The Sunrise/Sunset/Solstice Puzzle: Solved!

It’s obvious to most everyone that summer days are longer than winter days. There’s a quirky aspect to this change, though, one that’s often overlooked and seldom fully explained. In the Northern Hemisphere midlatitudes, the earliest sunrises occur a few days before the summer solstice, and the latest sunsets occur a few days after the solstice. The displacement is even more pronounced in winter: the earliest sunsets (as measured in standard time) can occur several weeks before the solstice, and the latest sunrises can happen well into the new year.

The map below, by Alaska climatologist Brian Brettschneider, shows how this effect varies with latitude around the northern summer solstice.

Figure 1. Dates of the earliest sunrise and the latest sunset in northern summer. Image credit: Courtesy Brian Brettschneider.

What is it that pushes the earliest and latest sunrises and sunsets away from the solstices that are their main trigger? I found a number of explanations when casting about on the Web recently, but for me, they didn’t quite get to the root of the question.

The most common explanation, which is correct as far as it goes, is that the middle of the astronomical day—solar noon, the point when the sun is as high in the sky as it will get on that particular day—shifts forward by a few seconds each day, over a period of about three months around each solstice. In June, this leads to the earliest sunrise happening a few days earlier than would be produced by the summer solstice alone. The same effect also delays the arrival of the latest sunset, to the delight of evening softball leagues and backyard barbecuers.

Why does solar noon creep forward around the solstices (and backward around the equinoxes)? It’s because for several weeks around each solstice, the length of a solar day is slightly more than 24 hours. Likewise, a solar day runs a bit less than 24 hours around the spring and fall equinoxes. To answer the next question—why is this so?—we have to turn to some more complex geometry and astronomy. The most helpful explanation I found came not in a highly produced 3-D animation but on a simple page of well-written text, with just one illustration, created by an interested layperson and self-proclaimed computer nerd, Larry Denenberg.

I encourage you to check out Denenberg’s explanation for yourself, but here’s a condensed version: The mechanism that lengthens the solar day for a few weeks around each solstice is a combined effect of Earth’s rotation and Earth’s orbit around the sun. 

We can consider this geometry from the perspective of the point on Earth where the sun is directly overhead at any moment—the SDO or “sun directly overhead” point. Let’s look at an image that breaks the SDO into its orbital and rotational components.

In Figure 2 below, the “rotation only” curve, depicted at the northern winter solstice (late December), follows the Tropic of Capricorn (around 23.4°S), the latitude where the sun is at the top of the sky at noon in late December. This “rotation only” curve shifts north over the subsequent six months (not shown here), still encircling the planet along latitudinal lines, until by June, it’s made it to the Tropic of Cancer (around 23.4°N).

Figure 2. Depiction of the SDO point (sun directly overhead) as it moves around the Tropic of Cancer on the northern summer solstice due to Earth’s spin (the line marked “rotation only”) and as it traverses a great circle across the tropics over the course of a year (the line marked “revolution only”). Image courtesy Larry Denenberg.

Where it gets more complicated—and what actually shifts solar noon forward and backward—is the “revolution only” curve. Though it appears in Figure 2 as a straight line, it’s actually a great circle that gets rounded into a shallow U-shape as it hits the tropics of Cancer and Capricorn (an important point to keep in mind below). It takes a whole year for the SDO point to complete this “revolution only” path around the globe. I’ll let Denenberg take it from here….

Now the crux of the matter: As the sun-directly-overhead point moves around this great-circle path, it is not moving directly east.  It moves generally east, but sometimes it's travelling a little northeast and sometimes a little southeast.  It moves due east only at its most northerly and southerly extent, which happens at the solstices.

So even though the overall speed of the point is constant, the eastward component of the speed is not constant, and that's what we care about:  it's fastest when the point is moving due east (at the solstices), and is smaller when the point is moving north or south as well as east.  The eastward speed is slowest when the point has the largest northerly or southerly motion, that is, at the equinoxes, when the point crosses the equator.

