C. David Parsons disputes the Hawaiian islands chain as evidence for an old earth in part on the grounds that "The gravitational tug of the moon is ... responsible for earthquakes" and "the gravitational attraction of the moon is the mechanism that facilitates the expansion and forced invasion of pressure solids through a geodic crack in the earth's crust." Does this claim stand up to scrutiny? Well, no, it doesn't.

Unfortunately for Parsons, we have an exceptionally good scientific understanding of gravity. Newton's theory is now over four hundred years old. During that time it has only been revised once, and that was over 100 years ago. If these theories were wrong, space flight (and GPS) would not be possible.

It is an elementary exercise to work out the magnitude of the moon's gravitational influence on the earth using Newton's formula:

F = G x m1 x m2 / r^2

where F is the force between two bodies, m1 and m2 and the masses of the bodies, r is the distance between them, and G is the gravitational constant, one of the fundamental constants of physics.

Let us work out the relative magnitudes of the gravitational influences of the earth and the moon on an object at the earth's surface. We could simply calculate the actual forces, which is not too hard, but it turns out that it's simpler to calculate the ratio directly because G and the mass of the test object cancel each other out and can be safely ignored. (If you don't believe me you can work this out for yourself. It's an elementary exercise in algebra.) The upshot is that although the moon is very heavy (about 7.22x10^22 kg) it is also very far away (about 3.84x10^8 meters) and the gravitational influence decreases with the square of the distance. So at the surface of the earth, the moon's gravitational influence is tiny -- only about 3

*millionths*as strong as the gravity of the earth itself.

Compare this to the gravitational influence of the sun, which is a lot further away (1.46x10^11 meters) but also a lot heavier (about 2x10^30 kg). The sun's gravitational influence at the surface of the earth is about

*190 times greater*than the moon's. Standing on the deck of the world's largest supertanker with a fully loaded mass of about half a million tons, the gravitational influence of the ship is about the same as the gravitational influence of the moon.

And yet, the moon clearly does have manifest influences at the surface of the earth, most notably, the tides. If the moon can push zillions of tons of seawater around, isn't it plausible that it could also move zillions of tons of magma around too? Well, no, it isn't. To see why you have to understand how the tides actually work. It is tempting to think that the moon causes the tides by pulling water towards itself via the force of gravity. But this theory has a major problem: if this were how tides worked, there should be one high tide every day (when the moon was overhead pulling the water towards it) and one low tide each day (when the moon was on the opposite side of the earth pulling the water away). But in fact there are

*two*cycles of high and low tides each day. How can this be?

The answer is that the moon does not cause tides by "pulling" on the water. It casues tides because of tidal forces (imagine that). Tidal forces are somewhat complicated to explain, but the easiest (though not quite correct) way to explain them is that the earth and the moon make up a two-body system that rotate around a common center of gravity. Because the moon's mass is a significant fraction of the earth's mass, this common center of gravity is not at the center of the earth, but lies about 3300 miles from the earth's center. As the earth rotates about this offset center of gravity, centrifugal forces "fling" the water away.

The important point is that the tidal force is not the force of gravity, but the

*difference*in the force of gravity on the two sides of the earth. And as small as the raw gravitational influence of the moon on the earth is, the tidal forces that it generates are even smaller. This is why the actual tides on earth, while they may appear significant to us on a human scale, are actually miniscule relative to the scale of the planet. There is nowhere near enough energy in the moon's tidal influences to account for volcanism. And it's a good thing too, because if there were then that energy would get dissipated in the world's oceans and they would all boil away.

The title of this post is "how to detect bullshit", and the answer is: do the math. Don't take my or anybody else's word for it. Do it yourself. It isn't hard. As an exercise, consider the Biblical claim that Joshua made the sun stand still (which is to say, that he made the earth stop rotating). Calculate how much rotational energy would have to be dissipated to make that happen. Compare that to the total amount of energy in, say, the world's nuclear arsenals. Here's all the information you need:

The formula for the rotational energy of a sphere is 2/5 x m x r^2 x omega^2 where m is the mass of the sphere, r is the radius, and omega is the rotational velocity in radians per second. The mass of the earth is about 5.97x10^24 kg. It rotates 360 degrees (or 2pi radians) in 24 hours. A kiloton of TNT is about 4x10^12 joules.

Go.

## 6 comments:

Great article! Just came across your blog (for obvious reasons). I like what I see so far. Will delve further!

http://blog.bullshitawards.com

Actually, I think you're confusing the issue a little since the moon does "pull" on the water, just as intuition would suggest. Figure 4 on the tidal forces wiki page you referenced makes this clear, i think. It all depends on your frame of reference, top half of that picture (an absolute reference frame) or the bottom half (standing on the earth).

