Ephemeris time

Ephemeris time

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The term ephemeris time can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:
  1. a former standard astronomical time scale adopted in 1952 by the IAU
    International Astronomical Union
    The International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...

    , and superseded in the 1970s. This time scale was proposed in 1948, to overcome the drawbacks of irregularly fluctuating mean solar time. The intent was to define a uniform time (as far as was then feasible) based on Newtonian theory (see below: Definition of ephemeris time (1952)). Ephemeris time was a first application of the concept of a dynamical time scale
    Dynamical time scale
    Dynamical time scale has two distinct meanings and usages, both related to astronomy:#In one use, which occurs in stellar physics, the dynamical time scale is alternatively known as the freefall time scale, and is in general, the length of time over which changes in one part of a body can be...

    , in which the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via the dynamical theory of its motion.
  2. a modern relativistic coordinate time scale, implemented by the JPL
    Jet Propulsion Laboratory
    Jet Propulsion Laboratory is a federally funded research and development center and NASA field center located in the San Gabriel Valley area of Los Angeles County, California, United States. The facility is headquartered in the city of Pasadena on the border of La Cañada Flintridge and Pasadena...

     ephemeris time argument Teph, in a series of numerically integrated Development Ephemerides. Among them is the DE405 ephemeris in widespread current use. The time scale represented by Teph is closely related to, but distinct (by an offset and constant rate) from, the TCB
    Barycentric Coordinate Time
    Barycentric Coordinate Time is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to orbits of planets, asteroids, comets, and interplanetary spacecraft in the Solar system...

     time scale currently adopted as a standard by the IAU
    IAU
    IAU may refer to:*International Astronomical Union*International American University*International American University College of Medicine*International Association of Universities*International Association of Ultrarunners...

     (see below: JPL ephemeris time argument Teph).


Most of the following sections relate to the ephemeris time of the 1952 standard.

An impression has sometimes arisen that ephemeris time was in use from 1900: this probably arose because ET, though proposed and adopted in the period 1948–1952, was defined in detail using formulae that made retrospective use of the epoch date of 1900 January 0 and of Newcomb
Simon Newcomb
Simon Newcomb was a Canadian-American astronomer and mathematician. Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.-Early life:Simon Newcomb was born in the town of...

's Tables of the Sun
Newcomb's Tables of the Sun
Newcomb's Tables of the Sun is the short title and running head of a work by the American astronomer and mathematician Simon Newcomb entitled "Tables of the Motion of the Earth on its Axis and Around the Sun" on pages 1–169 of "Tables of the Four Inner Planets" , volume VI of the serial publication...

.

The ephemeris time of the 1952 standard leaves a continuing legacy, through its ephemeris second which became closely duplicated in the length of the current standard SI second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

 (see below: Redefinition of the second).

History of ephemeris time (1952 standard)


Ephemeris time (ET), adopted as standard in 1952, was originally designed as an approach to a uniform time scale, to be freed from the effects of irregularity in the rotation of the earth, "for the convenience of astronomers and other scientists", for example for use in ephemerides
Ephemeris
An ephemeris is a table of values that gives the positions of astronomical objects in the sky at a given time or times. Different kinds of ephemerides are used for astronomy and astrology...

 of the Sun (as observed from the Earth), the Moon, and the planets. It was proposed in 1948 by G M Clemence
Gerald Maurice Clemence
Gerald Maurice Clemence was an American astronomer. Inspired by the life and work of Simon Newcomb, his career paralleled the huge advances in astronomy brought about by the advent of the electronic computer. Clemence did much to revive the prestige of the U.S...

.

From the time of John Flamsteed
John Flamsteed
Sir John Flamsteed FRS was an English astronomer and the first Astronomer Royal. He catalogued over 3000 stars.- Life :Flamsteed was born in Denby, Derbyshire, England, the only son of Stephen Flamsteed...

 (1646–1719) it had been believed that the Earth's daily rotation was uniform. But in the later nineteenth and early twentieth centuries, with increasing precision of astronomical measurements, it began to be suspected, and was eventually established, that the rotation of the Earth (i.e. the length of the day
Day
A day is a unit of time, commonly defined as an interval equal to 24 hours. It also can mean that portion of the full day during which a location is illuminated by the light of the sun...

) showed irregularities on short time scales, and was slowing down on longer time scales. The evidence was compiled by W de Sitter
Willem de Sitter
Willem de Sitter was a Dutch mathematician, physicist and astronomer.-Life and work:Born in Sneek, De Sitter studied mathematics at the University of Groningen and then joined the Groningen astronomical laboratory. He worked at the Cape Observatory in South Africa...

