How the VIRUS units were able to defeat the Stareaters
How could thing as tiny as a nano-machine (aka VIRUS unit) eventually digest something as huge as a Dyson Sphere (aka Stareater)?
In Rome's Revolution, Rei, with OMCOM's help, came up with a "simple" solution.
The answer lies in the exponent. I assumed the VIRUS units were so tiny, they only weighed a nanogram. I started with 1000 units and assumed they took 3 minutes to reproduce.
At the end of 3 minutes, you now have 2000 units with a weight of 2 micrograms. After six minutes, you have a weight of 4 micrograms and so on.
After an hour and a half, the mass weighs one kilogram. After 5.5 hours, the mass weighs the same as the Moon. After 5.7 hours it weighs the same as the Earth. After 6 hours, it weighs as much as Jupiter. Finally, after 7 hours, it weighs as much as the Sun and certainly that is big enough to kill a Stareater.
So the Stareater provided the mass resulting in its own death. Very much like a virus can kill its host, hence the clever name.
Entry 1-040: February 2, 2013
How did the Arks land?
Well, a better question would be how were they supposed to land?
Let's take Ark I because it was textbook. When the Ark I arrived at the Alpha Centauri star system, the AI examined the habitable world orbiting the B-star (later called Beth) and the one orbiting the A-star (later called Aleph) and decided the A-star planet was the better choice.
After circularizing its orbit around the target planet, the AI awakened the Captain who, in turn, awakened the Pilot and Co-pilot. Two of the men performed a two-step space-walk. Step one was going all the way to the back and jettisoning the propulsion module as it was no longer needed. After that was complete, the two men separated the cargo compartment in the back from the crew compartment in the front.
The command module and SSTO booster remained attached to the crew compartment.
Using solid rocket fuel retros, they began to descend into the atmosphere. As the hull began to heat up, they used their gigantic delta wings to force the ship to begin ascending again until it stalled nearly back at the edge of space.
With their velocity reduced by gravity, they began a second descent into the atmosphere, going much lower this time before re-ascending. They did this several times until they were going slow enough to stay within the atmosphere. The technique is a form of aero-braking. If you plotted the altitude as a function of time, you would see that it resembles a mathematical Bessel function.