Time standard
A time standard is a specification for measuring time: either the rate at which time passes; or points in time; or both. In modern times, several time specifications have been officially recognized as standards, where formerly they were matters of custom and practice. An example of a kind of time standard can be a time scale, specifying a method for measuring divisions of time. A standard for civil time can specify both time intervals and timeofday.
Standardized time measurements are made using a clock to count periods of some cyclic change, which may be either the changes of a natural phenomenon or of an artificial machine.
Historically, time standards were often based on the Earth's rotational period. From the late 17th century to the 19th century it was assumed that the Earth's daily rotational rate was constant.^{1} Astronomical observations of several kinds, including eclipse records, studied in the 19th century, raised suspicions that the rate at which Earth rotates is gradually slowing and also shows smallscale irregularities, and this was confirmed in the early twentieth century.^{2} Time standards based on Earth rotation were replaced (or initially supplemented) for astronomical use from 1952 onwards by an ephemeris time standard based on the Earth's orbital period and in practice on the motion of the Moon. The invention in 1955 of the caesium atomic clock has led to the replacement of older and purely astronomical time standards, for most practical purposes, by newer time standards based wholly or partly on atomic time.
Various types of second and day are used as the basic time interval for most time scales. Other intervals of time (minutes, hours, and years) are usually defined in terms of these two.
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Time standards based on Earth rotation
Apparent solar time ('apparent' is often used in Englishlanguage sources, but 'true' in French astronomical literature^{3}) is based on the solar day, which is the period between one solar noon (passage of the real Sun across the meridian) and the next. A solar day is approximately 24 hours of mean time. Because the Earth's orbit around the sun is elliptical, and because of the obliquity of the Earth's axis relative to the plane of the orbit (the ecliptic), the apparent solar day varies a few dozen seconds above or below the mean value of 24 hours. As the variation accumulates over a few weeks, there are differences as large as 16 minutes between apparent solar time and mean solar time (see Equation of time). However, these variations cancel out over a year. There are also other perturbations such as Earth's wobble, but these are less than a second per year.
Sidereal time is time by the stars. A sidereal rotation is the time it takes the Earth to make one revolution with respect to the stars, approximately 23 hours 56 minutes 4 seconds. For accurate astronomical work on land, it was usual to observe sidereal time rather than solar time to measure mean solar time, because the observations of 'fixed' stars could be measured and reduced more accurately than observations of the Sun (in spite of the need to make various small compensations, for refraction, aberration, precession, nutation and proper motion). It is well known that observations of the Sun pose substantial obstacles to the achievement of accuracy in measurement.^{4} In former times, before the distribution of accurate time signals, it was part of the routine work at any observatory to observe the sidereal times of meridian transit of selected 'clock stars' (of wellknown position and movement), and to use these to correct observatory clocks running local mean sidereal time; but nowadays local sidereal time is usually generated by computer, based on time signals.^{5}
Mean solar time was originally apparent solar time corrected by the equation of time. Mean solar time was sometimes derived, especially at sea for navigational purposes, by observing apparent solar time and then adding to it a calculated correction, the equation of time, which compensated for two known irregularities, caused by the ellipticity of the Earth's orbit and the obliquity of the Earth's equator and polar axis to the ecliptic (which is the plane of the Earth's orbit around the sun).
Greenwich Mean Time (GMT) was originally mean time deduced from meridian observations made at the Royal Greenwich Observatory (RGO). The principal meridian of that observatory was chosen in 1884 by the International Meridian Conference to be the Prime Meridian. GMT either by that name or as 'mean time at Greenwich' used to be an international time standard, but is no longer so; it was initially renamed in 1928 as Universal Time (UT) (partly as a result of ambiguities arising from the changed practice of starting the astronomical day at midnight instead of at noon, adopted as from 1 January 1925). The more current refined version of UT, UT1, is still in reality mean time at Greenwich. Greenwich Mean Time is still the legal time in the UK (in winter, and as adjusted by one hour for summer time). But Coordinated Universal Time (UTC) (an atomicbased time scale which is always kept within 0.9 second of UT1) is in common actual use in the UK, and the name GMT is often inaccurately used to refer to it. (See articles Greenwich Mean Time, Universal Time, Coordinated Universal Time and the sources they cite.)