 (1927) who wrote "If we accept this hypothesis, then the 'astronomical time', given by the earth's rotation, and used in all practical astronomical computations, differs from the 'uniform' or 'Newtonian' time, which is defined as the independent variable of the equations of celestial mechanics". De Sitter offered a correction to be applied to the mean solar time given by the Earth's rotation to get uniform time.

Other astronomers of the period also made suggestions for obtaining uniform time, including A Danjon
André Danjon
André-Louis Danjon was a French astronomer born in Caen.Danjon devised a method to measure "Earthshine" on the Moon using a telescope in which a prism split the Moon's image into two identical side-by-side images...

 (1929), who suggested in effect that observed positions of the Moon, Sun and planets, when compared with their well-established gravitational ephemerides, could better and more uniformly define and determine time.

Thus the aim developed, to provide a new time scale for astronomical and scientific purposes, to avoid the unpredictable irregularities of the mean solar time scale, and to replace for these purposes Universal Time
Universal Time
Universal Time is a time scale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC...

 (UT) and any other time scale based on the rotation of the Earth around its axis, such as sidereal time
Sidereal time
Sidereal time is a time-keeping system astronomers use to keep track of the direction to point their telescopes to view a given star in the night sky...

.

G M Clemence
Gerald Maurice Clemence
Gerald Maurice Clemence was an American astronomer. Inspired by the life and work of Simon Newcomb, his career paralleled the huge advances in astronomy brought about by the advent of the electronic computer. Clemence did much to revive the prestige of the U.S...

 (1948) made a detailed proposal of this type based on the results of H Spencer Jones
Harold Spencer Jones
Sir Harold Spencer Jones KBE FRS was an English astronomer. Although born "Jones", his surname became "Spencer Jones"....

 (1939). Clemence (1948) made it clear that his proposal was intended "for the convenience of astronomers and other scientists only" and that it was "logical to continue the use of mean solar time for civil purposes".

De Sitter and Clemence both referred to the proposal as 'Newtonian' or 'uniform' time. D Brouwer
Dirk Brouwer
Dirk Brouwer was a Dutch-American astronomer.He received his Ph.D. in 1927 at Leiden University in the Netherlands and then went to Yale University...

 suggested the name 'ephemeris time'.

Following this, an astronomical conference held in Paris in 1950 recommended "that in all cases where the mean solar second is unsatisfactory as a unit of time by reason of its variability, the unit adopted should be the sidereal year at 1900.0, that the time reckoned in this unit be designated ephemeris time", and gave Clemence's formula (see Definition of ephemeris time (1952)) for translating mean solar time to ephemeris time.

The International Astronomical Union
International Astronomical Union
The International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...

 approved this recommendation at its 1952 general assembly. Practical introduction took some time (see Use of ephemeris time in official almanacs and ephemerides); ephemeris time (ET) remained a standard until superseded in the 1970s by further time scales (see Revision).

During the currency of ephemeris time as a standard, the details were revised a little. The unit was redefined in terms of the tropical year at 1900.0 instead of the sidereal year; and the standard second was defined first as 1/31556925.975 of the tropical year at 1900.0, and then as the slightly modified fraction 1/31556925.9747 instead, finally being redefined in 1967/8 in terms of the cesium atomic clock standard (see below).

Although ET is no longer directly in use, it leaves a continuing legacy. Its successor time scales, such as TDT, as well as the atomic time scale IAT (TAI)
International Atomic Time
International Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...

, were designed with a relationship that "provides continuity with ephemeris time". ET was used for the calibration of atomic clocks in the 1950s. Close equality between the ET second with the later SI second (as defined with reference to the cesium atomic clock) has been verified to within 1 part in 1010.

In this way, decisions made by the original designers of ephemeris time influenced the length of today's standard SI second, and in turn, this has a continuing influence on the number of leap second
Leap second
A leap second is a positive or negative one-second adjustment to the Coordinated Universal Time time scale that keeps it close to mean solar time. UTC, which is used as the basis for official time-of-day radio broadcasts for civil time, is maintained using extremely precise atomic clocks...

s which have been needed for insertion into current broadcast time scales, to keep them approximately in step with mean solar time.

Definition of ephemeris time (1952)


Ephemeris time was defined in principle by the orbital motion of the Earth around the Sun, (but its practical implementation was usually achieved in another way, see below).

Its detailed definition depended on Simon Newcomb
Simon Newcomb
Simon Newcomb was a Canadian-American astronomer and mathematician. Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.-Early life:Simon Newcomb was born in the town of...

