March equinox, 2019
Click to enlarge
Prepared using Celestia

I’m posting this on March 20, the date of the first equinox of the year. In the northern hemisphere, we call it the spring or vernal equinox, because it marks the start of astronomical spring in northern latitudes. (The meteorological seasons follow the calendar months, so meteorological spring started on March 1.) Of course, for people who live in the southern hemisphere the same moment marks the onset of astronomical autumn—so it’s becoming more customary to refer to this equinox as the March or northward equinox, according to the month in which it occurs and the direction in which the sun is moving in the sky, thereby avoiding the awkward association with a specific season. Correspondingly, the other equinox is designated the September or southward equinox.

At the equinoxes, the sun stands directly above the Earth’s equator. Three months later, it reaches its most northerly or southerly excursion in the Earth’s sky, and begins to move towards the equator again, until another equinox occurs, six months after the previous one.

With the sun over the equator, the division between day and night runs through both poles. So every line of latitude is (almost) evenly divided between day and night, and (pretty much) everyone on Earth can expect to experience (something pretty close to) 12 hours of daylight and 12 hours of darkness around the time of the equinox. Hence the name, which is derived from Latin æquus, “equal”, and nox, “night”.

The previous paragraph is thick with disclaimers because an exact division into equal periods of day and night applies only to a strictly geometric ideal, in which a point-like sun illuminates an Earth with no atmospheric refraction. In the real world, the sun is about half a degree across, so it continues to shed daylight even when the centre of its disc is below the horizon. And atmospheric refraction serves to lift the solar disc into view even when it is, geometrically speaking, below the horizon. (I’ve written about these effects in more detail in my post about the shape of the low sun, and my calculation of which place on Earth gets the most daylight.) Both these effects serve to extent the period of daylight. At the equator, their combined effect means that the equinoctial day is almost quarter of an hour longer than the equinoctial night. And the effect increases the farther from the equator you travel, because the sun rises and sets on a more diagonal trajectory relative to the horizon. At the extreme, we find that the equinoctial sun is visible above the horizon at the north and south poles simultaneously, skimming along just above, and almost parallel to, the horizon. This year, the sun will rise at the north pole in the evening of March 18; it won’t set at the south pole until the very early morning of March 23. (Both according to Greenwich Mean Time.) So, counterintuitively, both poles are experiencing 24-hour daylight at the time of the equinox.

Now let’s consider the timing of the equinox. The image at the head of this post is the sun’s view of the Earth on 20 March 2019, at 21:59:34 GMT. You can see from the reflected highlight in the Pacific Ocean that the sun is shining directly down on the equator, somewhere in the Pacific to the east of the Date Line.

West of the Date Line, a new day has already begun, so for anyone in a time zone more than two hours ahead of Greenwich, this equinox is occurring on March 21. But here in the UK, which keeps GMT in March, we haven’t had an equinox on March 21 since 2007, and we won’t have another until 2102. In fact, all our March equinoxes will occur on March 20 until 2044, when we’ll start seeing them fall on March 19, one year in four.

What’s happening to make the dates shift like that?

The problem is that the average length of a tropical year (the time between one equinox and its equivalent the following year) is 365.2422 days. So in a sequence of 365-day years, the seasons will come around 0.2422 days (5 hours 49 minutes) later each year. The date of the equinoxes would very quickly run ahead through the calendar, if it weren’t for leap years. During a 366-day year, the equinox arrives 18 hours 11 minutes earlier than it did the previous year, because the extra day of February 29 has shoved the calendar date ahead by 24 hours, outstripping the movement of the equinox.

So the GMT timing of the March equinox looks like this, for the forty years spanning 2000 *:

March equinox times, 1980-2020
Click to enlarge

A sawtooth pattern, made up of three steps forward, totalling 17 hours 26 minutes, followed by one jump back of 18 hours 11 minutes. So the equinoxes actually drift back through the calendar year, at a rate of about 45 minutes every four years. Hence the fact we haven’t seen a March 21 equinox in the UK for more than a decade, and will start seeing March 19 equinoxes in a couple more decades.

And that was the problem with the old Julian calendar, and its regular repeating pattern of leap years. The seasons drifted steadily earlier in the calendar. The problem was addressed with the introduction of the Gregorian calendar in 1582, which drops three leap years in four centuries. Centuries not divisible by 400 are not leap years—so we dropped a leap year in 1700, 1800 and 1900, but had one in 2000. And we’ll drop leap years in 2100, 2200 and 2300. (I wrote more about the Gregorian calendar reform in my post concerning February 30.)

The interruption to the sawtooth regression of the equinox relative to the calendar will look like this in 2100:

March equinox times, 2090-2110
Click to enlarge

That extra forward drift is cumulative over the three centuries of dropped leap years. Here’s what the equinox timing looks like, on leap years between 1600 and 2400:

Leap-year March equinoxes, 1600-2400
Click to enlarge

Here we see the steady backwards drift during each century, as shown in my first chart. Then a jump forward at the turn of the century when the leap day is omitted, as was shown in my second chart. If we omitted the leap day every century, it’s evident that the trend would carry the time of the equinox steadily forward relative to the calendar. But by observing a leap day in 2000 we allowed the backward drift of the equinox to continue uninterrupted from the 1900s into the 2000s, undoing the forward drift incurred by the three missed leap days.

It’s neat, isn’t it? But there’s still a very slight mismatch. The average length of a Gregorian calendar year is 365.2425 years, a little longer than the tropical year of 365.2422. So there’s a very slow backward drift of the equinox relative to the calendar. Compare, for instance, the peak immediately after 1900 to the peak after 2300. The 1904 leap year equinox fell on March 21, whereas the one in 2304 will occur late on March 20. There were twelve March 21 equinoxes in a row (1900 to 1911, inclusive) at the start of the twentieth century. There will be just four (2300 to 2303, inclusive) at the start of the twenty-fourth.

Still, not to be sniffed at. That’s the longest run of March 21 equinoxes that will ever happen in the future, at least until the Gregorian calendar is revised in favour of something more accurate. Mark it on your calendar.

* All my figures for equinox timings come from Jean Meeus’s incomparable Astronomical Tables Of The Sun, Moon And Planets.

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