In the northern hemisphere, the Harvest Moon falls on 1 October in 2020, which is what provokes this post. The Harvest Moon is defined as the full moon that occurs closest to the autumnal equinox, which fell on 22 September (in the northern hemisphere, in 2020). You can find many lists of “names of the full moons” on-line (there’s a rather marvellous compilation of lists here), but the Harvest Moon is the only one that’s defined by the date of the equinox, rather than the month in which it falls—about three times in four it occurs in September, but the rest of the time (as on this occasion) it drifts into October.

The other thing about the Harvest Moon is that it has real astronomical and historical significance. Like many other full moon names, it obviously derives from what’s going on in the seasonal cycle at the time it appears—but there’s a deeper significance, which is what I want to write about here.

To understand what’s special about the full moon around the autumnal equinox, and its relevance to harvesting crops, we need to talk a bit about the orbit of the moon.

As is well known, the Earth’s rotation axis is inclined to the plane of its orbit around the sun, by about 23½º. So the Earth’s rotation and its orbit define two planes, tilted relative to each other—the celestial equator, which is the extension of the Earth’s equatorial plane; and the ecliptic, which is the plane of the Earth’s orbit. So from the vantage point of the Earth, the sun moves around the sky along the ecliptic plane, from west to east, completing one revolution per year. Like this:

The two points at which the celestial equator and the ecliptic intersect have names with complicated astrological origins. The point on the celestial equator which the sun crosses when heading north is called the First Point of Aries. The point opposite that is The First Point of Libra. Both are symbolized by the zodiacal symbols for their corresponding constellations. These are the locations of the sun at the times of the equinoxes—it crosses the First Point of Aries at the March equinox, spends six months bringing summer to the northern hemisphere, and then crosses the First Point of Libra at the September equinox, on its way south for the southern hemisphere summer.

The moon orbits close to the ecliptic plane. For the purposes of this discussion, we can treat it as travelling in the ecliptic plane, and come back to the slight deviation later. So the moon moves (roughly) along the ecliptic from west to east, taking a month to make a full revolution. It also passes through the First Points of Aries and Libra, spending two week over the northern hemisphere, and two weeks over the south.

The moon makes one complete circuit of the celestial sphere every 27.3 days. If it moved at a constant rate along the celestial equator, it would therefore be about 13º farther west every day. The Earth would need to rotate correspondingly farther between successive moonrises and moonsets, making each moonrise and moonset occur about fifty minutes later than its predecessor. And that’s true on average for the real moon. But the fact that the moon’s orbit follows the ecliptic, and not the equator, introduces a subtle variation.

Here’s what happens to successive moonrises at 50ºN latitude, when the moon is passing through the First Point of Aries.

Its 13º displacement along the ecliptic has a northward component in this part of its orbit, which means that it lies closer below the horizon on successive nights than it would do if it were moving parallel to the equator. So the Earth has to rotate less far between successive moonrises, and the moon rises only slightly later each night. (The effect becomes more pronounced at higher latitudes, and less so at lower latitudes.)

But at moonset, the northward movement at the First Point of Aries serves to lift the moon farther above the horizon than it would otherwise be. So successive moonsets show longer delays than the average 50 minutes when the moon is in this part of its orbit.

The situation is reversed two weeks later, as the moon passes through the First Point of Libra. Now each successive moonrise at northern latitudes is delayed more than 50 minutes, like this:

And it should come as no surprise that the delay between successive moonsets is correspondingly shortened at this point in the moon’s orbit.

So although it all averages out over the course of a month, there’s a regular variation in the delay between successive moonrises (and moonsets) during that period. Here’s a chart of the delays for a representative period (September and October 2018) at 50ºN; I’ve marked the passages through the First Point of Aries:

So this happens every month. Why is it particularly relevant only once a year, on the Harvest Moon? Because full moons occur only when the sun is on the opposite side of the sky from the moon. Which means the only time we see a full moon passing through the First Point of Aries is when the sun is in the vicinity of the First Point of Libra—which, you’ll recall from the top of this post, happens during the September equinox. So in the northern hemisphere, at the time of the autumnal equinox, the full moon rises at almost the same time for several successive evenings, but sets more than an hour later each morning. And if you’re bringing in the harvest (as you do in temperate latitudes in the autumn), and you don’t have access to artificial outdoor illumination, then that’s hugely advantageous. For several nights, the full moon rises before twilight fades, and sets only when the morning sky is already bright. You can work around the clock, day and night, to get the crops in, in other words. Which is what’s going on in Mason’s painting at the head of this post.

Does the southern hemisphere have a Harvest Moon? It surely does. All the geometry flips over, so the First Point of Libra assumes the role that the First Point of Aries does in the northern hemisphere. Like this:

Full moons occur at this point when the sun is passing through the First Point of Aries—the March equinox, which is the autumnal equinox for the southern hemisphere. Isn’t that neat? (Well, I think it’s neat.)

There are a couple of subtleties, which mean not every Harvest Moon is the same. The first complicating factor is that the moon’s orbit does not lie perfectly in the ecliptic, but inclined to it at about 5º. The inclined orbit of the moon twists continuously in the ecliptic plane, completing one rotation every 18.6 years, under the influence of the sun’s gravity. This means that the tilt of the moon’s orbit sometimes subtracts from the angle between the ecliptic and the celestial equator, and sometimes adds to it, like this:

So we have “seasons” when the Harvest Moon is delayed even less than average on successive nights, and seasons (nine years later) when it is delayed more than average.

The other complicating factor is that the moon doesn’t orbit in a perfect circle—it moves in an ellipse, and it crosses the sky more slowly when it’s farthest from the Earth (its apogee), and more quickly when it’s closest (perigee). This ellipse twists around in the plane of the moon’s orbit with a rotation period of about 8.8 years. When the apogee aligns with the First Point of Aries, the delay between successive Harvest Moon moonrises is shortened even farther. Conversely, a few years later, the perigee will prolong the delay between successive moonrises.

It so happens that apogee is passing through the First Point of Aries in 2020, and we can see a noticeable effect on moonrises and moonsets. Here’s the delay graph for September and October 2020, again at 50ºN.

The slow movement of the moon at the First Point of Aries shortens the delay between successive moonrises, and between successive moonsets. Conversely, the fast movement at the First Point of Libra lengthens these same time periods. So the delay graphs are dented downwards at Aries, and shoved upwards at Libra—you can see this most clearly in the flattened tops on the moonset curve.

There are few places left in the world where any of this is relevant to the life of farmers, of course. But it’s a fine astronomical curiosity, I hope you’ll agree.

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Note: Moonrise and moonset times used in the graphs were taken from the calculator at timeanddate.com.