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Tuesday, 28 December 2010 13:00

Equation: Sync Up With the Sunrise

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Illustration: Luke Shuman

Illustration: Luke Shuman

The winter solstice is, of course, the shortest day of the year. But if you watch the sun carefully, you’ll notice something odd: The solstice is neither the day with the latest sunrise

(that’s two weeks later) nor the one with the earliest sunset (two weeks before).

During the winter months, the solar day—the time from solar noon (when the sun is highest in the sky) to the next solar noon—is longer than 24 hours. Since your clock sticks with its regular, boring, 24-hour cycles, solar noon comes a bit later each day.

On January 1, for example, solar noon is 28 seconds later than on December 31 (relative to when your clock says it’s noon, that is). But January 1 also has more daylight—in the Northern hemisphere, sunrise comes 16 seconds earlier than the day before. Combine those two effects, and—again, according to your thick-headed clock—the sun seems to rise 12 seconds later than it did on December 31.

So that’s when you get daylight; where the sun is also changes. That’s why solar noon moves: Earth orbits the sun—duh—but over the course of the year, the sun appears to make its way around us on a path called the ecliptic. And each day, Earth has to rotate a wee bit farther around its axis to make a full rotation relative to the sun. (Watch it at the same time from the same spot on Earth every day and the sun traces an analemma, shown above.)

It gets weirder. In winter, Earth’s elliptical orbit carries it closer to the sun, which then covers a larger angle in the sky—and seems to move faster. And the 23.5-degree tilt of Earth’s axis slows the sun in spring and fall, but not winter or summer.

Sound complicated? Don’t worry. Here’s how scientists figure out when the sun is really going to rise.

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<![CDATA[ #solar_cont { display:block; float:left; position:relative; width:660px; margin:0px; padding:0px; } #content #solar_cont p { display:block; float:left; margin:0px 10px 0px 0px; width:100px; line-height:1.2em; } #content #solar_cont p.last { margin-right:0px; } ]]>

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The difference between solar time and clock time on a given date.

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How far the sun would have gotten on its annual trek around the ecliptic if the orbit of Earth were a perfect circle instead of an ellipse. This is measured as an angle, in degrees of travel around Earth.

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How far the sun actually appears to have gotten around the ecliptic. When Earth is closer to the sun, it travels through a bigger angle in a day, making the sun seem to move faster.

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How far the sun would have gotten on its annual path if Earth’s axis weren’t tilted.

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How far the sun has actually gotten, given that Earth’s axis is tilted.

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A factor that converts the number of degrees of distance to time—it takes 24 hours (or 86,400 seconds) to move through 360 degrees. That’s one degree every 240 seconds.



Authors: Julie Rehmeyer

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