The journey takes weeks, during which the Earth falls millions of kilometres closer to the Sol/Umbra binary system. Earth is not spiralling inevitably into Umbra, because spiral orbits don't exist. A black hole is not a magical cosmic magnet; it can be modelled as a point mass like any other and the laws of orbital mechanics apply to it as much as any other object (outside of its event horizon). Earth is merely adjusting to a new, elliptical orbit with an intolerably hot perihelion. There is no singular point at which a planet becomes uninhabitable to human life, but an absence of drinkable
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