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Solar time

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On a prograde planet like the Earth, the sidereal day is shorter than the solar day. At time 1, the Sun and a certain distant star are both overhead. At time 2, the planet has rotated 360° and the distant star is overhead again (1→2 = one sidereal day). But it is not until a little later, at time 3, that the Sun is overhead again (1→3 = one solar day). Or more simply, 1-2 is a complete rotation of the Earth, but because the revolution around the Sun affects the angle the Sun hits a position on the Earth, 1-3 is how long it takes noon to return

Solar time is a reckoning of the passage of time, and it is based on the Sun's position in the sky. The fundamental unit of solar time is the day. As observed from Earth, the Sun appears to rise in the sky from the east, and set in the west. When the Sun is visible in the sky, an observer at any longitude may measure the position of the Sun as an hour angle, which is interpreted as local time for that observer.

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).[1] Nowadays, however, there are newer methods of time reckoning that have been designed to be independent of the Earth's rotation; the first such modern method, ephemeris time, was developed in the 1950s.

Apparent solar time

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.[2][3] Solar time can also be measured (to a limited precision) by a sundial.

The length of a solar day varies throughout the year, and the accumulated effect of these variations (often known as the equation of time) produces seasonal deviations of up to 16 minutes from the mean. The effect has two main contributory 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 (often known as the obliquity of the ecliptic), the Sun moves 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 is moving at an angle to the equator, so the projection of this tilted motion onto the equator is slower than its mean motion; when the Sun is farthest from the equator at both solstices, the Sun moves parallel to the equator, so the projection of this parallel motion onto the equator is faster than its mean motion (see tropical year). Consequently, apparent solar days are shorter in March (26–27) and September (12–13) than they are in June (18–19) or December (20–21). These dates are shifted from those of the equinoxes and solstices by the fast/slow Sun at Earth's perihelion/aphelion. (In addition to these two main effects there are others, due to lunar and planetary perturbations, which can produce a few more seconds in the equation of time.)

In 2010, the greatest UT1 time interval between apparent midnights (at Greenwich) is 86471 seconds and the shortest interval is 86325 seconds.[4]

Mean solar time

Main article: Universal time

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.[5][6] Though the amount of daylight varies significantly, the length of a mean solar day is substantially constant, unlike that of an apparent solar day.[7] An apparent solar day can be up to 20 seconds shorter or 30 seconds longer than a mean solar day.[8][9][10] 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.[11] Since these periods are cyclical, they do not accumulate from year to year. The difference between apparent solar time and mean solar time is called the equation of time.

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 by the Moon.

History

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 second millennium BC until the early second millennium. Before the middle of the first 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.[12])

See also

References

  1. ^ For the three recognized kinds of time, see (for example) the explanatory section in the almanac Connaissance des Temps for 1902, page 759.
  2. ^ Astronomical Almanac Online (2010). United States Naval Observatory. s.v. solar time, apparent; diurnal motion; apparent place.
  3. ^ Astronomical Information Sheet No. 58. (2006). HM Nautical Almanac Office.
  4. ^ United States Naval Observatory. (April 2010). Multiyear Computer Interactive Almanac version 2.2.1. Willmann-Bell. Used to obtain equation of time for each day in 2010.
  5. ^ McCarthy, D. D. & Seidelmann, P. K. (2009). TIME From Earth Rotation to Atomic Physics. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA. ISBN 978-3-527-40780-4. pp. 68, 326.
  6. ^ Capitaine, N., Wallace, P. T., & McCarthy, D. D. (2003). "Expressions to implement the IAU 2000 definition of UT1", Astronomy and Astrophysics, vol.406 (2003), pp.1135-1149 (or in pdf form); and for some earlier definitions of UT1 see Aoki, S., H Kinoshita, H., Guinot, B., Kaplan, G. H., D D McCarthy, D. D., & Seidelmann, P. K. (1982) "The new definition of universal time", Astronomy and Astrophysics, vol.105 (1982), pp.359-361.
  7. ^ For a discussion of the slight changes that affect the mean solar day, see the ΔT article.
  8. ^ Jean Meeus, Mathematical astronomy morsels (Richmond, Virginia: Willmann-Bell, 1997) 346.
  9. ^ Equation of time in red and true solar day in blue
  10. ^ The duration of the true solar day
  11. ^ McCarthy, D. D. & Seidelmann, P. K. (2009). TIME From Earth Rotation to Atomic Physics. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA. ISBN 978-3-527-40780-4. p. 11.
  12. ^ :(1) In "The Physical Basis of the Leap Second", by D D McCarthy, C Hackman and R A Nelson, in Astronomical Journal, vol.136 (2008), pages 1906-1908, it is stated (page 1908), that "the SI second is equivalent to an older measure of the second of UT1, which was too small to start with and further, as the duration of the UT1 second increases, the discrepancy widens." :(2) In the late 1950s, the cesium standard was used to measure both the current mean length of the second of mean solar time (UT2) (result: 9192631830 cycles) and also the second of ephemeris time (ET) (result:9192631770 +/-20 cycles), see "Time Scales", by L. Essen, in Metrologia, vol.4 (1968), pp.161-165, on p.162. As is well known, the 9192631770 figure was chosen for the SI second. L Essen in the same 1968 article (p.162) stated that this "seemed reasonable in view of the variations in UT2".


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