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BartyDeCanter t1_j24som3 wrote

None! As long as it's heading in the right direction at the right time. Once something is moving at escape velocity it can go anywhere else, unless it is captured by something bigger.

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In this case, escape velocity from the Moon is 2.38km/sec and the orbital velocity of the Moon is 3.68km/sec. So, at most the baseball would be travelling at 6.06km/sec relative to the Earth if it was just at lunar escape velocity. Since that is less than the Earth's escape velocity of 11.19km/sec, it would be captured by the Earth as it moved away from the Moon. At that point, depending on the fine details of the orbits it could either orbit the Earth, crash into the Earth or be re-captured by the Moon.

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