Imperium, with many millions more on the fringes and under intermittent control. This leaves around 40-50 million world outside Imperial control and in all likelihood the Imperium knows nothing about them (The Galaxy really is a huge place!).
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Working out the Dark Age figures.
The Milky Way contains over 400 billion stars (in Rogue Trader it is stated as 'four hundred thousand million stars'). Of these 30 billion are thought to be similar to our Sun (a Population I star) with planetary systems, given a potential30 billions Earths (will update this link).
Potential Colonies: During the Dark Age of Technology humanity and their machine allies, claimed all these world. While very few were naturally Terra standard (fluke/ Slann) those that where near to Terra standard were terraformed, and those that could not support life but had 1G gravity were covered in artificial habitats.
Population: The population of Earth doubles every 50 years is unrestricted resource constraints. This gives 13,200,000,000 people by 2050AD, 432,537,600,000,000 by 10,000AD (10K) and a massive 56,693,568,307,200,000,000 by the year 10,900AD which would equate to around eight billion (8,589,934,592) worlds with populations similar to our current earth (6.6 billion), by 11,500AD that would have swelled to 116,108,427,893,145,600,000,000 which would be around 17 trillion (17,592,186,044,416) earth of 6.6 billion, which is far too many! So population growth is not a problem for humans!
Number of Colonies: All in all, I guesstimate around 50 billion or so colonies where set up during the Dark Age of Technology. In the timeline of 40K, humanity started taking conquering worlds from around 10-15,000AD (10-15K) onward, and I guess (using the number above) that they would run out of space around 20-25,000AD (20-25K) right about the time the age of strife kicks in (sweet timing!).
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(from Battle Fleet Gothic) In contemporary 40K each 200 light year (cube) sector on average contains 75 near earth like worlds, which equates to around 70 million for the whole of the universe. Other these only a fraction are under Imperial control.
Humanity lost over 49,930,000,000 colonies during the fall, this is all the worlds and moon colonies that were not terraformed or were unable to naturally support life. Any colony that relied on the artificial STC 'Ecorium' habitats were lost. The lost worlds are known as Dead Worlds or 'Necropolis'.
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These are planets with 1G gravity, a reasonable temp range, hostile atmosphere that is lethal and are totally devoid of all life.
These worlds are the most commonly re-discovered type by Rogue Traders who immediately alert the Adeptus Mechanicus so they may innate a holy Tech-Quest. A Rogue Trader can reap big rewards, especially if STC data is recovered, though this is beyond rare occurrence and most of the time nothing comes of it.
The surface of these worlds are covered with clusters of Ecoriums from the Dark Age of Technology. After 10,000 years the roofs have all but eroded away, the upper rooms filled with dust or lakes of chemicals. One some worlds with little atmosphere, those Ecorium which haven't been hit by mentors are remarkably well preserved.
When humanity fell into civil war during the Psyker epidemic and the machines left humanity to their fate, all those who lived in the Ecoriums of these worlds perished [Note: Only low population world like the Paradise Class survived]. Those who died at the hands of daemon possess Psykers where considered lucky compared to those who fled screaming into the wild only to die from asphyxiation and in utter terror. As all these worlds had hostile atmospheres no human could survive outside, and as the machines had left there was no way for any human to leave. Often littered with dry human remains on the surface unable to rot in the hostile air, arranged in bizarre sculptures and skull pyramids, some with fields of bones stuck into the ground like ivory grass with ‘crop circles' made of the smaller bones arrayed in arcane runes. Though it is rare to encounter a daemonic essence on these desolate worlds it is possible. With such an abundance of sacrifices during the fall, the power of several billion souls enabled some daemons to bind themselves to the material realm or open warp gates where they turned a section of the Ecorium or the bone fields into a mini daemon world. Even rarer is finding any technology that hasn't be smashed to bits by the rampaging daemon possessed Psykers 10,000 years ago.
Deep in the Ecoriums all are dead, but some life and strange ecosystems may remain powered by the eons old plasma rectors chugging away on low mode in the background that escaped the onslaught. The life is similar to other low light life, such as creatures which live in caves, pale white and often translucent evolved from the smallest of insets along with sea of stagnant algae.
Dead worlds remain dead worlds and are deemed unsuitable for human habitation. Much of the worlds recorded in Imperial space are dead worlds, since the great crusade the Rogue Traders in their millions have been in operation for just under 10,000 years have found and marked over 15 billion Dead Worlds and the number keeps growing year after year.
