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Column: Lighten the dark

14 November 2019

If you’re counting the days until you can see the Sun again in the evening, you need to know about the equation of time.

Canny Glasgow (1887).
Canny Glasgow (1887), by John Atkinson Grimshaw. Credit: Carmen Thyssen-Bornemisza Collection, via Wikimedia Commons, PD-US

What a dreary time of year this is.

Ever since June, daylight hours have been getting shorter here in the Northern Hemisphere. At this point in the season, the long, dark evenings can start to feel oppressive.

In most of the US, daylight saving time (DST) ended at the beginning of this month. In College Park, Maryland, where I live, sunset shifted from 6:07pm on Friday, 1 November—late enough for me to go for a walk in the park after work—to 5:04pm on Monday, 4 November. (I’m using the times reported by Today, 14 November, sunset is at 4:54, and it keeps getting earlier.

This is more than a minor annoyance. Seasonal affective disorder impacts the mental health of millions of people. And although I might not officially be one of them—I’ve never been formally diagnosed—I can tell that the dark evenings this time of year depress my mood and drain my energy.

Miller's Diary logo.

Miller’s Diary

Physics Today editor Johanna Miller reflects on the latest Search & Discovery section of the magazine, the editorial process, and life in general.

The good news is that the worst will be over in a few weeks. Even though the shortest day of the year, 21 December, is still 37 days away, the earliest sunset arrives considerably sooner than that. The difference is because of the equation of time.

For most of human history, time was marked by the Sun. The middle of the day was solar noon—when the Sun reached its highest point in the sky, or equivalently, when wherever you were on Earth was directly facing the Sun—and the hours were counted up to and from there.

The apparent solar day—the time between one solar noon and the next—is a little bit longer than the 23 hours, 56 minutes, and 4 seconds it takes Earth to turn once on its axis. As Earth rotates, it also revolves around the Sun, so it has to turn by an extra degree or so (1/365 of a rotation, on average) to bring any particular point back in line with the Sun.

But Earth’s orbit is not a perfect circle. So by Kepler’s second law of planetary motion, Earth’s speed in its orbit is not constant, and neither is the amount of extra rotation between successive solar noons. That effect, combined with the effect of the tilt of Earth’s axis, means that the apparent solar day can be as much as 30 seconds longer or shorter than 24 hours.

Nowadays, we mark time with mechanical and electronic clocks, and our days (discounting leap seconds) are exactly 24 hours long. Solar noon, therefore, can’t fall at the same time each day. The equation of time—it’s an “equation” in the sense of “the process of making things equal,” not a mathematical formula—describes how the discrepancy between clock time and solar time changes over the course of the year.

We’ve covered the equation of time before in Physics Today in the context of its implications for travelers and navigators (see the Quick Study by Anna Sajina, November 2008, page 76). Here, I want to look at what it means for those of us who just want to see some evening daylight again.

The winter solstice, as I said, is 37 days from now. So the daylight hours today are just as long as they will be on 27 January, 37 days after the solstice. If it weren’t for the equation of time, the sunrise and sunset times would be the same, too, and we’d have a 74-day stretch ahead of us of evenings at least as dark as tonight.

But today in College Park, solar noon is at 11:52 am, within a minute of its earliest value all year. Solar noon on 27 January, though, will be at 12:20 pm, which is close to its latest value. The sunrise and sunset times are shifted accordingly: Today’s sunset is at 4:54pm, and 27 January’s is almost half an hour later, at 5:23pm.

College Park’s earliest sunset of the year, therefore, is not on 21 December, but on 7 December—just 23 days from now. After that, our daylit evenings start coming back. By 29 December, the sunset will be back to 4:54, so we have just 45 days, not 74, of sunsets earlier than tonight’s. To me, just knowing how soon it will be over makes this dark time of year a little less daunting.

The equation of time is the same everywhere on Earth, so no matter where you live, the sunset on 27 January will be 28–29 minutes later than it is today. The date of the earliest sunset depends on where you are (in Miami, it’s on 29 November; in Quebec City, 10 December), but it’s always before the solstice.

The latest sunrise of the year, on the other hand, isn’t until after the solstice (5 January in College Park, plus or minus a few days for other locations). So if it’s early-morning daylight that you crave, you’ll just have to hang in there.

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