that's not much feedback so far ... anyway, here is how it starts.

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Part 1 - Leaving home

2083 was the year humanity began to anticipate its approaching end. It was the year when Hubble IV detected something new in the solar system. Something that came from outer space crossing the solar system. That something turned out to be a small exoplanet. The passing of the traveller resulted in excitement, once the first shock had been overcome and once it turned out that was no direct threat to earth, since it would pass in a safe distance of half an AE. Science was thrilled - and the traveller was the target of a whole armada of manned and unmanned expeditions. In the end, it was a rather boring piece of rock, ice and Helium. However... it was large enough to drag a significant part of the asteroid belt between Mars and Jupiter with it. And this tail of thousands of rocks turned into a cloud that tumbled through the inner solar system.
2083 was the year in which the first small asteroids hit earth and crashed in the atlantic ocean. The resulting tsunami spared the american continents - but it washed away all tracks of humanity from the canarian islands, cleared the north african west coast and Portugal. Of course, the tsunami was only one aspect of the catastrophe. Seismic effects, short term climatic changes from clouds and dust in the atmosphere, long term changes due to the effect on the gulf stream...
This impact would have long term consequences beyond the first half billion victims. And sooner or later, more impacts would occur. Impacts of larger asteroids.
It happened sooner.
By 2095, three more asteroids had hit earth, 4 more passed earth much too close.
Attempts to destroy approaching asteroids showed mixed success. The second and the third asteroid absorbed the majority of nuclear warheads earth could muster and had armed orbital defense satellites with. The second asteroid was again a rather small one and was blown to small pieces that rained down as in comparism harmless boulders. The third one was too large and at least broke down to pieces that at least only resulted in catastrophes - and not total destruction.
It became clear that attempts to blow the asteroids apart could only reduce the degree of destruction, but not avoid it. It was just a way to buy time, but destruction seemed inevitable.
If humanity was to survive, it would not be on earth.
Colonization of space seemed to be the only solution.

Earth by the mid of the 21st century looked in a discomforting way similar to how it looked a century ago. An increasing degree of nationalism, cold war in the rise again and again a highly instable south american and african continent. What economic progress the nations there had achieved was overcompensated by climate change and political and ideological instability.
If something had inhabited the traveller, it would have encountered a world with several competing blocks.
The European Union had survived a Phase of downsizing and was eventually refounded as a Federal Republic, much like the United States used to be and even more resembling the german republic. However, the borders had expanded to the North African coast which functioned as a heavily guarded border region and at the same time a belt of solar power plants.
With almost drained petrol depots, the arabic world steadily descended back to the state it inherited prior the petrol age.
The asian demisphere was dominated by 3 powers - the russian empire, the chinese federation and the United Protectorates of America which covered most of the pacific nations that refused to be consumed by chinese expansion.
No need to say that the UPAs territory covered the whole north american continent and about half of the south american. What was left effectively worked as a giant ghetto where UPA citizens that had lost their civil rights had been exiled. Canada had at first associated with the FSE - until it was krimed by the UPA

(krimed had at that time become a term that refers to the first russian expansion. Continuing with this method later led to the russian empire - whose borders resembled those of the UDSSR and that expanded further and further in FSE-territory.)
The Traveller would have seen a world just one step away from a hot war between the russian empire and the FSE.
Protection from the UPA was possible and not without precedence - but since 2025 every intervention came at the cost of sovereignity. The Exit of the USA from the NATO marked the rise of the UPA.
2112 was the year in which the last political block had started the construction of the first colonization ships in earth or moon orbit.
The FSE had built a fortified space port on the devastated and uninhabited canary Islands, since it had no more access to the Space Ports in Cape Caneveral, Baikonur or even the former ESA-Site.

All of the colonization expeditions faced common problems.

Where to go?
So far, no other inhabitable planet was known to mankind - there only had been a couple of destinations with a certain chance to find a planet fit for colonization. Once started, the trip would be a one-shot. If the destination turns out to be uninhabitable, chances that fuel will suffice to go somewhere else are close to non existent. The reason for that was quite simple... slowing down takes as much time and fuel as it took to speed up... and building up the speed for interstellar travel would require years to accelerate.
Even if the planet provides basic conditions that allow for colonization, that does not mean that no terraforming will be required. As a consequence, each expedition will need at least the capabilities to initiate terraforming - and to set up a colony that is able to survive even under conditions that will only eventually allow human survival.

Whom to take along?
Each block started with one ship - and chances were good that this would be the only ship that would get the opportunity to leave earth. One of the largest problems regarding the population was to ensure support for the mission. A mission that was not intended to evacuate the people, but to give humanity the opportunity for survival. On the cognitive level, it was apparent that each block would only be able to send a few thousand people - as opposed to billions of citizens. A few thousands also would be required to ensure a suffitienty diverse genetic pool to allow the population to survive. In addition, not only genetic but also educational diversity is required. Scientists, engineers, all kinds of crafters. But this lead to a couple of other problems. A certain degree of colonists already needed to have the required skills - and almost all skills needed to be available. On the other hand, depending on the kind of ship, those specialists would need to survive the trip, so they needed to be relatively young.

