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Solar time is a reckoning of the passage of time based on the Sun's position in the sky. The fundamental unit of solar time is the day. Two types of solar time are apparent solar time (sundial time) and mean solar time (clock time).
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If a tall pole is fixed vertically in the ground, at some instant during any sunny day, the shadow points exactly north or south - or disappears, if the sun is directly overhead. That instant is local apparent noon-- 12:00 local apparent time. About 24 hours later, the shadow will again point north/south, the sun seeming to have covered a 360-degree arc around the earth's axis. When the sun has covered exactly 15 degrees, that is 1/24 of a full circle (both angles being measured in a plane perpendicular to the earth's axis), local apparent time is 13:00 exactly; after 15 more degrees it will be 14:00 exactly.
The problem is that in September the sun takes less time (as measured by an accurate clock) to make an apparent revolution than it does in December; nowadays 24 "hours" of solar time can be 21 seconds less or 29 seconds more than 24 hours of clock time. This discrepancy is due to the ellipticity of the Earth's orbit and the fact that the Earth's axis is not perpendicular to the plane of its orbit, and is quantified by the equation of time.
We like our clocks to run at a constant rate, so we cannot set them to follow the actual sun—instead they will follow a nonexistent object called the "mean sun" that moves along the celestial equator at a constant rate that matches the real sun's average rate over the year. This is "mean solar time", which is still not perfectly constant from one century to the next but is close enough for most people. Currently the length of a mean solar day is about 86,400.002 SI seconds.
The two kinds of solar time (apparent solar time and mean solar time) are among the three kinds of time reckoning that were employed widely by astronomers until the 1950s. (The third kind of traditional time reckoning is sidereal time, which is based on the apparent motions of stars other than the Sun.) By the 1950s it had become clear that the earth's rotation rate was not constant, so astronomers developed ephemeris time, a time scale based on the positions of solar system bodies in their orbits.
Apparent solar time or true solar time is given by the daily apparent motion of the true, or observed, Sun. It is based on the apparent solar day, which is the interval between two successive returns of the Sun to the local meridian. Solar time can be crudely measured by a sundial.
The length of a solar day varies through the year, and the accumulated effect of these variations produces seasonal deviations of up to 16 minutes from the mean. The effect has two main causes. First, Earth's orbit is an ellipse, not a circle, so the Earth moves faster when it is nearest the Sun (perihelion) and slower when it is farthest from the Sun (aphelion) (see Kepler's laws of planetary motion). Second, due to Earth's axial tilt (known as the obliquity of the ecliptic), the Sun's annual motion is along a great circle (the ecliptic) that is tilted to Earth's celestial equator. When the Sun crosses the equator at both equinoxes, the Sun's daily shift (relative to the background stars) is at an angle to the equator, so the projection of this shift onto the equator is less than its average for the year; when the Sun is farthest from the equator at both solstices, the Sun's shift in position from one day to the next is parallel to the equator, so the projection onto the equator of this shift is larger than the average for the year (see tropical year). Consequently, apparent solar days are shorter in March and September than they are in June or December.
|Date||Duration in mean solar time|
|February 11||24 hours|
|March 26||24 hours − 18.1 seconds|
|May 14||24 hours|
|June 19||24 hours + 13.1 seconds|
|July 26||24 hours|
|September 16||24 hours − 21.3 seconds|
|November 3||24 hours|
|December 22||24 hours + 29.9 seconds|
These lengths will change slightly in a few years and significantly in thousands of years.
Mean solar time conceptually is the hour angle of the fictitious mean Sun. Currently (2009) this is realized with the UT1 time scale, which is constructed mathematically from very long baseline interferometry observations of the diurnal motions of radio sources located in other galaxies, and other observations. Though the duration of daylight varies during the year the length of a mean solar day is nearly constant, unlike that of an apparent solar day. An apparent solar day can be up to 20 seconds shorter or 30 seconds longer than a mean solar day. Because many of these long or short days occur in succession, the difference builds up so that mean time is greater than apparent time by about 14 minutes near February 6 and mean time is less than apparent time by about 16 minutes near November 3. An analemma is a graph of this relationship. Since these periods are cyclical, they do not accumulate from year to year.
The length of the mean solar day is increasing due to the tidal acceleration of the Moon by the Earth, and the corresponding deceleration of the Earth rotation rate by the Moon.
Many methods have been used to simulate mean solar time throughout history. The earliest were clepsydras or water clocks, used for almost four millennia from as early as the middle of the 2nd millennium BC until the early 2nd millennium. Before the middle of the 1st millennium BC, the water clocks were only adjusted to agree with the apparent solar day, thus were no better than the shadow cast by a gnomon (a vertical pole), except that they could be used at night.
Nevertheless, it has long been known that the Sun moves eastward relative to the fixed stars along the ecliptic. Thus since the middle of the first millennium BC, the diurnal rotation of the fixed stars has been used to determine mean solar time, against which clocks were compared to determine their error rate. Babylonian astronomers knew of the equation of time and were correcting for it as well as the different rotation rate of stars, sidereal time, to obtain a mean solar time much more accurate than their water clocks. This ideal mean solar time has been used ever since then to describe the motions of the planets, Moon, and Sun.
Mechanical clocks did not achieve the accuracy of Earth's "star clock" until the beginning of the 20th century. Even though today's atomic clocks have a much more constant rate than the Earth, its star clock is still used to determine mean solar time. Since sometime in the late 20th century, Earth's rotation has been defined relative to an ensemble of extra-galactic radio sources and then converted to mean solar time by an adopted ratio. The difference between this calculated mean solar time and Coordinated Universal Time (UTC) is used to determine whether a leap second is needed. (The UTC time scale now runs on SI seconds, and the SI second, when adopted, was already a little shorter than the current value of the second of mean solar time.)
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