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According to relativity, the universe is expanding, at an accelerating rate. Far away planets and stars will soon leave our observable universe. But as planets and stars leave our observable universe, they would also leave Earth's gravitational field (Even though at that point it would be so incredibly minuscule), correct? Doesn't that mean they'd lose their gravitational potential energy? Doesn't this violate local conservation of energy?


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The universe isn't expanding. Spacetime is being stretched. The curvature of spacetime will become less and less to an object orbiting around the Earth. So the object will lose some of its potential energy. In order to reduce an object's potential energy, work must be done on the object. In our case, this work comes from dark energy.

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