Universal Time (UT) is a time scale based on the mean solar day, defined to be as uniform as possible despite variations in Earth's rotation.
 UT0 is the rotational time of a particular place of observation. It is observed as the diurnal motion of stars or extraterrestrial radio sources.
 UT1 is computed by correcting UT0 for the effect of polar motion on the longitude of the observing site. It varies from uniformity because of the irregularities in Earth's rotation.
Time standards for planetary motion calculations
Ephemeris time and its successor time scales described below have all been intended for astronomical use, e.g. in planetary motion calculations, with aims including uniformity, in particular, freedom from irregularities of Earth rotation. Some of these standards are examples of dynamical time scales and/or of coordinate time scales.
 Ephemeris Time (ET) was from 1952 to 1976 an official time scale standard of the International Astronomical Union; it was a dynamical time scale based on the orbital motion of the Earth around the Sun, from which the ephemeris second was derived as a defined fraction of the tropical year. This ephemeris second was the standard for the SI second from 1956 to 1967, and it was also the source for calibration of the caesium atomic clock; its length has been closely duplicated, to within 1 part in 10^{10}, in the size of the current SI second referred to atomic time.^{6} This Ephemeris Time standard was nonrelativistic and did not fulfil growing needs for relativistic coordinate time scales. It was in use for the official almanacs and planetary ephemerides from 1960 to 1983, and was replaced in official almanacs for 1984 and after, by numerically integrated Jet Propulsion Laboratory Development Ephemeris DE200 (based on the JPL relativistic coordinate time scale T_{eph}).
For applications at the Earth's surface, ET's official replacement was Terrestrial Dynamical Time (TDT), since redefined as Terrestrial Time (TT). For the calculation of ephemerides, TDB was officially recommended to replace ET, but deficiencies were found in the definition of TDB (though not affecting T_{eph}), and these led to the IAU defining and recommending further time scales, Barycentric Coordinate Time (TCB) for use in the solar system as a whole, and Geocentric Coordinate Time (TCG) for use in the vicinity of the Earth. As defined, TCB (as observed from the Earth's surface) is of divergent rate relative to all of ET, T_{eph} and TDT/TT;^{7} and the same is true, to a lesser extent, of TCG. The ephemerides of sun, moon and planets in current widespread and official use continue to be those calculated at the Jet Propulsion Laboratory (updated as from 2003 to DE405) using as argument T_{eph}.
 Terrestrial Dynamic Time (TDT) replaced Ephemeris Time and maintained continuity with it. TDT is a uniform atomic time scale, whose unit is the SI second. TDT is tied in its rate to the SI second, as is International Atomic Time (TAI), but because TAI was somewhat arbitrarily defined at its inception in 1958 to be initially equal to a refined version of UT, TT is offset from TAI, by a constant 32.184 seconds. The offset provided a continuity from Ephemeris Time to TDT. TDT has since been redefined as Terrestrial Time (TT).
 Barycentric Dynamical Time (TDB) is similar to TDT but includes relativistic corrections that move the origin to the barycenter. TDB differs from TT only in periodic terms. The difference is at most 2 milliseconds.
In 1991, in order to clarify the relationships between spacetime coordinates, new time scales were introduced, each with a different frame of reference. Terrestrial Time is time at Earth's surface. Geocentric Coordinate Time is a coordinate time scale at Earth's center. Barycentric Coordinate Time is a coordinate time scale at the center of mass of the solar system, which is called the barycenter. Barycentric Dynamical Time is a dynamical time at the barycenter.^{8}
 Terrestrial Time (TT) is the time scale which had formerly been called Terrestrial Dynamical Time. It is now defined as a coordinate time scale at Earth's surface.
 Geocentric Coordinate Time (TCG) is a coordinate time having its spatial origin at the center of Earth's mass. TCG is linearly related to TT as: TCG  TT = L_{G} * (JD 2443144.5) * 86400 seconds, with the scale difference L_{G} defined as 6.969290134e10 exactly.
 Barycentric Coordinate Time (TCB) is a coordinate time having its spatial origin at the solar system barycenter. TCB differs from TT in rate and other mostly periodic terms. Neglecting the periodic terms, in the sense of an average over a long period of time the two are related by: TCB  TT = L_{B} * (JD 2443144.5) * 86400 seconds. According to IAU the best estimate of the scale difference L_{B} is 1.55051976772e08.
