Starts With A Bang

# Ask Ethan: When Is The Earliest Sunrise And Latest Sunset Of The Year?

#### The summer solstice is the longest day of the year, but doesn’t have the earliest sunrise or the latest sunset. Here’s why.

The length of a day on planet Earth might always appear to be the same, at 24 hours, but how much sunlight we get changes dramatically throughout the year. The summer solstice gives us the greatest amount of daylight, with the more polar latitudes experiencing the longest-duration days. If you’re near the equator, however, there’s hardly a difference at all between the number of hours the Sun spends in the sky all throughout the year, from summer solstice to equinox to winter solstice and back again. But solstices don’t determine everything about a day’s length, and that’s what Patreon supporter Ben Turner wants to know, asking:

We all know the solstices are the longest/shortest days off the year, but given the analemma, when are the earliest/latest sunrise/sunset times? Is it consistent at all latitudes?

It’s not consistent, and it’s a very complicated story. Let’s explore why.

This is the analemma: the shape you get if you take a photo of the Sun every day throughout the year from the same location at the same time of day. This particular analemma was taken from the northern hemisphere of Earth, and it was taken some time in the afternoon. You can tell this from the shape and orientation of the analemma. From the northern hemisphere, the small loop of this figure-8 is always higher up; from the southern, the larger loop is on top.

If you were to photograph the analemma at high noon, when the Sun reaches its greatest angular height above the horizon, the analemma would be completely vertical, while it tips as though it were rotated counterclockwise earlier in the day and clockwise later in the day. In all cases, the summer solstice is the tip of the long axis of the analemma, while the winter solstice is at the opposite tip.

The reason the analemma has the particular shape it does is due to two factors working in combination:

1. the Earth is tilted on its axis, at 23.5° relative to the Earth’s orbital plane, as it rotates,
2. and the Earth moves around the Sun in an elliptical fashion, rather than in a perfect circle.

If the Earth’s axis weren’t tilted as it rotated, and our planet also orbited in a perfect circle around the Sun, our analemma would merely be a single point: the Sun would follow the same path every day. With each day that passed, our planet would rotate a full 360° in 23 hours and 56 minutes, and would then spend an extra 4 minutes to “catch up” to the Sun’s previous position in the sky, since we’re also revolving around the Sun. That extra 4 minutes is why our days are 24 hours: because we have to rotate more than 360° to complete a full day.

Once we realize this is how the Solar System works, we can start adding in the other effects. Our planet is tilted on its axis, which means that the Sun’s path through the sky will change throughout the year. When you compare the June solstice to the December solstice, the difference in the apparent position of the Sun will differ by twice our axial tilt: 47°. If you were to examine the top-to-bottom angular scale of our analemma, across its long axis, you’d find it was 47° on the sky from every location on Earth.

If our planet was only tilted but still orbited in a perfect circle, our analemma would be a perfectly symmetric figure-8. Both lobes of the “8” would be symmetric, and they’d cross in the middle: during the equinoxes. In the spring and fall, after the equinoxes, the Sun would rise and set later than average, while in the summer and winter, after the solstices, the Sun would rise and set earlier than average.

But the eccentricity adds another effect in. When the Earth is farther from the Sun (closer to aphelion), it orbits the Sun more slowly than average, so that our planet advances more than it needs to in a 24 hour time period. When the Earth is closest to the Sun (near perihelion), it orbits faster than the average, so our planet rotates slightly less than it needs to in order to return the Sun to the same exact position after 24 hours.

Because of this effect, and the fact that perihelion occurs just after the December solstice (with aphelion happening shortly after the June solstice), the “December solstice” side of the analemma is much larger, with bigger time differences, while the “June solstice” side is much narrower, with smaller departures from the mean time. There’s constructive interference of these two effects during the end of the year, but destructive interference during mid-year.

The equation of time, which is the combined effect of our revolution around the Sun and its orbital eccentricity with the effect of our rotation and axial tilt, is the same across all latitudes on Earth. When we’re close to the June solstice, everything is earlier.

In the northern hemisphere, even though the days are longer, sunrise and sunset are both shifted towards slightly earlier times at earlier dates. Someone close to the Arctic circle will see their earliest sunrise occur 1–3 days before the solstice, while someone at mid-latitudes (around where Washington, D.C.) is gets it about a week before the solstice, and someone near the Tropic of Cancer gets the earliest sunrise about two weeks prior to solstice. In the southern hemisphere, similar shifts occur in a latitude-dependent fashion, except this gives you your earliest sunsets, as the days are shorter.

Similarly, because of the way the equation of time changes (where it switches sign very close to each solstice), the latest sunsets for northern hemisphere observers see the same latitude-dependent shifts, except after the June solstice. Close to the Arctic circle, latest sunsets occur 1–3 days after the solstice; mid-latitudes see their latest sunsets about a week after solstice; Tropic of Cancer-like latitudes get their latest sunsets right around the 4th of July.

In the southern hemisphere, similar shifts occur in the same latitude-dependent fashion. The big difference is that you’ll get your latest sunrises of the year at those times.

What’s interesting about all of this is that what the northern and southern hemisphere experience during the June solstice isn’t exactly flipped during the December solstice. Because the equation of time has much more pronounced changes when the effects of obliquity and ellipticity constructively interfere, the time shifts are larger around the December solstice than the June solstice.

This is something you might have intuited by looking at the shape of the analemma. On the side where the lobe of the figure-8 is bigger and it displasy greater time differences, you can expect that sunset/sunrise times will be shifted by a greater amount than where the lobe of the figure-8 is smaller. The big lobe, corresponding to the December solstice, sees much more dramatic changes.

As a result, you not only need to flip the hemispheres and sunrise/sunset effects from June to December, but the combined effects of obliquity and ellipticity increase the effects of early/late sunrise/sunset times by approximately 50%. When planet Earth swings close by the Sun, its motion is significantly faster than at any other time, meaning that we experience large changes in how much our clocks depart from an astronomical “mean time” between sunrise and sunset.

Travel the Universe with astrophysicist Ethan Siegel. Subscribers will get the newsletter every Saturday. All aboard!

There are two other points where the equation of time goes back to a symmetric state: on April 14th and August 30th. These points, approximately 3 weeks after the March equinox and 3 weeks before the September equinox, have no special significance. They are determined by the way our seasons, determined by axial tilt, align with our planet’s orbit around our Sun.

The shape of our analemma, and Earth’s equation of time, are not fixed. Approximately 5,000 years from now, our planet’s perihelion and aphelion will be aligned with our equinoxes, which means our analemma will change from a figure-8 shape to a teardrop shape.

When this alignment reaches perfection, headed our way in the relatively distant future, our earliest sunrise and latest sunset will occur on the summer solstice, and our latest sunrise and earliest sunset will occur on the winter solstice. Although the specific times at which those events occur will vary by latitude, they will all occur on the same dates for all observers on Earth. As long as our planet’s axis precesses, which should continue for longer than our Sun shines, our sunset and sunrise times will continue to change from year-to-year. Thanks to our axial tilt and elliptical orbit, we can finally come to understand how.

Send in your Ask Ethan questions to startswithabang at gmail dot com!

Ethan Siegel is the author of Beyond the Galaxy and Treknology. You can pre-order his third book, currently in development: the Encyclopaedia Cosmologica.

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