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Cult World: The Cult of the Machine, the larger 'umbrella' cult for many divisions with the Adeptus Mechanicus being one, have been known to lay claim to some of these dead worlds, reclaiming them for the machine ghod. Cult worlds are strictly off limits to everyone except members of the Cult. They are marked 'Dead World under quarantine' like all the other dead worlds. Considering the number of dead worlds, finding a cult world is like search for a needle in haystack.

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Whether terra-formed during the Golden Age of Technology, natural with a few tweaks or the super rare worlds corrected by the Slann in antiquity, all paradise worlds have one thing in common; they are able to support life naturally.
Paradise worlds are the base for nearly all the worlds in the Imperium and come in a verity of technological levels from base nomad worlds, to high-tech new Hive worlds and single purpose worlds like marigolds. All these worlds are post fall, and are the survivors of the fall. The one remarkable think about all Paradise Worlds with survivors is that during the Dark Age of Technology they were designated as 'Noble Worlds'. All the descendants are form Dark Age of Technology's Noble families or their immediate subordinates. There are no Ecorium on any Noble World from the Dark Age, though the Adeptus Mechanicus have been building them anew...
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These are lush virgin worlds that have no human populations inhabiting them when re-discovered. The perfect world naturally support life and are renowned for the health restoring properties. These worlds are re-colonised, and often reserved for Imperial nobility and institutions. Massive underground bunker complexes with sprawling surface mansions are built to house the rich and powerful. These worlds soon become heavily guarded, and a place where various factions come together to negotiate treaties and form alliances.
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Very similar to the Eden world above, but with an indigenous people who have devolved through choice or need to a nomadic existence. Nomads live in harmony with their environment, though quite often for them to continue to be nomads often means the conditions are harsher the the Terran standard or the population was reduce to a mere handful of families during the fall. Nomads have often lost the genetic distinctiveness of the original Noble families through the castes mixing and various trait becoming recessive.
On occasion the Imperium will clear out the indigenous people to make way for Noble World, or leave them to eventually act as workers.
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Similar to the Nomad world though further along in their re-development. Often select families retain some of the traits of the original Noble families though this is rare. Those that are part of the Imperium enjoy the benefits of it's 'protection' and civil wars are rare.
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Further advanced and fully on their way to recovery. The population has increased significantly and science and technology are starting to emerge. The Adeptus Mechanicus step in to guide this world to a brighter future.
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Teeming with human life. Very similar to our world, or what our world will become in the next 50-100 years. Such massive populations would not be possible without Adeptus Mechanicus assistance, and often these super massive populations are only possible because of the Ecorium based technologies they bring. Many worlds have welcomes the technology, only to find out later that it will consume them all and turn the world into a hive.
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Proto-Colony: These worlds are where the violent thugs and criminals of the Imperium are dumped. It is usually where revolutionaries who are judged by the Inquisition to be free of chaos taint end up, and whole armies can end up here. Prison worlds have limited resources where warbands roam the land (mad max style) and are fighting constant wars. This constant warfare is further helped by the 'wardens' who provoke trouble be destroying settlements from orbit, dropping food and weapon packages, and sometimes 'recruiting' whole warbands for Imperial service (leaving a power vacuum). Sometimes on more established worlds the wardens play favourites and allow certain factions to rise. Humans who have lived on a prison world gain an appreciation of the Imperium.
It is of note that some nomad and feudal worlds are in fact prison worlds. The clue to the actual status is the presence of satellites and space stations (guard towers). Quite a few of the prime recruiting worlds of the Imperial Guard are 'artificial' with new prisoners dumped into polar or desert regions. On such worlds the Imperium often hides it's true nature and the locals will not believe the 'otherworldly' visitors. The culture and myths of these these worlds often put forward an idea of daemons in human form who come from the wastes.
As such this world is a sub-class and can be applied to any other world. Almost any world can become a prison world and often the line between good government and prison world is blurred. A prison world can become a regular world in time and start shipping 'criminals' to newly founded prison worlds. in many ways a prison world is also an early stage to being a colony world (hence proto-colony).
Note: This is because the Imperium view certain types as 'pioneers' or 'frontiersmen' and these personalities act up in civilized worlds. Hence these types, which have often committed crimes in civilized society are packed off to the frontier to do what they do best - grab everything for themselves (often from foul xenos), and in time return to the Imperium. All human types are sacred and there to serve the Emperor. There are no pirates for example, because the pirates are caught given papers and become privateers. their only restriction is that they can not return to civilized society (unless they go through the Imperial Guard and win resettlement rights).