Hence this once-around-per-year motion of the point, which makes each day a little longer, has a different effect at different times of the year.  At the solstices the motion is due east, so its eastward motion is fastest and lengthens the solar day more.  That is, at the solstices, the solar day is longer than its average length.  At the equinoxes, the point is moving northeast or southeast as much as it ever does, so the eastward component of its speed is at its slowest and has the least effect at making the day longer.  That is, at the equinoxes, the solar day is a little shorter than average.  And we're done.

I asked Denenberg, a technical manager at TripAdvisor who lives in the Boston area, what got him interested in this admittedly arcane topic.

“The original motivation really was my eagerness for more sunlight. I used to get The Old Farmer's Almanac every year to follow the times of sunset; their tables make the phenomenon obvious, though they don't explain it. I thought people would like to know why. Later, explanations started appearing on the Web, but to my annoyance most of them were wrong! People would say that it was due to the ellipticity of the earth's orbit. But that's only part of the story, and not the most important part. I've had plenty of correspondence with astronomy bloggers trying to set them straight, not always successfully.”

The winter solstice and the Daylight Saving Time effect

There’s one other thing to know about the solar-noon displacement process: it’s more pronounced around the (northern) winter solstice than it is around the summer solstice. From early November to early February, northern solar noon moves forward by about 30 minutes, whereas it only moves ahead by about 10 minutes from early May to early August. At lower latitudes, where the summer-to-winter day-length changes are comparatively modest, the solar-noon displacement effect can have an outsized impact. The earliest standard-time sunset of the year sometimes happens on Thanksgiving Day at Key West, Florida (see Figure 3 below)—almost a month ahead of the winter solstice.

Figure 3. Dates of the latest sunrise and the earliest sunset in northern winter, and the number of days between the two dates by latitude. This graphic is based on standard time and does not take Daylight Saving Time into account. Image credit: Courtesy Brian Brettschneider.

When you throw Daylight Saving Time into the picture, things get even more complicated (as is often the case with DST!). Because the end of DST in early November instantly pushes sunrise back by a full hour, there are many U.S. locations that actually see their latest sunrises of the year in early November, just before DST ends. (The advent of DST in March doesn’t have a similar effect, because it occurs much closer to an equinox than to a solstice.)

Here’s a cheat sheet for locations in the 50 U.S. states, based on calculations and input from Brian Brettschneider.

• Latest sunrise always in late December:  Alaska
• Latest sunrise always in January:  Arizona (outside of the Navajo Nation) and Hawaii
• Latest sunrise always in early November, on the last day of DST:  All other locations south of about 39°N
• Latest sunrise sometimes on the last day of DST and sometimes in January, depending on what date DST ends in a given year:  Contiguous U.S. north of about 39°N

The asymmetry between the solar-noon displacement effects on the winter vs. summer solstice is a function of Earth’s not-quite-circular orbit around the Sun: Earth is actually closer to the Sun in early January than it is in July. The asymmetry can also be grasped by looking at a chart called an analemma, which traces the location of solar noon in the sky over an entire year. You can see in the Northern Hemisphere example depicted below that the “summer” side of the analemma (the one higher above the horizon) is smaller than the “winter” side, a result of the asymmetry described above.

The Stanford Solar Center has a website with several great analemma photos and more information. This short, colorful TEDEx animation does a great job illustrating in the various orbital/rotational components that lead to the analemma. For a deeper dive, check out this analemma tutorial video posted as part of an environmental science course.

Southern Hemisphere: It’s not as complicated

All the strange consequences above (except for DST) are mercifully minimized in the Southern Hemisphere. Here, the combination of rotational and orbital factors works to dampen the solar-noon displacement effect, as well as the winter-to-summer asymmetry, as compared to the Northern Hemisphere.

Special thanks go to Larry Denenberg, Brian Brettschneider, and Brian Donegan for assistance with this post.