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Say hello to Bary
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this post was submitted on 03 Sep 2025
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I guess your conclusion is right. In situations where the barycenter of two (or more) objects is not sufficiently different from the center of mass of the heaviest object, we simplify the description by assuming that the barycenter and the center of mass of the heavier object are equal.
Just because I’ve already edited it, here’s an animation of Earth orbiting the Earth–Moon barycenter: