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Worst case scenario, the temperature on the nox and lux zones are incredibly low and high, respectively.
Lux, Nox & Terminator zones
Luxterna (Eternal Day):
The lux zone may reach up to 110°C, the lowest 80°C. These hot temperatures are torturous for living things. No animal or plant can sustain this ferocious heat. Obviously, no humans can survive in this place, making it inhabitable and hostile.
Noxterna (Eternal Night):
With the immense snowfall and hail, the night zone is almost impossible to live in. The Nox zone sits in -70°C. Hails are immense and strong, causing giant ice cubes and ice shards to fall towards the land, which ultimately can destroy the ecosystem. This really low temperature also causes plants to wilt and die, decreasing the food resources for animals and humans to consume. However, with the use of an Artificial sun (which you can learn more on another page), the Nox zone may be habitable for some plants and animals.
Terminator zone:
Terminator zone is the only habitable place to live. This causes most of the population to live in the terminator zones, which increase population density. This however will mean that the population can only reach a small amount. Furthermore, the resources in the terminator zone will be the most used up and may result in a scarcity of food and water, which can cause a global outage of resources.
Life on the Terminator Zone
Life here will probably be a little harsh but still hospitable. Temperature may change drastically in this zone. However, we can adapt to this easily. Due to the low population in the zone, life here will be peaceful with the lowest crime rates. However, jobs may be limited.
Lux & Nox Zones
Luxterna (Eternal Day):
Even though the Lux Zone is incredibly hot, we can't deny that we could use it to our advantage. The abundance of light energy there would be incredibly useful as we can place solar panels there, and since it cannot be used for anything else, the entire space can be utilized for solar panels, giving us a plethora of renewable energy.
Noxterna (Eternal Night):
The Nox Zone might be tough as unlike the day side, we can deal with the intense heat using heat-resistant armor, the night side might be useless if we don't do something. Using our plethora of energy, we would have enough power to create an artificial sun, a heat and light source that would stabilize the other half of the planet, and make the terminator zone not the only habitable place. But it would require getting far into the extreme weather and freezing temperatures which might take decades or even centuries.