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the planet's there the Sun has to be here.
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So, what will happen is,
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the Sun will go around on a circle of smaller radius,
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the planet will go around on a circle of a bigger radius,
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always around the center of mass.
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So, you've got this picture now, it's like a dumbbell,
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asymmetric, big guy here, small guy here,
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fix that and turn it.
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You get a trajectory for the Sun,
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and you get a trajectory for the Earth on a bigger circle;
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the center remains fixed.
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So, if you apply loss of gravity,