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say the first two -- forget the third one --
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take these two,
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find their center of mass,
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let's call it x12
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and with that total mass M12, which is just m1 + m2,
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trade these two for a new fictitious object
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and put that here, and forget these two.
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But on that one point it deposits the mass of these two;
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now, you take the center of mass of this object with the third object,
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by the same weighting process,
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m3·x3 + M12·X12 divided by the total mass;
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you'll get the same answer as here