Wrong. Due to the Hive hollowing it out, the mass of the moon decreased (also explains why the moon is falling apart) so Earth's gravitational pull is applying more force to the moon.
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The moon losing that mass would allow it to accelerate away from Earth, not get closer. Of course the mass of the Moon is likely higher than today since the gravity appears to be the same as Earth normal. Which would probably cause the Earth and Moon to get closer, tides would be higher, earthquakes would increase, the Moon's tidal lock would drift, etc.
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Not how gravity works. Smaller objects do not fall faster. The moon having less mass would mean it affects Earth less. Overall there is less attraction from the combined gravity of both objects.
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This is correct. Think of the moon as "falling" around earth.
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I prefer to think of the Earth as "falling" around the moon. (and the Sun...)
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The moon still contains a great mass. Also fun fact: Every 100+ years the moon get one centimeter closer.
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The moon drifts away form Earth every year, not closer. About 4 cm each year, to be exact.
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I could be wrong on this but i swear i read that it is getting farther not closer
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You are absolutely right.
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Farther away actually!
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Oh I know it does. But it would still have less, assuming the Hive took the excavated moon dirt somewhere else. Probably slightly increasing in the amount it gets closer all the time.