The moon versus the mosquito

by Ξ

full_moon_luc_viatour 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 $M$ and $m$ respectively is given by

$\frac{GMm}{r^2}$

where $G$ is the gravitational constant and $r$ is the radius between the two objects.

In order to compare the force exerted by the moon and a mosquito, $G$ and $M$ (the mass of the individual) are the same in both equations, so we really just need to compare the values of $\frac{m_{moon}}{{\left(r_{moon}\right)}^2}$ and $\frac{m_{bug}}{{\left(r_{bug}\right)}^2}$ .

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 $\frac{m_{moon}}{{\left(r_{moon}\right)}^2}$ is just about 497,300 mg/mm². This amount might be an underestimate, too, because the distance $r_{moon}$ 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 $\frac{m_{bug}}{{\left(r_{bug}\right)}^2}$ 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.

Isn’t that a great photo of the full moon? Luc Viatour took it in Belgium (© Luc Viatour GFDL/CC). The mosquito comes from the Centers for Disease Control and Protection.

Tags: gravitational force, gravity, moon, mosquito

This entry was posted on March 22, 2009 at 10:05 am and is filed under Math Mistakes. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

4 Responses to “The moon versus the mosquito”

Ted Says:
March 26, 2009 at 3:39 am | Reply
Thanks, it did seem rather odd. Imagine swamps full of mosquitoes influencing the tides half a world away. Lorenz’s Butterfly has got nothing on them.

Now please to figure out if the urban math is true that your spouse emits more radiation to you in bed at night than living a mile from a nuclear reactor.
TwoPi Says:
March 26, 2009 at 7:28 am | Reply
Does your spouse work at the reactor, by chance? Or do they have radium embedded in their wristwatch?

Certainly they emit more infrared radiation than any other industrial source in your community.
Tidal force, or The Moon and the Mosquito revisited « 360 Says:
March 30, 2009 at 7:09 pm | Reply
[…] force, or The Moon and the Mosquito revisited By TwoPi As Ξ noted in an earlier post, the claim that the gravitational pull of a mosquito is stronger than the gravitational pull of the […]
jd2718 Says:
April 4, 2009 at 3:54 pm | Reply
So, off by a factor of between 100,000 and half a million. With a range of 1 – 5 mg, that means we’ll need something between 100g and 2.5kg to be sitting on the opposite side of your body from the moon, if we want to cancel out its gravity.

So we are talking about something between a small lab rat and a small rabbit.

Jonathan