At the end of my previous post on this topic, I left you with a diagram of the solar system’s orientation and approximate trajectory in its orbit around the Milky Way galaxy. Below, we’re looking past the solar system towards the galactic core. The plane of the galaxy runs horizontally across the image, north is at the top, and the solar system is travelling around the galaxy in a clockwise direction when viewed from galactic north. For more on all that, consult my first post via the link above.

This time, I want to give some more detail of the exact direction in which the solar system is moving, to the extent that this is known. And this will bring me to my gripes about Wikipedia‘s discussion of the topic, as I promised last time.

Although my arrow marks the general direction followed by the Sun and other stars in its vicinity, in practice this movement is reminiscent of a swarm of bees—they’re all heading in the same direction, but they’re all moving relative to each other as well. Astronomers find it useful to break this orbital motion down into two components—they separate out the general trend of motion from the smaller random relative movements.

To do this, they invoke something called the Local Standard of Rest, which (somewhat paradoxically) is actually in motion around the galaxy. It applies only to our local solar neighbourhood, and it moves at a speed such that a star at rest in the LSR would follow a circular orbit around the galaxy. There’s some uncertainly about the LSR’s velocity, which depends on getting an accurate measurement of the Sun’s distance from the centre of the galaxy, among other things. But it seems to be somewhere around 220 km/s.

Within the LSR, individual stars have their own random motions, typically of a few kilometres per second—these small deviations from the perfect local circular velocity mean that each star is following its own, slightly elliptical, slightly tilted orbit around the galaxy. The relatively small additional velocity component of each star is called its peculiar motion—“peculiar” because it’s unique to that star, not because it’s odd in some way.

Here’s how it fits together:

While stars have very different peculiar motions within the LSR, they’re actually all heading in pretty much the same direction around the galaxy.

The Sun has its own peculiar motion, too. If we add up all the peculiar motions of stars in our local neighbourhood, they don’t average down to zero—the residual velocity is the result of the Sun’s motion relative to the other stars. In practice, this is tricky to work out—we have to sample only stars that belong to the “thin disc” of the galaxy, which share similar orbits with the Sun, and also allow for some complicated dynamics that I won’t go into here. Because of this trickiness, estimates of the Sun’s peculiar motion vary considerably. But my twenty-year-old copy of the fourth edition of Allen’s Astrophysical Quantities gives some fairly typical values—9 km/s towards the galactic centre, 7 km/s towards galactic north, and moving around the galaxy 12 km/s faster than the LSR—giving it an overall velocity (relative to the LSR) of about 16.5 km/s directed towards a point near the star Mu Herculis.

This point, marking the direction in which the Sun is moving relative to the other stars in its neighbourhood, is called the solar apex. (The astronomer William Herschel called it “the apex of the Sun’s way” in the eighteenth century, and you’ll still see that phrase floating around the internet.) There’s a solar antapex, too, on the other side of the sky in the constellation Columba.

Over the years, the constellation of Hercules has become pretty much peppered with solar apex candidates, as each new study samples different stars and makes different dynamical allowances. But here’s the thing to remember about the solar apex—it’s the point towards which the Sun is moving relative to our local stars. But all those local stars, and the Sun, are also whooshing around the galaxy, with the Local System of Rest, at 220 km/s. So the solar apex is not the Sun’s direction of travel in its orbit around the galaxy. As my diagrams above show, the Sun’s peculiar motion will slightly modify the velocity it inherits from the LSR, but not by much.

Which brings me to my first gripe about the Wikipedia page I mentioned in my first post. (Because Wikipedia changes from time to time, my link goes to a copy of the relevant page capture on 19 October 2023, just so you can see what I’m talking about.) Here’s the vexatious text:

The apex of the Sun’s way, or the solar apex, is the direction that the Sun travels through space in the Milky Way. The general direction of the Sun’s Galactic motion is towards the star Vega near the constellation of Hercules, at an angle of roughly 60 sky degrees to the direction of the Galactic Center.

Well, no, the solar apex is very much not “the direction the Sun travels through space in the Milky Way”, or “the general direction of the Sun’s Galactic motion”. Nor is the solar apex particularly near Vega, though Vega is easier to pick out, for the uninitiated, than is Hercules.