's Tables of the Sun
Newcomb's Tables of the Sun
Newcomb's Tables of the Sun is the short title and running head of a work by the American astronomer and mathematician Simon Newcomb entitled "Tables of the Motion of the Earth on its Axis and Around the Sun" on pages 1–169 of "Tables of the Four Inner Planets" , volume VI of the serial publication...

 (1895), interpreted in a new way to accommodate certain observed discrepancies:

In the introduction to Newcomb's Tables of the Sun
Newcomb's Tables of the Sun
Newcomb's Tables of the Sun is the short title and running head of a work by the American astronomer and mathematician Simon Newcomb entitled "Tables of the Motion of the Earth on its Axis and Around the Sun" on pages 1–169 of "Tables of the Four Inner Planets" , volume VI of the serial publication...

 (1895) the basis of the tables (p. 9) includes a formula for the Sun's mean longitude, at a time indicated by interval T (in Julian centuries of 36525 mean solar days) reckoned from Greenwich Mean Noon on 0 January 1900:
Ls = 279° 41' 48".04 + 129,602,768".13T +1".089T2 . . . . . (1)


Spencer Jones' work of 1939 showed that the positions of the Sun actually observed, when compared with those obtained from Newcomb's formula, show the need for the following correction to the formula to represent the observations:
ΔLs = + 1".00 + 2".97T + 1".23T2 + 0.0748B


(where "the times of observation are in Universal time, not corrected to Newtonian time", and 0.0748B represents an irregular fluctuation calculated from lunar observations).

Thus a conventionally corrected form of Newcomb's formula, to incorporate the corrections on the basis of mean solar time, would be the sum of the two preceding expressions:
Ls = 279° 41' 49".04 + 129,602,771".10T +2".32T2 +0.0748B . . . . . (2)


Clemence's 1948 proposal did not adopt a correction of this kind in terms of mean solar time: instead, the same numbers were used as in Newcomb's original uncorrected formula (1), but now in a reverse sense, to define the time and time scale implicitly, based on the real position of the Sun:
Ls = 279° 41' 48".04 + 129,602,768".13E +1".089E2 . . . . . (3)


where the time variable, here represented as E, now represents time in ephemeris centuries of 36525 ephemeris days of 86400 ephemeris seconds. The 1961 official reference put it this way: "The origin and rate of ephemeris time are defined to make the Sun's mean longitude agree with Newcomb's expression"

From the comparison of formulae (2) and (3), both of which express the same real solar motion in the same real time but on different time scales, Clemence arrived at an explicit expression, estimating the difference in seconds of time between ephemeris time and mean solar time, in the sense (ET-UT):
. . . . . (4)


Clemence's formula, now superseded by more modern estimations, was included in the original conference decision on ephemeris time. In view of the fluctuation term, practical determination of the difference between ephemeris time and UT depended on observation. Inspection of the formulae above shows that the (ideally constant) unit of ephemeris time such as the ephemeris second has been for the whole of the twentieth century very slightly shorter than the corresponding (but not precisely constant) unit of mean solar time (which besides its irregular fluctuations tends gradually to increase), consistently also with the modern results of Morrison and Stephenson (see article ΔT
Delta T
ΔT, Delta T, delta-T, deltaT, or DT is the time difference obtained by subtracting Universal Time from Terrestrial Time : ΔT=TT−UT....

).

Secondary realizations by lunar observations


Although ephemeris time was defined in principle by the orbital motion of the Earth around the Sun, it was usually measured in practice by the orbital motion of the Moon around the Earth. These measurements can be considered as secondary realizations (in a metrological
Metrology
Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...

 sense) of the primary definition of ET in terms of the solar motion, after a calibration of the mean motion of the Moon with respect to the mean motion of the Sun.

Reasons for the use of lunar measurements were practically based: the Moon moves against the background of stars about 13 times as fast as the Sun's corresponding rate of motion, and the accuracy of time determinations from lunar measurements is correspondingly greater.

When ephemeris time was first adopted, time scales were still based on astronomical observation, as they always had been. The accuracy was limited by the accuracy of optical observation, and corrections of clocks and time signals were published in arrear.

Secondary realizations by atomic clocks


A few years later, with the invention of the cesium atomic clock
Atomic clock
An atomic clock is a clock that uses an electronic transition frequency in the microwave, optical, or ultraviolet region of the electromagnetic spectrum of atoms as a frequency standard for its timekeeping element...

