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Q: If Earth was flat, would there be a horizon? If so, what would it look like? If the Earth was flat and had infinite area, would that change the answer?

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The only difference between a finite flat Earth and an infinite flat Earth is that no matter how tall you are on an infinite flat Earth, the horizon always stays in the same place. However, even though the horizon of an infinite and flat Earth might actually be in the same place, it wouldn’t appear to be. An infinite plane has an extremely simple gravitational field; uniform and exactly the same regardless of distance. Normally the higher you are the weaker the gravity, but for a flat Earth that isn’t the case. The effect would require tremendous distances (as in; interstellar distances), but if you’ve got an infinite plane, that kind of distance is cheap.