Once we factor in the relatively high velocity of the Local Standard of Rest, the Sun is heading pretty much at right angles to the direction of the galactic centre. Here’s a map of the relevant bit of sky, with significant locations superimposed on a base map from In-The-Sky.org:

Around the big label “SOLAR APEX” in Hercules, I’ve dotted a few estimates of the solar apex from different sources—my old Allen’s Astrophysical Quantities (2000), Schönrich et al. (2010) and Ding et al. (2019). The grey horizontal line marks the plane of the galaxy, and the black cross is at 90 degrees galactic longitude—the direction in which the Sun would be headed if it were at rest in the LSR, in a perfectly circular orbit around the galaxy. The point marked “True direction of motion” is what happens when we added 220 km/s of tangential velocity to Ding’s solar apex—the large orbital velocity dominates over the relatively small northward and inward components of the Sun’s peculiar motion. So forget Vega—we’re headed towards Deneb, in the constellation Cygnus.

But, you’ll see, we’re heading slightly inwards and rising northwards out of the galactic plane as we go. Back in 1986, the astronomer Frank Bash wrote a chapter in the textbook The Galaxy And The Solar System, entitled “The Present, Past and Future Velocity of Nearby Stars: The Path of the Sun in 10⁸ Years”, in which he used the current orbital motion of the Sun to predict its future movement around the galaxy. In astronomical terms, this is a positively prehistoric reference, but Bash’s calculations are still commonly quoted, despite the fact our understanding of the galaxy has moved on considerably since he wrote. And I haven’t been able to find a more recent reference. What follows is therefore probably accurate in its broad picture, but wrong in the details.

So (Bash writes), the Sun is moving gently inwards, but will reach its closest approach to the galactic centre (perigalacticon) in 15 million years’ time, at which point it will be at about 99.5% of its current distance. It will then move outwards, reaching a maximum distance (apogalacticon) of about 114.5% after completing half an orbit of the galaxy—so about 135 million years from now. And it’ll continue to move between those extremes, tracing out a rosette pattern around the galactic centre, unless it has some sort of catastrophically close encounter with another star.

Meanwhile, its velocity will loft it northwards at a steadily slowing rate until (14.6 million years from now) it reaches a peak at about 77 parsecs (250 light years) above the galactic plane, after which it will fall back to, and through, the galactic plane, making an excursion to a similar distance on the southern side. And so on. Bash calculated that a full cycle would take about 66 million years. The exact number of north-south oscillations per galactic orbit depends on the vertical mass distribution within the plane of the galaxy—Bash’s figures suggest about 3½ cycles per orbit, but you’ll see other figures quoted.

And that concludes my post about the movement of the solar system within the galaxy. But I now need to briefly return to that annoying Wikipedia page, to highlight another bit of misinformation. Having just assured us we’re all heading for Vega, the page goes on to contradict itself:

The Solar System is headed in the direction of the zodiacal constellation Scorpius, which follows the ecliptic.

Scorpius is a long way from Vega. It’s aligned with the centre of the galaxy—in fact, you can see it in the background of my diagram of the solar system’s orbital motion, above—pretty much at 90 degrees to the Sun’s real direction of orbital travel. Where on Earth does that piece of misinformation come from?

It comes from a 2011 article in National Geographic, headed:

Solar System’s “Nose” Found; Aimed at Constellation Scorpius

A NASA craft has uncovered the solar system’s “nose,” which points in the direction our sun is moving through the Milky Way, a new study says.

The study cited actually says no such thing—the whole bit about the “direction our sun is moving through the Milky Way” seems to be a bit of improvisation by the journalist who wrote the National Geographical article.

This is all about the shape of the heliosphere, which is defined by the location of the heliopause—the surface at which the solar wind of particles radiating outwards from the Sun runs into the gas and dust of the interstellar medium. As the Sun ploughs through the interstellar medium, the heliosphere experiences an opposing drag, and develops a “nose” and a “tail”, like this:

The “nose” of the heliosphere therefore points in the direction from which the interstellar medium is flowing past the Sun—and that “nose” is aimed at the constellation Scorpius. But if the solar system were actually “moving through the Milky Way” in that direction, we’d all be falling towards the centre of the galaxy, rather than orbiting around it. So this is just another case of relative velocities—the interstellar medium is also in orbit around the galaxy, and what we’re seeing is the result of the “peculiar motion” of the interstellar medium relative to the LSR.

As this post goes live, it’s only a few days until an annular solar eclipse, like the one pictured above, will sweep across the Americas on 14 October 2023.

Annular eclipses get their name from Latin anulus, “small ring”, which refers to the ring of sunlight that’s visible around the lunar disc, as shown in the image at the head of this post. They’re the poor relations of total eclipses, in which the lunar disc entirely obscures the Sun.

October’s annular eclipse will follow the track shown in red in the map below.

