Even if the Moon were shrunk...
Even if the Moon could be shrunk down to the size of a softball, it would still retain its mass, and would not change its effect on the Earth's tides.
Unless of course its a movie, :-)
Are we sure it retained it's mass though? It seems that when the volume was shrunk the mass was shrunk at the same proportion. If that weren't true then they wouldn't be able to carry it.
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