The Earliest Sunset

Two happy facts: today is my birthday, and this evening the sun set at 4:13 PM. Depending on your latitude, 4:13 may sound pretty dismal, but consider this. Last week the sun was setting at 4:12 PM. I call that progress.

For years I’ve been talking about the happy fact that in December the earliest sunset happens well in advance of the solstice. This little known and little noticed boon helps me get through the dark days of December, because I know that, starting on December 9th, the afternoons are going to be getting a little longer. This year I decided to spend a little more time explaining why this should be.

How Long is the Day? Apparent Solar Time

Even if you have no clock, you can still tell when it’s noon. Noon is defined as the instant at which a straight stick leaves the shortest shadow. At that moment, the sun is as high in the sky as it’s going to get. This is the principle of the sundial, and it’s how the ancients told time. But suppose you now have a stopwatch, and you can accurately measure how much time passes between two noons. You’ll notice something strange about your measurements: the length of the day varies up to half a minute.

This is the length of the day, as measured from noon to noon.

It might not seem like a big deal, and in fact nobody cared at all until the first accurate clocks were invented starting in the 1600s. But this discrepency ends up being a big inconvenience for the sorts of people who make schedules. Think about it this way: if a day is 24 hours long, then what we’re saying is that the length of an hour depends on what day of the year it is.

What to do? To smooth things over, astronomers created a mean solar day that is the average length of all the days in one year. So the time from noon to noon is declared by fiat to be 24 standard unvarying hours. But now you have a different problem. Instead of the hour misbehaving because of the sun, we now have the sun misbehaving because of the hour. That is, we modern folks simply decree that it is noon even when the sun isn’t close to being overhead. These variations of the day’s length pile up at different times of the year, leading the sun to be out of step with the clock by as much as 16 minutes.

It’s a little ironic that the sun gave us our very definition of time, and then we turn around and call it out for its flaws in timing. But there you go.

Fudge Factor: The Equation of Time

The degree to which the sun is out of step with the clock is called the Equation of Time. That’s a grand name, but this equation solved a problem that people had in the days before you could call up official time on your phone or a website. To set your clock accurately, you just figure out when it’s noon (using a sundial or a sextant), and then add or subtract the Equation of Time factor.

Here’s what the Equation of Time looks like. I’m not going to bother explaining why it wiggles around other than to say that it results from two factors: the elliptical nature of the earth’s orbit and the tilt of the earth on its axis.

The Earliest Sunset

Now we are ready to tackle the problem of the earliest sunset. We’ve done the hard part. In the ancient sundial world, there were always as many hours between sunrise and noon as there were hours between noon and sunset. That’s the old definition of noon: it splits the day into equal parts forenoon and afternoon.

Here’s what the length of the day might look like in the mid-northern latitudes as we pass through the winter solstice. Each blue line represents the length of a single day. Calendar days are going from the top to the bottom. The sun rises on the left, passes through noon in the middle, and sets on the right.

The red circles show the earliest sunset and the latest sunrise happening as expected on the shortest day, the winter solstice. The symmetry of the diagram is very satisfying.

But we don’t live in the ancient world. The modern world has the sun shifted away from overhead when our clocks tell us it’s noon. That’s the Equation of Time. That means that extra minutes are being added to the morning and removed from the afternoon, or vice versa. So imagine we’re taking these days, which are like stacked plates in this visualization, and skewing them as shown by the leaning black line. Now the day length is shown in light blue (the dark blue lines from the previous plot are left in place for comparison).

Behold! The earliest sunset now arrives a few days in advance of the solstice. Similarly, the latest sunrise has been shifted to a few days later than the solstice. As for the timing of the solstice itself, no amount of shifting noon this way or that will change the length of the day, so we experience solstice on the same day as the Romans and the Babylonians.

2 thoughts on “The Earliest Sunset”

  1. Ned,

    Very good post. This factoid is in the “well known but not widely known” category.

    Also, I learned that you and I share a birthday! (I am sure you know famous others, but look up Piet Hein if you don’t know him.) I got Rock Band 3, and my son is home from college, so it was a great day.

    the cyclist

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