The Moon’s shadow crosses the Earth from west to east, moving at the Moon’s orbital velocity, about a kilometre per second—equivalent to about three and a half hours to cross the full width of the Earth. The noticeable tilt in the eclipse track above, from northwest to southeast, is because of the inclination of the Earth’s equator to the plane of the Moon’s orbit. You can see the same effect in the track followed by the total eclipse of 9 March 2016, here seen in time-lapse from a Japanese weather satellite stationed above Indonesia:

Notice that the tilt in the March eclipse track is the reverse of what we see in the October eclipse map, above. This is because the Earth is more or less on opposite sides of the Sun in March and October.

The large shadow you can see in the video above is the region in which the Moon’s disc partially obscures the solar disc (a partial eclipse). Only right in the middle of that large patch of shadow does the Moon traverse the exact centre of the Sun’s disc. For a short distance either side of that central eclipse (anything from a few kilometres to something more than a hundred) we can still see either a total eclipse, or the ring of light that characterizes an annular eclipse, but the shift in position will make the eclipse lopsided and of shorter duration.

So we’ve got a narrow region in which we can observe either of the two kinds of central eclipse, annular or total, and a much broader region in which we can see a partial eclipse. These regions correspond to separate areas of the Moon’s shadow cone, which I’ve labelled below:

The blue lines mark off the Moon’s entire shadow—if we stand anywhere within that spreading cone, we’ll see the Moon overlapping the solar disc, to a greater or lesser extent. Within the red lines, the entire lunar disc is superimposed on the Sun. These lines mark off two shadow regions—the umbra, within which the Moon completely obscures the Sun; and the antumbra, from which we can see the Moon outlined against the larger solar disc. The umbra is where we need to be to see a total eclipse; the antumbra is where annular eclipses happen. And the whole surrounding shadow area, called the penumbra, is the region from which partial eclipses can be observed.

So why do we see a mix of the two types of central eclipse?

It’s because of a remarkable coincidence—the Moon is about 400 times smaller than the Sun, but is also 400 times closer, making the two bodies appear to have almost the same size in the sky. So small variations in the relative distance of Sun and Moon can make the Moon look either bigger than the Sun, and able to block out all its light in a total eclipse, or smaller than the Sun, and able only to produce an annular eclipse.

Our distance from the Sun varies a little during the course of a year—we come closest (and the Sun appears largest) in early January; and we’re farthest away six months later, in early July. But the distance to the Moon varies more widely during the course of a month, and also over a longer period of a little over 200 days, in a way a described in detail in my recent post about “supermoons”.

So here’s a comparison of the apparent diameters of the Sun and Moon at maximum, mean and minimum:

In the bottom row, I’ve superimposed the lunar disc on the solar. In the middle, the mean lunar and solar discs match to within a hundredth of a degree. At left, the maximum moon serves to completely block the maximum sun (represented by the yellow circle around the edge of the moon); at right, the minimum moon is unable to block even the minimum sun. So when the Moon is at its closest to Earth (called perigee), it will always cause a total eclipse if it correctly aligns with the Sun; but when it’s at its farthest (apogee), it can never cause a total eclipse. (And, obviously, between those extremes we can get a mixture of annular and total eclipses.) Looking back at my shadow diagram, above, the Moon sometimes comes close enough to Earth for the tip of its umbra to reach the Earth’s surface, causing a total eclipse; and sometimes it’s so far away that the umbra doesn’t reach the Earth at all, and we experience an annular eclipse within the antumbra.

You’d perhaps think that, given how closely the mean sizes of Sun and Moon match, we’d have equal numbers of annular and total eclipses. But that turns out not to be the case, because the Moon moves more quickly near perigee, and more slowly when it’s near apogee. So it actually spends more time at distances greater than its mean distance. Which means we end up with more annular than total eclipses.

Looking at NASA’s Five Millennium Catalog of Solar Eclipses, we can see that there are a whole lot of eclipses in which the Moon’s shadow either just misses or barely grazes the Earth’s surface, but if we concentrate on “pure” annular and total eclipses, during which it’s possible to stand exactly in the centre of the Moon’s shadow with a full eclipse track on either side, there are 3827 annular solar eclipses in the 5000-year catalogue, and only 3121 totals.

And, given that the apparent diameter of the Sun is at its greatest in January and least in July, we might expect to see a corresponding periodicity in the ratio of annular to total eclipses—total eclipses should be “easier” to achieve in July, when the solar disc is smaller. And so it turns out to be:

Finally, one other kind of eclipse is worth mentioning—the hybrid eclipse. These occur when the Earth is positioned almost exactly at the point at which the umbra becomes antumbra. In these circumstances, the curvature of the Earth becomes significant, so that the rim of the Earth can lie in the antumbra while the central bulge extends into the umbra. Like this:

So these eclipses start as annular eclipses when they first make contact with the Earth’s surface, evolve into total eclipses as they cross the Earth, and then turn back into annular eclipses just before they lose contact. They’re fairly rare, but not vanishingly so—there are 569 in the Five-Millennium Catalog. The most recent crossed Indonesia in April 2023, but we’ll need to wait until November 2031 for the next one, which will cross mainly open ocean.

