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The fact that orbital motion is slowly spiraling inward is a highly debated topic. You asked a doozy of a question. It may or may not eventually hit the sun. There are several arguements, but the one I'm most familiar with is that due to the exact shape of the orbits (ovular, not circular), neither the planets nor the moon will ever stop orbiting with the way the galaxy is now unless something changes. However, I could always be wrong.
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