Constructed time standards
International Atomic Time (TAI) is the primary international time standard from which other time standards, including UTC, are calculated. TAI is kept by the BIPM (International Bureau of Weights and Measures), and is based on the combined input of many atomic clocks around the world, each corrected for environmental and relativistic effects. It is the primary realisation of Terrestrial Time.
Coordinated Universal Time (UTC) is an atomic time scale designed to approximate Universal Time. UTC differs from TAI by an integral number of seconds. UTC is kept within 0.9 second of UT1 by the introduction of onesecond steps to UTC, the "leap second". To date these steps have always been positive.
Standard time or civil time in a region deviates a fixed, round amount, usually a whole number of hours, from some form of Universal Time, now usually UTC. The offset is chosen such that a new day starts approximately while the sun is crossing the nadir meridian. See Time zone. Alternatively the difference is not really fixed, but it changes twice a year a round amount, usually one hour, see Daylight saving time.
Other time scales
Julian day number is a count of days elapsed since Greenwich mean noon on 1 January 4713 B.C., Julian proleptic calendar. The Julian Date is the Julian day number followed by the fraction of the day elapsed since the preceding noon. Conveniently for astronomers, this avoids the date skip during an observation night.
Modified Julian day (MJD) is defined as MJD = JD  2400000.5. An MJD day thus begins at midnight, civil date. Julian dates can be expressed in UT, TAI, TDT, etc. and so for precise applications the timescale should be specified, e.g. MJD 49135.3824 TAI.
See also
Further reading
 ^ Before the time of John Flamsteed it was widely believed that the Earth's rotation had seasonal variations comparable in size with what is now called the equation of time. See articles on Vincent Wing and Thomas Streete for examples of astronomers before Flamsteed who believed this. The equation of time, correctly based on the two major components of the Sun's irregularity of apparent motion, i.e. the effect of the obliquity of the ecliptic and the effect of the Earth's orbital eccentricity, was not generally adopted until after John Flamsteed's tables of 1672/3, published with the posthumous edition of the works of Jeremiah Horrocks. See S Vince, "A Complete System of Astronomy", 2nd edition, volume 1, 1814, at p.49; see also Equation of time  history.
 ^ See Ephemeris time  history, and sources shown there.
 ^ See for example a recent description of "temps vrai" by the Bureau des Longitudes; and for an older example S Vince, 'A complete system of astronomy' (1814), esp. at page 46.
 ^ See H A Harvey, "The Simpler Aspects of Celestial Mechanics", in Popular Astronomy 44 (1936), 533541.
 ^ A E Roy, D Clarke, 'Astronomy: Principles and Practice' (4th edition, 2003) at p.89.
 ^ W Markowitz, R G Hall, L Essen, J V L Parry (1958), 'Frequency of caesium in terms of ephemeris time', Phys Rev Letters v1 (1958), 105107; and Wm Markowitz (1988) 'Comparisons of ET(Solar), ET(Lunar), UT and TDT', in (eds.) A K Babcock & G A Wilkins, 'The Earth's Rotation and Reference Frames for Geodesy and Geophysics', IAU Symposia #128 (1988), at pp 413418.
 ^ P K Seidelmann & T Fukushima (1992), "Why new time scales?", Astronomy & Astrophysics vol.265 (1992), pages 833838, including Fig. 1 at p.835, a graph giving an overview of the rate differences and offsets between various standard time scales, present and past, defined by the IAU.
 ^ V Brumberg, S Kopeikin (1990), 'Relativistic time scales in the solar system', Celestial Mechanics and Dynamical Astronomy (1990), Vol. 48, 2344
 Explanatory Supplement to the Astronomical Almanac, P. K. Seidelmann, ed., University Science Books, 1992, ISBN 0935702687
External links
 Current time according to the United States Naval Observatory. (Refresh the site to get the current time.)
 Systems of Time by Dr. Demetrios Matsakis, Director, Time Service Dept., United States Naval Observatory
 USNO article on the definition of seconds and leap seconds
 A history of astronomical time scales by Steve Allen
 Astronomical times
 Why is a minute divided into 60 seconds, an hour into 60 minutes, yet there are only 24 hours in a day? Ask the Experts  March 5, 2007. SCIENTIFIC AMERICAN



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