* The steady speed at which the Moon’s shadow crosses the Earth is not reflected in the speed at which the shadow moves across the ground, however. The Earth rotates in the same direction as the shadow moves, and that reduces the ground velocity a bit, depending on latitude. And there’s a geometric effect just after the shadow contacts the Earth’s surface, and just before it leaves, when a small sideways movement of the shadow results in a large movement across the ground, because the Earth’s surface is at an acute angle to the axis of the shadow.

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:

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.

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.)

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

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, timeanddate.com 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:

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

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”.

On 31 August 2023 we’re going to have a blue supermoon, which will be neither particularly blue, nor particularly super, though to read some of the media coverage of these events, you might expect to see something like the image above. So I thought I might write a bit about blue moons (this post) and supermoons (to follow).

So: a blue moon, in current usage, is the second of two full moons falling in the same calendar month—the full moon of 31 August is a blue moon because there has already been a full moon on 1 August.

The phrase once in a blue moon, meaning “very occasionally”, has been around since the nineteenth century. The current astronomical usage is more recent—it originated in 1946, with a notorious error in a Sky and Telescope article, and became popular only during the 1980s, when it was included as a question in the game of Trivial Pursuit. (I’ll write a little more about all that at the end of this post, if you’re still with me.)

To show how blue moons work, I need to introduce the idea of a lunation, which (for our purposes) is the time between two successive full moons. Although the moon looks full to a casual observer for a couple of nights each month, in astronomical terms there is a precise time at which the full moon occurs—the moment at which it’s on exactly the opposite side of the sky from the sun. The time between two of those full moons averages around 29.53 days, but can vary by six or so hours in either direction, as the moon responds to the gravitational tug-of-war between the Earth and the sun. And, given that the astronomical timing is precise, I need to specify the time zone I’m using in what follows—a full moon that occurs before midnight in one part of the world can easily occur after midnight (and perhaps therefore in a different month) somewhere else. But it seems to be customary to figure the blue moon calendar according to Greenwich Mean Time, or its astronomical equivalent, Coordinated Universal Time.

So there’s room, in any calendar month of 30 or 31 days, for an entire lunation to take place. If there’s a full moon very early in the month, there can be another at the end of the month. For a 31-day month, there’s a window of about 1½ days at the start, during which a full moon can occur while still leaving room for another one in the same month, 29½ days later. For a 30-day month, the window is just half a day—meaning that blue moons will be about three times more common in 31-day months than in 30-day months. (When Steve Holmes of the British Astronomical Association crunched the numbers, taking into account the variable duration of a lunation, he determined that any given 31-daymonth has a 1:250 chance of hosting a blue moon; for 30-day months it’s just 1:835.) But February, even in a leap year, is too short to accommodate even the shortest lunation, and is therefore the only month that never has a blue moon.

A “normal” year plays host to twelve full moons. But twelve lunations add up to only 354.36 days, which is almost eleven days less than an average calendar year of 365.25 years, and those “missing” eleven days have a couple of consequences.

Firstly, the date of the full moon in any given month will drift earlier in the month, by about eleven days, with each successive year. The first full moon of 2021 came on 28 January; in 2022 it fell on 17 January; in 2023 on 6 January. In 2024 it will leap back towards the end of the month, 25 January—which we can think of as the 5 February full moon of 2023 coming eleven days earlier in 2024, as a January full moon.

Secondly, if a full moon falls in the first eleven (or so) days of January, that allows room in the calendar year for a thirteenth full moon before the end of December. Thirteen full moons in a twelve-month year means there will be a blue moon in some month during such a year. So the late-January full moons of 2021 and 2022 “prevented” a blue moon; whereas the early January full moon of 2023 provided the opportunity for the blue moon of August. But there will be no blue moon in 2024, when the January full moon skips back towards the end of the month.

It seems like there’s a cycle here, with 13-moon years interspersed with 12-moon years. How often do we get a blue-moon year? We can make a rough-and-ready estimate by realizing that there are eleven days at the start of January during which a full moon will be associated with a blue-moon year, and twenty days in the rest of January when a full moon will prohibit a blue-moon year. So that suggests that a blue moon will appear in 11/31 of years, or about 35%. (Steve Holmes’s detailed calculations came up with a figure of 36.3%, so my quick estimate turns out not to be too shabby.)