, an alternative offered itself. Increasingly, after the calibration in 1958 of the cesium atomic clock by reference to ephemeris time, cesium atomic clocks running on the basis of ephemeris seconds began to be used and kept in step with ephemeris time. The atomic clocks offered a further secondary realization of ET, on a quasi-real time basis that soon proved to be more useful than the primary ET standard: not only more convenient, but also more precisely uniform than the primary standard itself. Such secondary realizations were used and described as 'ET', with an awareness that the time scales based on the atomic clocks were not identical to that defined by the primary ephemeris time standard, but rather, an improvement over it on account of their closer approximation to uniformity. The atomic clocks gave rise to the atomic time scale
International Atomic Time
International Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...

, and to what was first called Terrestrial Dynamical Time and is now Terrestrial Time
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....

, defined to provide continuity with ET.

The availability of atomic clocks, together with the increasing accuracy of astronomical observations (which meant that relativistic corrections were at least in the foreseeable future no longer going to be small enough to be neglected), led to the eventual replacement of the ephemeris time standard by more refined time scales including terrestrial time
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....

 and barycentric dynamical time
Barycentric Dynamical Time
Barycentric Dynamical Time is a relativistic coordinate time scale, intended for astronomical use as a time standard to take account of time dilation when calculating orbits and astronomical ephemerides of planets, asteroids, comets and interplanetary spacecraft in the Solar system...

, to which ET can be seen as an approximation.

Revision of time scales


In 1976 the IAU
International Astronomical Union
The International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...

 resolved that the theoretical basis for its current (1952) standard of Ephemeris Time was non-relativistic, and that therefore, beginning in 1984, Ephemeris Time would be replaced by two relativistic timescales intended to constitute dynamical timescales
Dynamical time scale
Dynamical time scale has two distinct meanings and usages, both related to astronomy:#In one use, which occurs in stellar physics, the dynamical time scale is alternatively known as the freefall time scale, and is in general, the length of time over which changes in one part of a body can be...

: Terrestrial Dynamical Time (TDT) and Barycentric Dynamical Time (TDB)
Barycentric Dynamical Time
Barycentric Dynamical Time is a relativistic coordinate time scale, intended for astronomical use as a time standard to take account of time dilation when calculating orbits and astronomical ephemerides of planets, asteroids, comets and interplanetary spacecraft in the Solar system...

. Difficulties were recognized, which led to these being in turn superseded in the 1990s by time scales Terrestrial Time (TT)
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....

, Geocentric Coordinate Time GCT(TCG)
Geocentric Coordinate Time
Geocentric Coordinate Time is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to precession, nutation, the Moon, and artificial satellites of the Earth...

 and Barycentric Coordinate Time BCT(TCB)
Barycentric Coordinate Time
Barycentric Coordinate Time is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to orbits of planets, asteroids, comets, and interplanetary spacecraft in the Solar system...

.

JPL ephemeris time argument Teph


High-precision ephemerides
Ephemeris
An ephemeris is a table of values that gives the positions of astronomical objects in the sky at a given time or times. Different kinds of ephemerides are used for astronomy and astrology...

 of sun, moon and planets were developed and calculated at the Jet Propulsion Laboratory
Jet Propulsion Laboratory
Jet Propulsion Laboratory is a federally funded research and development center and NASA field center located in the San Gabriel Valley area of Los Angeles County, California, United States. The facility is headquartered in the city of Pasadena on the border of La Cañada Flintridge and Pasadena...

 (JPL) over a long period, and the latest available were adopted for the ephemerides in the Astronomical Almanac
Astronomical Almanac
The Astronomical Almanac is an almanac published by the United States Naval Observatory and Her Majesty's Nautical Almanac Office, containing solar system ephemeris and catalogs of selected stellar and extragalactic objects....

 starting in 1984. Although not an IAU standard, the ephemeris time argument Teph has been in use at that institution since the 1960s. The time scale represented by Teph has been characterized as a relativistic
Principle of relativity
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....

 coordinate time that differs from Terrestrial Time
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....

 only by small periodic terms with an amplitude not exceeding 2 milliseconds of time: it is linearly related to, but distinct (by an offset and constant rate which is of the order of 0.5 sec/yr) from the TCB
Barycentric Coordinate Time
Barycentric Coordinate Time is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to orbits of planets, asteroids, comets, and interplanetary spacecraft in the Solar system...

 time scale adopted in 1991 as a standard by the IAU
IAU
IAU may refer to:*International Astronomical Union*International American University*International American University College of Medicine*International Association of Universities*International Association of Ultrarunners...

. Thus for clocks on or near the geoid
Geoid
The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest , and extended through the continents . According to C.F...

, Teph (within 2 milliseconds), but not so closely TCB, can be used as approximations to Terrestrial Time, and via the standard ephemerides Teph is in widespread use.

