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Day length as a function of latitude and the day of the year

Day length, or length of day, or length of daytime, refers to the time each day from the moment the upper limb of the sun's disk appears above the horizon during sunrise to the moment when the upper limb disappears below the horizon during sunset. Due to the diffusion and refraction of sunlight by the atmosphere, there is actually daylight even when the sun is slightly below the horizon. The period when it is still somewhat light even though the sun is below the horizon is called twilight.

In general, the length of a day varies throughout the year, and depends upon latitude. This variation is caused by the tilt of the Earth's axis of rotation with respect to the ecliptic plane of the earth around the sun. At the solstice occurring about June 20-22, the north pole is tilted toward the sun, and therefore the northern hemisphere has days ranging in duration from just over 12 hours in the southern portion of the Tropic of Cancer to 24 hours in the Arctic Circle, while the southern hemisphere has days ranging in duration from just under 12 hours in the northern portion of the Tropic of Capricorn to zero in the Antarctic Circle. At the equinox occurring about September 22-23, the poles are neither tilted toward nor away from the sun, and the duration of a day is generally about 12 hours all over the earth. At the solstice occurring about December 20-22, the south pole is tilted toward the sun, and therefore the southern hemisphere has days ranging in duration from just over 12 hours in the northern portion of the Tropic of Capricorn to 24 hours in the Antarctic Circle, whereas the northern hemisphere has days ranging in duration from just under 12 hours in the southern portion of the Tropic of Cancer to zero in the Arctic Circle. At the equinox occurring about March 19-21, the poles are again aligned so that the duration of a day is generally about 12 hours all over the earth.

In each hemisphere, the higher the latitude, the shorter the day during winter. Between winter and summer solstice, the day's duration increases, and the rate of increase is larger the higher the latitude. A fast increase of day length is what allows a very short day on winter solstice at 60 degrees latitude (either north or south) to reach about 12 hours by the spring equinox, while a slower increase is required for a much longer day on winter solstice at 20 degrees latitude (again, either north or south) to reach 12 hours by the spring equinox. The rate of change of day duration is generally fastest at the equinoxes, although at high latitudes the change is similar for several weeks before and after the equinoxes. The rate of change of day duration at each solstice is zero as the change goes from positive to negative, or vice versa.

Some interesting facts are as follows:

• On the Equator, the duration of daylight is not exactly 12 hours all the year round, but rather — due to atmospheric refraction and the size of the Sun — exceeds 12 hours by about 7 minutes each day;

• Because the sun is north of the equator for almost 4 days more than half the year, the duration of the average day at a given latitude in the northern hemisphere exceeds the duration of the average day at the same latitude in the southern hemisphere by a few minutes;

• During a few days around the equinoxes-- about March 19-22 and September 21-24-- both poles experience 24 hours of daytime, due mainly to atmospheric refraction. At the poles there is only one sunrise and one sunset in the course of a year. This occurs around the time of the equinoxes.

Alternate definition

More conveniently, atmospheric refraction is ignored and the center of the sun is often used in place of the upper limb for computing a day's duration. When sunrise and sunset do occur, the day duration can be computed as 2ω_o/15°, where ω_o is the sunset hour angle in degrees (°) given by the sunset equation. When sunrise and sunset do not occur during the course of a day, the day duration is either 0 or 24 hours.

To considerable accuracy, all the points at the same latitude on the same calendar date can be considered to have the same day length. The contour plot in the figure is computed using the sunrise equation.

With this definition the following features can be observed:

• At a given latitude, the duration of the longest day in the northern hemisphere (on or about June 21) is the same as the duration of the longest day in the southern hemisphere (on or about December 21);

• Similarly, at a given latitude, the duration of the shortest day in the northern hemisphere (on or about December 21) is the same as the duration of the shortest day in the southern hemisphere (on or about June 21);

• When the northern polar cap of certain range has duration of daytime of 24 hours, the southern polar cap of the same range has duration of nighttime of 24 hours, and vice versa.

• In the northern hemisphere, the Arctic Circle is the southernmost latitude where 24-hour daylight can occur at least on one day of a year (northern summer solstice on or about June 21);

• In the southern hemisphere, the Antarctic Circle is the northernmost latitude where 24-hour daylight can occur at least on one day of a year (southern summer solstice on or about December 21);

See also

• Sun declination
• Solar day
• Postglacial rebound
• Photoperiodism (for effects on living organisms)

External links

• http://www.jgiesen.de/SME/ , a good applet that allows you to find the altitude and azimuth of the sun and moon at any point on earth at any time, by Jurgen Giesen.
• Formulae to calculate day length, by Herbert Glarner
• Calculate sun rise/set, by U.S. Naval Observatory
• Datasets on earth rotation and alignment, IERS, International Earth Rotation and Reference Systems Service (formerly: International Earth Rotation Service)
• Sun chart generator with Daylight Sunrise Sunset table values