Getting the Long and Short on the Length of Days


Four times a year, at the solstices and equinoxes, Science File receives a raft of similar questions:

Why don't sunrise and sunset occur at the same time on the equinoxes when day and night are the same length?

Why don't the latest sunrise and the earliest sunset both occur on the winter solstice, when the day is shortest? Why don't the earliest sunrise and the latest sunset occur at the summer solstice, when the day is longest?

The short answer is that the apparent disparities arise from human beings' attempts to force an artificial form of timekeeping upon the rhythms of nature.

The technical answer is somewhat more complicated.

At least nine factors affect the precise times of sunrise and sunset, often with unexpected results, according to astronomer Bradley Schaeffer of Yale University. "We can measure the distance to the sun and the moon to the nearest centimeter, but we can't predict the time of sunset to the nearest minute," he said.

The most important factors are the Earth's speed in its orbit and the inclination of its axis. Because the Earth's orbit is an ellipse rather than a perfect circle, its orbital speed varies--faster when we are closer to the sun and slower when we are farther away. The height of the sun in the sky, as a result of the inclination of the Earth's axis, also affects the apparent speed of the sun across the sky.

The net effect is that the time from local high noon to local high noon at any one site is not exactly 24 hours, but may be a few minutes more or less, depending on where the Earth is in its orbit.

That small difference is cumulative. At the beginning of November, the sun is about 16.25 minutes behind an accurate clock, so that noon, as measured by a sundial, actually occurs at 12:16 p.m. The earliest sunset comes at 4:44 p.m. Nov. 27 through Dec. 11, according to astronomer Patrick So of the Griffith Observatory, while the latest sunrise comes at 7:00 a.m. Jan. 5 through Jan. 9.

By the middle of February, solar time has raced ahead of humanity's clocks by about 14 minutes, so the sun is at the highest point in the sky at 11:46 a.m.

The difference between clock time and true solar time is given by the so-called equation of time shown in the illustration. Good sundials usually have a representation of the equation of time engraved on them, astronomer Owen Gingerich of Harvard University said. When the correction indicated by the equation is made to sundial time, he said, "they are generally quite accurate."

If time were kept with sundials, said amateur astronomer Eric Werme of the DEC Corp., sunrise and sunset would come at the same time on the equinoxes and the latest sunrise and earliest sunset would come on the winter solstice. "But it would play havoc with airline schedules," he added.

Other factors have a smaller effect. Sunrise and sunset times are projected for a given time zone, but are truly accurate only for the center of that time zone. Residents on the western edge of a zone will see sunrises and sunsets as much as 30 minutes later than predicted, while those on the eastern edge will see them 10 minutes earlier. (Los Angeles is near the middle of the Pacific time zone.)

Refraction (bending) of the sun's light by the Earth's atmosphere can also change sunrise and sunset times by allowing us to see over the horizon. When the sun is on the horizon, its light gets bent about half a degree, around the curve of the Earth. Looking westward over the ocean, therefore, one is able to see the sun for about two minutes after it has physically dropped below the horizon.

A newly recognized source of error, Schaeffer said, comes from thermal inversion layers, such as those that trap smog in the Los Angeles Basin. Such layers, which come and go on their own unpredictable time scales, can change observed sunrise and sunset times by "as much as a couple of minutes in either direction," he said.

Schaeffer noted that he often gets phone calls from lawyers, who need to know the exact time of sunset for an accident case, or from Islamic clerics, who are forbidden from evening prayers at the moment of sunset. "I simply cannot tell them the time with the degree of accuracy they require," he said.


The Equation of Time

The equation of time shows the correction that must be made to a sundial reading to obtain accurage clock time. The difference is caused by the Earth's varying speed in its orbit and the inclination of its axis. For example, in November (month "11" on the chart) sundial time and clock time can differ by more than 16 minutes.

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