Was the Moon Super or Not?

Recently I have been studying some of the interesting mathematics involved in DNA profiling.  That led to some even more interesting new ideas (or at least new to me) about card shuffling, of all things.  I planned on discussing one or both of these semi-related topics this weekend… but after seeing the rather beautiful “Super Moon” last night, along with several commentaries on its media coverage, I felt compelled to make a brief detour.

The motivation here comes from several online sources: blog posts at Wired, ScienceBlogs, and Bad Astronomy… and NASA.  The blog posts in particular are rather dismissive of the media hype surrounding the so-called “Super Moon,” or the coincidence of the full moon with lunar perigee.

First, most of the criticism seems to be directed, justifiably so, at the suggested links between the super Moon and natural disasters such as earthquakes, volcanoes, etc.  For astrologers, the religious, and others who seek to find patterns where none exists, the unfortunate timing of the tragedy in Japan will probably only fuel that fire.

On the other hand, I thought the treatments of the changes in the apparent size of the Moon were slightly misleading.  Perhaps it is simply that I am not an astronomer and had not bothered to perform these calculations before; at any rate, I thought the extent of the difference was not ho-hum, but actually rather interesting.

As the blogs correctly point out, the effect is due to nothing more complicated than the fact that closer objects appear larger than more distant objects of the same actual size.  The Moon’s orbit is elliptical, and last night the (full) Moon was at perigee, or the point in its orbit that is nearest the center of the Earth, about 356,577 km away.  By my calculation, at that distance the Moon (with mean radius 1,737 km) subtends an angle of about 0.56 degree in the sky, compared with only 0.49 degree at apogee (406,655 km, about 50,000 km farther away).

(Note that I am focusing on the change in actual angle subtended by the Moon, and not the so-called Moon illusion, which is admittedly a larger effect.)

The NASA site has a nice image comparing these two extremes of views of the Moon.  What I found interesting was that there, as well as everywhere else I looked, the increase in size was expressed as a ratio of apparent diameters.  That is, the common anecdote was that “the Moon appears 14% larger at perigee than at apogee.”  This comparison of linear (angular) dimension does not seem appropriate when evaluating how large a nearly-spherical object appears to a human observer.  Comparing solid angles makes more sense to me in this context, in which case the difference is more like 30%.


How much larger is the first circle than the second?


Consider the extreme example of the two circles in the above figure.  Would you say that the first circle is 100% larger than the second; that is, twice as large?  Or would you say that the first circle is 300% larger than the second, or four times as large?  The radii are in ratio 2:1, while the areas are in ratio 4:1.

(Along these same lines, beware of misleading pictorial graphs and charts in the media; USA Today has a particularly amusing track record in this regard.)

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