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The AU is, by definition, exactly 149,597,870,700 m. This is based not on a distance to the sun (which varies) but on the shape of an ellipse that closely approximates the orbit of the Earth. An ellipse has two foci. In a Keplerian, two-body orbit, the combined centre of mass of the two bodies lies at the focus of the ellipse. For the Earth/sun this is only ...


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The sun's center is not the solar system center of mass and sun is not so big for this question to be important. Just compute the ratio of the quantities — you will find that the difference is negligible. There is a more important problem: the orbit of the earth is elliptical, not circular. So the distance to the sun is not constant. Just take it as ...


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James K's answer, which seems cogent and self-referential enough that I'm willing to buy it without researching his points would, by the logic of his points, require it to be the center of the sun. This is mainly because the foci are mathematical points, not smeared objects in real life that have "width", so to speak, and even vary as the sun ...


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