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Doesn't it seem dark on early December evenings? And it is dark, because every year the earliest sunset falls sometime around December 7 or 8, two full weeks before the shortest day of the year. TV meteorologists like Greg Fishel love to point this out to us, but they don't have time to explain it. What's going on?
Let's start with some data. The following sunrise, transit, and sunset times times were computed for Chapel Hill in 1997, using the popular planetarium software package Voyager II. ("Transit" is when the Sun appears due south in the sky; it's the time of local noon.) The times don't vary much across our area, or from year to year.
|
Date |
Sunrise (am) |
Transit (pm) |
Sunset (pm) |
Day length |
|
November 23 |
7:00 |
12:03 |
5:04 |
10 hr 4 min |
|
December 7 |
7:13 |
12:08 |
5:02 |
9 hr 49 min |
|
December 21 |
7:23 |
12:14 |
5:06 |
9 hr 43 min |
|
January 4 |
7:27 |
12:21 |
5:15 |
9 hr 48 min |
|
January 18 |
7:25 |
12:26 |
5:29 |
10 hr 4 min |
We can see the culprit: the time of transit, which is astronomical noon, drifts later and later, by about two and half minutes per week, throughout this period. It's as if the Sun were slow: every day it shows up later for noon!
The cause of this odd tardiness was discovered by Johannes Kepler (1571-1630), the German astronomer who was the first to understand the true shape of planetary orbits. As Kepler discovered, the orbit of the Earth is not a circle or some complicated combination of circles; it is an ellipse. Instead of having a center, an ellipse has two foci. A point on the ellipse has the property that the sum of its distances from these two foci is a constant. Kepler found that the orbit of a planet is an ellipse with the Sun at one of its foci.
This means the Earth is closer to the Sun at some times that at others. Surprisingly, the Earth is actually closest to the Sun during the Northern Hemisphere winter (this causes our winters to be milder than they would be otherwise). The time of closest approach, called perihelion, occurs around January 4, two weeks after the Winter Solstice.
Now the Sun is a powerful center of gravity, of course, and as the Earth approaches the Sun it speeds up, pulled by the Sun's gravity. During the winter, we are moving faster through space than we are during the summer.
Now what makes the Sun seem to move across the sky is the Earth's rotation, which does not change its length more than a tiny fraction of a millisecond from day to day. Astronomers have measured that the Earth turns once on its axis in 23 hours 56 minutes 4 seconds. If we measure this period of time, starting when the Sun is due south, then at its end we'll be facing the same direction in space we were before. But the Sun won't appear in quite the same direction, because we've also moved 1/365 of the way around the Earth's orbit ellipse. On the average, it takes another 3 minutes 56 seconds for continued rotation to bring the Sun back to due south.
"On the average." When the Earth moves faster in its orbit, it takes a little more time to bring the Sun back to its highest point in the southern sky, and when the Earth moves slower, it takes a little less time. In the winter, when the Earth is speeding past its closest approach to the Sun, the extra time required comes to a maximum. Local noon gets later every day, as we see in the data.
Now think about this a moment. This means the longest days are in the winter! In the middle of the winter, the Earth needs 40 or 50 seconds more than 24 hours to bring the Sun from one noon to the next, and winter days are actually about 90 seconds longer than summer days. Of course, here we're talking about the entire day, from one noon to the next, and not the period of daylight. By this measure, New Year's Day is one of the longest days of the year.
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Posted December 1, 1997. Features remain online as long as they remain current; they may be updated if new information becomes available.
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Copyright © 1997, Center for Mathematics and Science Education. Teachers have permission to duplicate this page for use in teaching their own classes. All other rights reserved. You are welcome to link to this page, but do not copy its contents. http://www.unc.edu/depts/cmse/nature/snowbird.html |
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