Model the earth with and without the moon to gravitationally simulate the trajectory of meteoroids. Is there a significant difference in impact rate? Without the moon, add to the earth the mass of the moon, but possibly subtracting the mass of the impactor that created the moon.
Theory is, the freak giant impact that created our (almost) double planet is another of the reasons there is life, or intelligent life, on earth. If it weren't for the moon, we might be seeing Chicxulub-like impacts, and consequent mass extinctions, more often.
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