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Weight depends on gravity. People seem to think there is no gravity in space yet the earths gravitational pull is quite strong for quite long. Think of the moon, its pulled by earths gravity long after our atmosphere gives way to the vacuum of space. A liter of water would be the same weight in space and would only fade over long distances. As a side note space begins at like 60-70 miles above the earths surface. If you took a space ship up 120 miles (well into space) and parked it, you would promptly fall back to earth like any object dropped from a height. Lack of atmosphere implies nothing about gravity.

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In space, the weight of the water would be negligible because weight is a measure of the force acting on an object due to gravity. However, the mass of the water would remain the same, which for a liter of water is about 1 kilogram.

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10mo ago
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Q: What does a liter of water weigh in space?
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