Last month Scientific American reported on whether scientific studies showed an association between the full moon and strange behavior. The short answer is no, despite a wide-spread belief in the connection.
In the article, Scott O. Lilienfeld and Hal Arkowitz mention that some people (ancient and current) believe that the moon’s supposed effect might have something to do with its gravitational effect on water, which makes up most of the human body. But then they add that this effect isn’t strong enough:
As the late astronomer George Abell of the University of California, Los Angeles, noted, a mosquito sitting on our arm exerts a more powerful gravitational pull on us than the moon does.
“Hmmm,” I thought to myself upon reading this, “Is that true? Is a mosquito really a more significant graviational force than the moon?”
The force of gravity between two objects of mass and respectively is given by
where is the gravitational constant and is the radius between the two objects.
In order to compare the force exerted by the moon and a mosquito, and (the mass of the individual) are the same in both equations, so we really just need to compare the values of and .
So what are these two amounts? NASA says that the mass of the moon is 7.3483×1022 kg, which translates to 7.3483×1028 milligrams. The average distance to the earth is 3.844 x 105 km, which is the same as 3.844 x 1011 mm. [I’m using tiny units because we’re about to compare this to a mosquito.] So the ratio is just about 497,300 mg/mm2. This amount might be an underestimate, too, because the distance I used was the distance between the moon and earth, but I suspect that is the distance between the centers; we only need to go from the center of mass of the moon to the surface of the earth where our individual is sitting. But for rough purposes, it will do.
Mosquitoes, on the other hand, appear to weigh 1-5 milligrams each (though some sites say only 1-2 milligrams). We’ll use the upper bound of 5 milligrams. For the distance, I feel like we should use the distance between the centers of the mass of the mosquito and individual if we want the overall gravitational effect, but I’m willing to limit the effect to just a few cells near the mosquito. A reasonable estimate for the distance from the mosquito’s body to the skin is 1 mm. The formula then becomes only 5 mg/mm2. And this amount is really an overestimate, since I used the largest possible value for the mass and chose the smallest distance.
So if my estimates here are accurate and I haven’t missed anything significant, the gravitational pull of the moon is on the order of 100,000 times as strong as the gravitational pull of a mosquito; George Abell — debunker of pseudoscience himself — appears to be quite wrong.