I can put all this together in a chart:

The years run from 2011 to 2030, from top to bottom. The grey dots marking full moons form up into long diagonals, sweeping down and left through the years, illustrating the 11-day-per-year mismatch between twelve lunations and the calendar year. Blue moon are marked with larger, blue dots. Notice the interesting effect in 2018, when we had two blue moons—an early first full moon in January left room for a blue moon at the end of that month, which was so close to the end of the month that the lunation skipped February entirely and put the next full moon in early March, leaving room for another blue moon.

In blue-moon years, the earlier the first full moon of the year occurs, the earlier the month of the blue moon tends to be. 2018 had its first full moon on 2 January, giving us the January/March blue-moon pair. The first full moon of 2026 falls on 3 January, and brings a May blue moon. Whereas the first full moon of 2028 is on 12 January, pushing the blue moon to 31 December. (And if 2028 wasn’t a leap year, there wouldn’t be room for a blue moon at all.)

Another example of this “leap year effect” occurred in 2012, when the extra day in February moved the blue moon by two months from where it “would otherwise” have been. If the 9 January full moon of 2012 had happened in a non-leap year we’d have seen a full moon on 1 September instead of the blue moon of 31 August, then a full moon on the first day of October (rather than the last day of September), turning the full moon at the end of October into a blue moon.

So there’s a lot to see in my little twenty-year chart. I’ll just point out one final thing—take a look at the positions of the full moons in the top and bottom rows of the chart. They look pretty much the same! This approximate return of lunar phases to the same dates after nineteen years is called the Metonic Cycle. It turns out that 235 lunations are very similar in duration to 19 tropical years—years as measured by the turn of the seasons, which is what our modern Western calendar approximates with its occasional leap years. For instance, if you care to use my little chart to count off 235 full moons after the first full moon of 2011, which fell on 19 January, you’ll find yourself, 19 years later, at the first full moon of 2030, also on 19 January.

To fit 235 lunations into 19 years, we need to have twelve normal years and seven blue-moon years, since (12×12) + (7×13) = 235. Take a look at my chart again and, sure enough, you’ll find seven blue-moon years. (2018 contains two blue moons, to be sure, but the missing full moon in February ensures that the full-moon count is just thirteen.) And 7/19 = 36.8%, another close approximation to Steve Holmes’s more exact calculated figure, above.

The Metonic Cycle gets its name from Meton of Athens, a Greek mathematician of the 5th century BCE, who incorporated the cycle into a lunisolar calendar—that is, a calendar that tracks both the seasons and the lunar phases. People all over the world have used this sort of calendar, counting off the full moons as a guide to how the seasons are progressing, with three full moons in each “normal” season, and a four-moon season cropping up in seven years out of nineteen.

Well into the twentieth century, there were farmers who would keep an eye on the lunar cycle as a guide to their seasonal activities. In the United States they were aided in this practice by the yearly publication of various “farmers’ almanacs”. And one of those, the Maine Farmers’ Almanac, seems to have originated the idea of applying the name “blue moon” to the extra full moon in a four-moon season. So every year the almanac would publish a list of dates of full moons, together with seasonal names from Christian European tradition like Lenten Moon and Moon Before Yule, interspersed with the occasional Blue Moon, but without an explanation of why specific full moons had been chosen to be blue moons.

In 1946, an amateur astronomer called James Pruett tried to figure out the blue-moon rule used by the Maine Farmers’ Almanac, and in a Sky & Telescope article entitled “Once In A Blue Moon” he described the familiar Metonic Cycle:

Seven times in 19 years there were—and still are—13 full moons in a year. This gives 11 months with one full moon each and one with two. This second in a month, so I interpret it, was called Blue Moon.

Sky & Telescope went on to use Pruett’s definition, and the rest is history.

But in 2006, Daniel Olson, Richard Tresch Fienberg and Roger Sinnott pored over a lot of copies of the Maine Farmers’ Almanac, and figured out the underlying blue-moon rule that had actually been used, which is very different from Pruett’s version:

At last we have the “Maine rule” for Blue Moons: Seasonal Moon names are assigned near the spring equinox in accordance with the ecclesiastical rules for determining the dates of Easter and Lent. The beginnings of summer, fall, and winter are determined by the dynamical mean Sun. When a season contains four full Moons, the third is called a Blue Moon.
Why is the third full Moon identified as the extra one in a season with four? Because only then will the names of the other full Moons, such as the Moon Before Yule and the Moon After Yule, fall at the proper times relative to the solstices and equinoxes.

You can read their full Sky and Telescope article, with much more detail, here.

• Move on to Part Two