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the earth will not fall into the sun when it becomes a red giant. the force of the sun on the earth depends only on the mass of the two objects (assuming each possess a certain symmetry, which they do to a very good approximation). since the mass of the sun and the mass of the earth will be essentially unchanged when the sun goes giant, the earth's orbit will be stable. unless the sun does "swallow" the earth, in which case friction from the earth traveling throught the sun's "atmosphere" will cause it to slow down and spiral inward.
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