Furthermore, it's not just the water that goes through tides, the crust itself experiences tides, apparently on the order of 25 cm in Geneva.

http://www.sciam.com/article.cfm?id=letters-june-2008

Here are some articles discussion the correlation between tides and earthquakes:

http://uwnews.washington.edu/ni/article.asp?articleID=38142

http://www.sciencedaily.com/releases/2004/10/041022103948.htm

http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2007/11/23/MNPATFJNL.DTL

This article denies correlations between tides and earthquakes, but says that correlations between tides and volcanoes have been identified:

http://vulcan.wr.usgs.gov/Outreach/AboutVolcanoes/do_tides_affect_volcanoes.html

http://www.sciencemag.org/cgi/content/full/sci;297/5580/348

I would summarize the articles with the last sentence from that last article:

"By themselves the tidal forces are too small to generate earthquakes, but in the critical stage of faulting they can trigger volcanic earthquakes."

This doesn't contradict the point of your previous blog post. But I do want to point out that the "do the math" advice is a bit misleading since there are often correction factors, misunderstandings, data with error margins, approximations, and mistakes, etc. One thing to point out is that geology is not like math -- in math, we can look at formulas, in geology we have to look at models.

The Hawaii islands discussion is quite interesting, I'll have to bring this up next time i'm talking with a geologist.

Lastly, I definitely do not think this is a futile exercise. You may not see it yourself, but people do change their minds on a lot of topics. Perhaps it's not so often that people change their minds by reading 1 article, or by 1 argument, but the aggregation over time can make a difference.

> the moon does "pull" on the water, just as intuition would suggest.

Yes, of course it does. I never said otherwise. What I said was that *the moon pulling on the water is not what causes tides*. What causes tides is tidal forces, which are related to gravitational forces, but are not the same. In particular, tidal forces are much weaker than gravitational forces.

BTW, tidal forces *can* be the source of enough energy to melt a planet. Io and Europa are both kept warm by the tidal forces from Jupiter. In Europa's case we don't know for sure, but there is evidence that this provides enough energy to melt the water on Europa and produce a liquid ocean covered by a thick sheet of ice. In the case of Io it provides enough energy to produce volcanoes spewing magma made mostly of sulphur.

> correlations between tides and volcanoes have been identified

"In the Hawai'i example of 52 eruptions since January 1832, there have been nearly 3,900 tidal maximums, of which roughly 3,850 of them went by without causing an eruption. Statistically, this is about a one percent chance that any tidal maximum will affect the start of an eruption."

So the effect is very, very small. It's certainly not fair to say that the moon *causes* volcanic eruptions.

You concede this:

> "By themselves the tidal forces are too small to generate earthquakes, but in the critical stage of faulting they can trigger volcanic earthquakes."

At the critical stage of faulting, a butterfly flapping its wings can trigger an earthquake. That does not mean that earthquakes are caused by butterflies.

> One thing to point out is that geology is not like math -- in math, we can look at formulas, in geology we have to look at models.

Even geology is subject to the fundamental laws of physics. Just because we don't have perfectly predictive models doesn't mean that we can't rule out many possibilities based on first principles and quantitative considerations. (Have you done the sun-standing-still exercise? The answer is quite surprising.)

> Lastly, I definitely do not think this is a futile exercise.

Thanks. :-)

You argue that:

"If the moon can push zillions of tons of seawater around, isn't it plausible that it could also move zillions of tons of magma around too? Well, no, it isn't."

It takes the same amount of force to move a ton of water as it does a ton of magma. There is a causal link between the moon and the motion of the crust.

You then claim that:

"There is nowhere near enough energy in the moon's tidal influences to account for volcanism. "

But you didn't explain why this is the case because I don't know how big forces have to be. I know that there are indirect links, so there must be some effect. You merely stated that the effects were too small, and this hardly counts as "deconstruction". How do I know if 25 cm in Geneva is a lot?

Apparently there are some people who (albeit controversially) attribute some plate movement to the moon:

http://en.wikipedia.org/wiki/Plate_tectonics#External_forces

I don't want to defend that other guy's arguments, since as far as I can tell it was all crap. My point is that if he read your rebuttal, he's not going to be convinced.

Fair enough. I guess it's actually not inconceivable that the moon does have measurable causal effects on volcanism. But that doesn't change the fact that the evidence for plate tectonics is overwhelming, and hence the evidence that the Hawaiian islands are very old is overwhelming. The moon is really a red herring in this case.

My (astronomer) roommate agrees with your conclusion about the moon. As a side note, he said there were spots that don't change with the tide:

http://en.wikipedia.org/wiki/Amphidromic_point

Now there's an example of something I never would have guessed, and why sometimes physical principles behave subtly.

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