SOLSTICE IS COMING - The Astronomical Hijinks Of The Shortest Day Of The Year
If you live around latitude 42N—a well-populated latitude in North America and Europe, taking in Boston, Rome, and Vladivostok—today is the day you'll experience the earliest sunset of the year. Those who live farther north, in London or Moscow, can expect the earliest sunset on Thursday. Those farther south, in Miami or Mumbai, already had their earliest sunset a few days ago.
The earliest sunset really comes in the first week in December, and the latest sunrise occurs in early January. Yet December 21 really is the shortest day of the year. Why?
Wait a minute. Isn't the solstice, December 21, still more than a week away, the day of the earliest sunset? And the date of the year's latest sunrise, as well? The late sunrise and early sunset combine on the solstice to create the day with the shortest amount of daylight. Right?
Actually, that's a fantasy. The earliest sunset really comes in the first week in December, and the latest sunrise occurs in early January. Yet December 21 really is the shortest day of the year. What sort of astronomical hijinks are responsible for this absurd state of affairs?
Blame it on Earth's non-circular orbit and its tilt in relation to the Sun.
Normally, we don't think of the Earth’s orbit as being anything but a circle. For the really lopsided orbits, look at Mercury or Mars, whose distances from the sun vary by millions of miles at different points in their years.
The Earth’s orbit is almost a perfect circle by comparison.
Almost. On average, Earth's distance from the sun is approximately 92,955,000 miles. The Earth’s orbital eccentricity (the degree to which the orbit deviates from a perfect circle) makes the distance at perihelion—the point in a year where the Earth is at its closest to the Sun—about 91,402,000 miles. Every go around the sun, perihelion occurs around January 4, two weeks after the solstice. And that makes all the difference to the timing of the earliest sunrise.
Why? As Johannes Kepler discovered in the 1600s, when an object is closer to the Sun, it moves more quickly; when it is farther away, it moves more slowly. On average, the Earth orbits the Sun at 18.508 miles per second. But in December and January, as it gets closer to the Sun, the Earth speeds up, until, at perihelion, on or around January 4, it zooms along in its orbit at 18.664 miles per second. A paltry difference of .156 miles per second at first glance, but it means that near perihelion, the Earth is moving around the Sun just under an “extra” 13,500 miles each day.
In our provincial Earthbound way, we experience this speed change as the Sun moving farther to the east each day. Because of this, the Earth has to rotate a few seconds more each day to 'catch up' to the sun rise, and a few seconds even more to see the sun set. Over the course of the year, this difference of seconds—the “perihelion change”—adds up. On some days of the year, the Sun can rise and set nearly 8 minutes earlier or later than it “should” if the Earth's orbit were a perfect circle.
The Equation of Time reaches exactly zero on December 25.
But the riddle of the Sun's rise and set is yet more complicated. The Earth is also tilted 23.5 degrees. (Did you ever wonder why every globe you have ever seen is not straight up and down, with the North Pole directly on top? Globe makers align their product to replicate the natural tilt of the Earth.) When a tilted planet orbits the sun, the amount of sunlight that falls on any given location changes depending on whether that location is tilted toward the sun, as in summer, or away from the sun, as in winter. Because of this tilt, called the planet's obliquity, the sun can rise and set nearly 10 minutes later than it “should” if the planet were not tilted.
Library of Congress
In early November, the orbital movement towards perihelion coincides with the Earth's obliquity to put the Sun more than 16 and a half minutes ahead of where it “should” be if the Earth were in a not-tilted, perfectly circular orbit. This offset is called the “Equation of Time” (equation, in this sense, being an old fashioned term meaning ”adjustment”). As a result, the sunrise and the sunset are earlier than they should otherwise be. This +16 minute offset rapidly dwindles as the Earth continues its orbit: the Sun is 14 minutes ahead by mid-November, and only 10 minutes ahead by early December. This adjustment is large enough to cause the earliest sunset to occur during the first week of December.
By December 21, the sunset is about three minutes later than it was in early December. But, spurred on by the double effect of the perihelion change and the tilt change, the sunrise has been getting later as well, gaining nearly fifteen minutes. This means that despite all of the time shifting, the solstice is still the day with the shortest amount of daylight.
Things start to change more rapidly after the solstice. The Equation of Time reaches exactly zero on December 25, and thereafter starts to go negative for the next two months. Advancing toward the Spring and Summer, the Earth's tilt tends to make the amount of daylight longer, by making the sunrise earlier and the sunset later. However, that's not the only force acting on the Sun—we still have the perihelion to deal with. It's not until January 4, after the Earth passes closest to the sun, that the increasing hours of daylight overtake the Equation of Time. At this point, the sunrise occurs earlier every day, while the sunset continues to occur later every day—exactly what we expected to happen on the solstice.