Use of ephemeris time in official almanacs and ephemerides


Ephemeris time based on the standard adopted in 1952 was introduced into the Astronomical Ephemeris (UK) and the American Ephemeris and Nautical Almanac
American Ephemeris and Nautical Almanac
The American Ephemeris and Nautical Almanac was published for the years 1855 to 1980, containing information necessary for astronomers, surveyors, and navigators...

, replacing UT in the main ephemerides in the issues for 1960 and after. (But the ephemerides in the Nautical Almanac, by then a separate publication for the use of navigators, continued to be expressed in terms of UT.) The ephemerides continued on this basis through 1983 (with some changes due to adoption of improved values of astronomical constants), after which, for 1984 onwards, they adopted the JPL ephemerides.

Previous to the 1960 change, the 'Improved Lunar Ephemeris' had alrady been made available in terms of ephemeris time for the years 1952-1959 (computed by W J Eckert
Wallace John Eckert
Wallace John Eckert was an American astronomer, who directed the Thomas J. Watson Astronomical Computing Bureau at Columbia University which evolved into the research division of IBM.-Life:...

 from Brown
Ernest William Brown
Ernest William Brown FRS was a British mathematician and astronomer, who spent the majority of his career working in the United States....

's theory with modifications recommended by Clemence (1948)).

Redefinition of the second


Successive definitions of the unit of ephemeris time are mentioned above (History). The value adopted for the 1956/1960 standard second:
the fraction 1/31,556,925.9747 of the tropical year
Tropical year
A tropical year , for general purposes, is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice...

 for 1900 January 0 at 12 hours ephemeris time.


was obtained from the linear time-coefficient in Newcomb's expression for the solar mean longitude (above), taken and applied with the same meaning for the time as in formula (3) above. The relation with Newcomb's coefficient can be seen from:
1/31,556,925.9747 = 129602768.13 / (360×60×60×36525×86400).


Caesium
Caesium
Caesium or cesium is the chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-gold alkali metal with a melting point of 28 °C , which makes it one of only five elemental metals that are liquid at room temperature...

 atomic clocks became operational in 1955, and quickly confirmed the evidence that the rotation of the earth fluctuated randomly. This confirmed the unsuitability of the mean solar second of Universal Time as a measure of time interval for the most precise purposes. After three years of comparisons with lunar observations, Markowitz
William Markowitz
William Markowitz was an American astronomer, principally known for his work on the standardization of time....

 et al. (1958) determined that the ephemeris second corresponded to 9,192,631,770 ± 20 cycles of the chosen cesium resonance.

Following this, in 1967/68, the General Conference on Weights and Measures (CGPM) replaced the definition of the SI second by the following:
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

Although this is an independent definition that does not refer to the older basis of ephemeris time, it uses the same quantity as the value of the ephemeris second measured by the cesium clock in 1958. This SI second referred to atomic time was later verified by Markowitz (1988) to be in agreement, within 1 part in 1010, with the second of ephemeris time as determined from lunar observations.

For practical purposes the length of the ephemeris second can be taken as equal to the length of the second of Barycentric Dynamical Time (TDB)
Barycentric Dynamical Time
Barycentric Dynamical Time is a relativistic coordinate time scale, intended for astronomical use as a time standard to take account of time dilation when calculating orbits and astronomical ephemerides of planets, asteroids, comets and interplanetary spacecraft in the Solar system...

 or Terrestrial Time (TT)
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....

 or its predecessor TDT.

The difference between ET and UT is called ΔT; it changes irregularly, but the long-term trend is parabolic
Parabola
In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface...

, decreasing from ancient times until the nineteenth century, and increasing since then at a rate corresponding to an increase in the solar day length of 1.7 ms per century (see leap second
Leap second
A leap second is a positive or negative one-second adjustment to the Coordinated Universal Time time scale that keeps it close to mean solar time. UTC, which is used as the basis for official time-of-day radio broadcasts for civil time, is maintained using extremely precise atomic clocks...

s).

International Atomic Time
International Atomic Time
International Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...

 (TAI) was set equal to UT2
Universal Time
Universal Time is a time scale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC...

at 1 January 1958 0:00:00 . At that time, ΔT was already about 32.18 seconds. The difference between Terrestrial Time (TT) (the successor to ephemeris time) and atomic time was later defined as follows:
1977 January 1.0003725 TT = 1977 January 1.0000000 TAI, i.e.

TT − TAI = 32.184 seconds


This difference may be assumed constant—the rates of TT and TAI are designed to be identical.