So some jackass realized that the moon doesn’t orbit in a perfect circle and decided that he alone in the annals of history was in possession of the information that Earthquakes and other doom might ensue, and since the Moon was closer than usual (more on that in a bit), something *bad* was about to happen. No big deal. There are about 7,000,000,000 people on planet Earth, and a good percentage of them are, even now, right as you’re reading this, drooling uncontrollably from their slack jaws. However, this happened to make what now passes for news just before a massive earthquake hit off the coast of Japan, and so now the idiots who have taught themselves to operate a television are convinced that they’re correct. Oh, dear.
There are so many problems here, it’s hard to know where to start. Possibly that the moon isn’t actually especially close to Earth right now, and couldn’t cause this earthquake even if it was. Anyway, Phil Plait has a nice takedown up right now, and he knows a lot more about planetary physics than I do anyway, so just go read what he has to say. I’m writing this for another reason. One of my Facebook friends wondered what the actual plot of earthquake frequency and magnitude versus lunar distance actually would look like. That sounded like a fun little exercise in programming.
There are basically two questions that need to be answered. First, when have there been major earthquakes? I went to Wikipedia and grabbed a list of the 24 largest earthquakes in known history (today’s Japanese quake comes in number six). This gives me the magnitudes, but also the dates the quakes occurred. The range of dates covered by these 24 mega-quakes spans from a 1575 Chilean quake right up to today’s Japanese quake. The second thing we need is an ability to calculate the distance between the Earth and moon on any given day in history. That’s a tougher problem, but a bit of Google-fu turned up the ELP2000-82B model of lunar ephemerides. That’s what we need here. However, it’s a very complex model, and I didn’t want to spend a week debugging scientific code, but fortunately, I found an implementation on Github.
A bit more reading of code and comments showed that the model needs Julian dates. A bit more searching to find the exact formula for this conversion, and a quick implementation of said formula in Clojure yields the following.
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Because this was intended to be quick and dirty, I just manually set up a simple data structure for my earthquake data, and rather than spend lots of time integrating my Clojure code with the C library that implemented the lunar model, I simply used the C code to compute the distances, and then copied them directly into Clojure as well.
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To get the Julian dates for each quake, it’s sufficient to just run a quick and dirty map over the quake data as follows.
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Now we feed that data into the C code from Github to calculate the distance the moon was from the earth at noon on the day of the quake (I made that approximation rather than look up the precise time each quake occurred). After those distances have been computed, I just copied them back into a Clojure data structure.
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With that, we have enough data to plot earthquake strength versus lunar distance for the 24 largest quakes in recorded history. Clojure has a really nice library available called Incanter that makes charting and statistical analysis very easy.
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The resulting plot is shown below. As you can see, there’s no relationship at all between the strength of the strongest quakes and the current distance from the Earth to the moon. Note that the Y-axis is scaled to the minimum and maximum distances the moon has been in about 450 years, so the quakes really are distributed all over the place.
One last thing. Although the graph is pretty obvious, we really shouldn’t try and use intuition as a substitute for actual analysis, so let’s go ahead and fit a linear model to the data. Again, using Incanter,
we get an value of 0.1193, or basically no relationship at all.