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Hugely overpopulated and repeating the mistakes of the past. The Adeptus Mechanicus are forced to use Ecorium (Ecopolis) technology though in a highly modified and in a far more open format. These worlds often have extensive industry overseen by the Adeptus Mechanicus, and often become Forge Worlds in time.
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This is a habitable planet that has being consumed with the industries of the Adeptus Mechanicus. The natural world ecosystem is dying, and more and more of the population is house in ecopolis and have to wear environment suits. This is considered a transitional stage to becoming a full Forge World.
These worlds supply the local needs of many the planets of the Imperium which are self governing and not affiliated to a single Imperial institution. This includes eden, nomad, feudal, civilized and global worlds with supplemental support of hive worlds.
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The Inerex (from the Horus Heresy Novel) was one. On these worlds colony level technology remains (mostly) intact though the Iron Men are long gone and the core of the STC with it. The humans have a good level of technology and use implant technology for instant learning similar to the technologies used by the Adeptus-Mechanicus.

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The surface of this world is overrun with a vast techo-gothic sprawl of industry covering virtually every square inch. The surface of these worlds no longer naturally support life, the atmosphere poisoned beyond repair. Hideously over populated they rely on the Dark Age technology to house the population and surgery (servitor) to control them while the carry out the mind numbingly repetitive tasks the assembly lines without errors.
Forge Worlds supply the Imperium's institutions (those above local planetary level) and the Imperial war machine. Security is exceptionally tight, even for an Imperil world, and are effective 'no fly zones' to everything except the Adeptus Mechanicus.
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Orbital Ecorium or full Ecopolis. Massive Space Stations arrayed in geostationary orbit around the world's equator, often with gravity lifts to the surface below or atmosphere siphons. These are literally Terra in Space can house millions of people and are often sued to supply ship yards with personnel. These are basically an extension of the forge world and are class as a sub-category of forgeworlds.
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Some of the Imperial Navy's ships are so vast and contain so may Ecoria that they are literally a world in their own right. Powered by the never ending Plasma Engines, the environment recycling systems will last for eons. Along with smelting and scrap recovery to manufacture munitions, these ships are highly self sufficient. They can stay in deep space for hundreds of years if need be, prowling the dark like great sharks.
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The Imperium
The rule elite are made up of noble houses, the powers that be.
World Governments
Using the feudal system of the Imperium the worlds themselves are run as a manor under a lord. The prime minister would be equivalent of a Villain.
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The Imperium operates a complex banking system that levies a tithe on all member worlds. The money of the Imperium is pegged to these tithes. The standard imperium currency is the Throne Gelt, a 'credit' redeemable against the tithe due on a given world. Collection of Gelt offset the tithe, and if a world collects enough gelt through trade can hand it back to the imperium as 'proof' of tithe fulfilled. Any shortfall is made up in the removed of valuables.
This creates and interesting system where the Gelt has not set value, and it deemed a percentage of tithe. This mean on any given world, the gelt will vary in value tremendously. This is done so that a worlds are not over taxed in goods that are rare, a power-field generator will be fantastically expensive on a primitive world (may be the only one) and would require masses of Gelt, whereas on a Forge World it would be relatively cheap. However, on the primitive world water is cheap, but on a forge world it is expensive.
Gelt are pegged at percentage of tithe due, and the tithe is measures against the world actually local (world) economy and uses their prices. The standard Imperial Credit, the Throne Gelt, if worth 0.000000000001% of the tithe due. It is written a '1' (as in 0.00000000000# where the face value replaces the '#'). This affects all the credits in circulation, and half Gelt as not stamped '.5' (as it s already assume to be part of a decimal number written in shorthand - 0.00000000000# + 0.5 = 0.000000000000.5 which has too decimals!). Therefore a half Gelt is stamped '05', Centi-Gelt 001. The is not such thing as a Gelt with a value being higher that 1. Multiples of Gelt are referred to '# Gelt' and are are usually traded as notes*
* error: (They do not Promissory Notes). Only Governmental banks can trade in gelt (they have to pay it, and it comes via taxation on off planetary goods (as only off planets have them, all currency has to be exchanged for local currency to be spent, though some worlds do take Gelt as a tradable commodity.) The Government is reasonable for the payment of Gelt and the Imperium only takes Gelt. The alternative is to supply raw materials (which includes people/ draft) but these are traded as Imperium values and can be very expensive in some cases (much better to acquire gelt from other worlds).
The only way to obtain Gelt is from another world or from an Imperium institution.
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