Blue Supermoon: Part 2

We recently had a blue supermoon (on 31 August 2023). If you saw it, did you think it was super? Me neither.

In my previous post, I wrote about blue moons—what they are, why they happen—and in this post I aim to do the same for supermoons.

Supermoons happen when a full moon occurs at a time when the Moon is a little closer to the Earth than usual. The Moon’s orbit is slightly elliptical—its distance from the Earth varies between a close approach (called perigee) of about 363000 km, and a farthest excursion (apogee) of about 405000 km. The line connecting the perigee and apogee, forming the long axis of the orbital ellipse, is called the line of the apsides, for obscure reasons that I explained in my post “Keplerian Orbital Elements”. It turns out that the Moon’s orbit gets a little more elliptical when the line of the apsides is pointing at the Sun. This is a tidal effect, caused by the Sun’s gravity tugging on the Moon, in the same way the Moon’s gravity tugs on the Earth to raise the ocean tides. For brevity, I’m going to refer to those episodes when the apsides align with the Sun as apsidal alignments.

So there’s a rhythmic variation in the Earth-Moon distance, like this:

Moon distance, 2022-2024
Click to enlarge

The short-period cycle is just the time it takes the Moon to move from one perigee to the next—this is called the anomalistic month*, and it lasts about 27.55 days. The longer-period cycle is that of the recurring apsidal alignments, which drive more extreme perigees and apogees. If the line of the apsides always pointed in the same direction, then that cycle would take half a year, repeating whenever either perigee or apogee points towards the Sun. But, just to make matters more complicated, the line of the Moon’s apsides is rotating slowly, completing one revolution every 8.85 years. So apsidal alignments actually happen at intervals of about 206 days.

Why lunar apsidal alignments take longer than six months to recur
Click to enlarge

In my post about blue moons, I introduced the lunation, the time between two successive full moons, which averages 29.53 days. So a lunation is about two days longer than an anomalistic month. (This happens because, by the time the Moon makes one orbit from perigee to perigee, the Earth has moved around the Sun through an angle of about 27°, which means that the Moon has to orbit for another couple of days to “catch up” with the changed angle of illumination.)

Why a lunation is longer than an anomalistic month
Click to enlarge

So now I’ll plot full moon dates on my previous diagram:

Moon distance and full moons, 2022-2024
Click to enlarge

If you choose a full moon near perigee, and follow the progress of successive full moons across the diagram, you can see how they come progressively later, relative to perigee, with each anomalistic month that passes. But after 14 lunations and 15 anomalistic months, the full moon returns to approximately the same relationship with perigee—because 14×29.53 and 15×27.55 are both approximately 413 days. And, remarkably and (I think) coincidentally, that’s almost the same as two cycles of apsidal alignment, 412 days.

So you can see from the diagram that successive full moons creep only slowly past perigee—once we have one supermoon, we tend to get a season of them. It varies somewhat according to the definition of “supermoon” you use, but by one definition we’re currently passing through a four-supermoon season extending from the start of July to the end of September 2023. And then, after 14 lunations and 15 anomalistic months, we’ll get another four-supermoon season, from mid-August to mid-November in 2024—the slippage of about a month-and-a-half from year to year of course reflecting the amount by which 413 days exceeds the calendar year.

Strictly speaking, there’s another, invisible cycle of supermoons taking place, precisely out of phase with the one I’ve just plotted—that’s the cycle of new supermoons, which can be contrasted with the full supermoons I’ve just been talking about. These are (as you’ve guessed) new moons that occur near perigee, and you can imagine their cycle as a sinusoid that reaches perigee in the empty gaps between the full-moon perigees on my diagram. No-one talks much about new supermoons, because they’re dark and therefore invisible, so the word supermoon on its own usually designates the full-moon version. Then there are the micromoons, a horrible name that designates full or new moons occurring at apogee. You can see a couple of full-micromoon seasons on my diagram above, spanning January-February 2023 and February-March 2024. New micromoons fill in the gaps between the full micromoons, and are perhaps even less popular than new supermoons.

So far, I’ve given no indication of how close to perigee a full moon must be to qualify as a supermoon. And that’s because definitions vary. The first thing to know is that the term supermoon didn’t come from astronomers—it was invented by an astrologer called Richard Nolle in 1979, in the now blessedly defunct Dell Horoscope magazine, and used in the context of doom and disaster, summarized in the marvellous phrase geocosmic shock window. Because supermoons (full and new) are associated with unusually high tides, called perigean spring tides, Nolle chose to associate them with all sorts of potential disasters, none of which have actually materialized in any statistically defensible way. Nolle wrote that the name supermoon described “a new or full moon which occurs with the Moon at or near (within 90% of) its closest approach to Earth in a given orbit”. I find this phrasing a bit impenetrable, but when Nolle gives a worked example, it’s evident that he takes the distance between apogee and perigee, and if the full or new moon occurs when the moon is 90% or more of the way from apogee towards perigee, it’s a supermoon. Although Nolle’s original definition stipulated “a given orbit”, by 2011 he had revised this, using the most extreme apogee and perigee for a given year. This shift in definition somewhat reduces the number of supermoons that can occur in a year. Astrophysicist Fred Espenak, who uses Nolle’s original definition, counts four full supermoons in 2023 (the July-to-September grouping I mentioned above; Nolle’s own list classifies only the central two, in August, as “super”. Some other sources forget all about the apogee/perigee thing, and instead choose a simple distance cut-off—for instance, use a cut-off of 360000 kilometres, and list only two full supermoons for 2023.

But why are supermoons so unexceptional in appearance? The difference in distance looks extremely impressive on my graphs above, after all. But if I ensure that my vertical axis starts from zero, to give a correct impression of how the distance from Earth varies, it looks like this:

Moon distance and full moons, 2022-2024, with zero distance plotted
Click to enlarge

That rather modest wobble means that a typical supermoon isn’t hugely different from an average moon:

Comparison of typical "supermoon" with the Moon seen at its average distance

We can see that difference when they’re presented side by side, but it’s not particularly striking when we’re viewing a supermoon in isolation.

A supermoon is also brighter than usual, reflecting light in proportion to its apparent diameter squared. A figure that gets trotted out every supermoon season is that the full moon will appear 30% brighter than it does when it’s at its farthest away (a micromoon). Which is certainly true, but our eyes are very good at adjusting to differing light levels. Outdoor sunlight is a hundred times brighter than a brightly lit room indoors—but we just don’t perceive the difference unless we walk from one to the other. So our clever eyes actually make it impossible for us to pick up on a comparatively trivial 30% difference, given that we’re unable to make a direct comparison, but have to work from memory of previous full moons.

And that’s why I find it difficult to get excited about supermoons. (Except, of course, for the lovely mathematical patterns they generate.)

* The name anomalistic refers to the way in which an object’s position in orbit is measured, using its angular distance from closest approach, which is called its anomaly. So from one perigee to the next, the Moon moves through a full 360 degrees of anomaly. Why this angle is called the anomaly is a complicated story that I covered in my post “Keplerian Orbital Elements”.

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