How to survive the trip?
In each and any scenario, the voyage would last centuries, maybe millenia. That alone leaves only two alternatives- generation ships or hibernation. Generation ships of course have a much higher need for room, life support systems and supplies. In addition, they bear the risk that the colonists adapt too much to life in space and maybe even loose the abilities required later. After all, those skills would have no practical use on the trip and would need to be given down from generation to generation.
Hence, UPA and FSE decided to research hibernation techniques. China went for a generation ship - in part due to access to almost unlimited building supplies from the mining facilities on the moon. The russian solution was still not decided upon when the other three ships finally left earth.

The decision about what to research was something worth mentioning - because none of the blocks had the technologies required for colonization when they began building the ships. They started with what they knew and the design and capabilities evolved with scientific progress. There was not really another choice - building a single ship would take at least ten years and no one was willing to take the risk to begin only when every problem was already solved. In the end, "at least ten years" became 17 years.

What drive to use?
A chemical drive was out of the question due to the massive requirements of fuel and no practical way to replace used fuel on the trip.
Informal and involuntary knowledge exchange finally led to all ships using the same drive technology. Fusion technology was finally available and provided both an energy source for the ship and a drive. Since Hydrogen and Helium are both fit as fuel and have at least a chance to be found somewhere on the way, the solution appeared practical.

The FSE eventually found a combined solution for the problems of survival on the journey and the required education of the limited number of colonists.
Stuffed deeply away in a drawer with useless inventions was a technique for direct neural knowledge induction. Basically, it allowed to let a person to learn while asleep. At the time of the first practical demonstration, it was awarded with a Nobel Price. Afterwards, it went directly to the drawer due to extreme inefficiency - the process was so slow that transporting the equivalent of 1 page of plain text information took about 20 hours with some tolerance depending on the recipient. Transfer of motoric skills took extremely longer. As a matter of fact, that technology was pretty useless - with a few exceptions that quickly became illegal in the FSE.
With the development of an hibernation technique that let the subject sleep in a state similar to a coma while reducing vital functions to an absolute minimum, the neural induction was dug out again. Time was no limiting factor in this case and the formerly useless method became a practical solution.
It was Common Sense that the ultimate priority of each expedition was to set up a colony that was able to survive on its own. Hence, every ship was required to carry the equipment to quickly set up industrial capacity for mining and refinery.
However, at this time the UPA had already followed a doctrine first implemented in the early 21st century that allowed a different approach. In a nutshell, the argumentation was that the UPA had ensured peace, freedom and democracy in the world for about a century, so it was deemed only fair if it claims compensation for that role. A reduction of industrial equipment allowed for more american citizens to be taken along. The know-how in those areas was inferior anyway - natural resources on UPA Territory had been depleted decades ago and almost any sophisticated civil technology had been imported for a long time. Local products concentrated on the traditional sectors of information technologies and military equipment. Almost every other industry was still existent, but everybody who could afford it chose Chinese or European products.
Since nobody could see a reason why a colony would need weapons - beyond hunting equipment - no expedition wasted space, fuel and training on weapons. Wasted. The UPA did not intend to waste any of it. The weapons and specialized personnel they made room for in their ship were an investment in American citizens future.
In early 2127, the UPA ship „Ranger“ was the first to leave earth orbit. Its destination had been kept secret - for good reason. The trip was extremely short - „Ranger“ flew no further than Mars. Mars would have made a poor alternative to earth for colonization - not only because of the required terraforming, but also because Mars was just like earth subject to continuous asteroid bombardment. But Mars was not „Rangers“ destination. „Ranger“ waited in Mars orbit.
The summer of 2127 saw the start of the FES ship named „Daedalus“. As its destination, the Trapist-1 system in the Aquarius-sector had been chosen. With 7 planets resembling earth - as far as scientists could tell - it bore the best chances for founding a colony. With a distance of just 40 light years, the system was also extremely close. It seemed unfair - and from an objective perspective it actually was. Trapist-1 would have been the best choice for any ship, but due to the short distance it should have been the destination for the chinese generation ship. But building of that ship had not yet been completed and FSE was not willing to give up that opportunity. There was no price for good sportsmanship in this competition after all. If diplomacy and intelligence was to be trusted, „Ranger“ did not go to Trapist-1 as well.
„Daedalus“ did not set direct course. To build up speed, a complicated course from one gravitational field of solar systems planets to another was much more efficient - though, longer. And due to the positions of Mars and Jupiter also predictable.
There was one unique field of technology the UPA researched with maximum priority: The means to detect and follow a space ship. When „Daedalus“ performed its slingshot maneuver around Mars onwards to Jupiter, „Ranger“ picked up the track and followed unnoticed by „Daedalus“, whose every maneuver was analyzed and mimicked ever after by „Ranger“.
„Daedalus“ left the solar system, all the time under full thrust of the fusion drive. Acceleration lasted for 5 years, until the drive could not increase velocity any more. The engine was shut down and „Daedalus“ fell towards Trapist-1 at 0.6c.
„Ranger“ followed.

At home, humanity finally found a way to avert destruction. Ironically, the further development of the fusion drive led to the solution and earths destruction was postponed for a few millennia. „Daedalus“ and „Ranger“ never learned about it - which would also have been pointless, because fuel would have sufficed to slow down, but not to build up speed for returning.