Could an asteroid aerocapture around Earth?

Would it be possible for an asteroid in solar orbit to go near enough to the Earth that the Earth's atmosphere slows it down into an orbit that is, aside from its low perigee, stable without using a third object (such as the moon) to slow down? Or would the necessary forces destroy the asteroid?

If this is possible, could it then gravity assist off of the moon to get in a truly stable orbit? Also, if it is possible, what would happen on Earth?

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Could an asteroid aerocapture around Earth?

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