# Ephemeris time

The term ephemeris time (often abbreviated ET) 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 a former standard astronomical time scale adopted in 1952 by the IAU,[1] and superseded in the 1970s.[2] This time scale was proposed in 1948, to overcome the drawbacks of irregularly fluctuating mean solar time.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, 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.[3]
2. a modern relativistic coordinate time scale, implemented by the JPL 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 time scale currently adopted as a standard by the IAU (see below: JPL ephemeris time argument Teph).[4]

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's Tables of the Sun.[5][6]

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 (see below: Redefinition of the second).

## History (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 of the Sun (as observed from the Earth), the Moon, and the planets. It was proposed in 1948 by G M Clemence.[7]

From the time of John 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) showed irregularities on short time scales, and was slowing down on longer time scales. The evidence was compiled by W de Sitter (1927)[8] 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 (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.[9]

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 (UT) and any other time scale based on the rotation of the Earth around its axis, such as sidereal time.

The American astronomer G M Clemence (1948)[7] made a detailed proposal of this type based on the results of the English Astronomer Royal H Spencer Jones (1939).[10] 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".[11]

De Sitter and Clemence both referred to the proposal as 'Newtonian' or 'uniform' time. D Brouwer suggested the name 'ephemeris time'.[12]

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 approved this recommendation at its 1952 general assembly.[12][13] 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;[12] and the standard second was defined first as 1/31556925.975 of the tropical year at 1900.0,[12][14] and then as the slightly modified fraction 1/31556925.9747 instead,[15] 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), were designed with a relationship that "provides continuity with ephemeris time".[16] ET was used for the calibration of atomic clocks in the 1950s.[17] 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.[18]

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

## Definition (1952)

Ephemeris time was defined in principle by the orbital motion of the Earth around the Sun,[12] (but its practical implementation was usually achieved in another way, see below).

Its detailed definition depended on Simon Newcomb's Tables of the Sun (1895),[5] interpreted in a new way to accommodate certain observed discrepancies:

In the introduction to Tables of the Sun 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[19]) 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[10] 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[20]).

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"[21]

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):

${\displaystyle \delta t=+24^{s}.349+72^{s}.3165T+29^{s}.949T^{2}+1.821B}$ . . . . . (4)[20]

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[22] (see article ΔT).

## Implementations

### Secondary realizations by lunar observations

Although ephemeris time was defined in principle by the orbital motion of the Earth around the Sun,[23] it was usually measured in practice by the orbital motion of the Moon around the Earth.[24] These measurements can be considered as secondary realizations (in a metrological 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.[25]

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, an alternative offered itself. Increasingly, after the calibration in 1958 of the cesium atomic clock by reference to ephemeris time,[17] 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[25] 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.[26] The atomic clocks gave rise to the atomic time scale, and to what was first called Terrestrial Dynamical Time and is now Terrestrial Time, defined to provide continuity with ET.[16]

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),[27] led to the eventual replacement of the ephemeris time standard by more refined time scales including terrestrial time and barycentric dynamical time, to which ET can be seen as an approximation.

## Revision of time scales

In 1976 the IAU 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: Terrestrial Dynamical Time (TDT) and Barycentric Dynamical Time (TDB).[28] Difficulties were recognized, which led to these being in turn superseded in the 1990s by time scales Terrestrial Time (TT), Geocentric Coordinate Time GCT(TCG) and Barycentric Coordinate Time BCT(TCB).[16]

## JPL ephemeris time argument Teph

High-precision ephemerides of sun, moon and planets were developed and calculated at the Jet Propulsion Laboratory (JPL) over a long period, and the latest available were adopted for the ephemerides in the Astronomical Almanac 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 coordinate time that differs from Terrestrial Time 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 s/a) from the TCB time scale adopted in 1991 as a standard by the IAU. Thus for clocks on or near the geoid, 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.[4]

Partly in acknowledgement of the widespread use of Teph via the JPL ephemerides, IAU resolution 3 of 2006[29] (re-)defined Barycentric Dynamical Time (TDB) as a current standard. As re-defined in 2006, TDB is a linear transformation of TCB. The same IAU resolution also stated (in note 4) that the "independent time argument of the JPL ephemeris DE405, which is called Teph" (here the IAU source cites[4]), "is for practical purposes the same as TDB defined in this Resolution". Thus the new TDB, like Teph, is essentially a more refined continuation of the older ephemeris time ET and (apart from the < 2 ms periodic fluctuations) has the same mean rate as that established for ET in the 1950s.

## Use 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, replacing UT in the main ephemerides in the issues for 1960 and after.[30] (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 already been made available in terms of ephemeris time for the years 1952-1959[31] (computed by W J Eckert from Brown'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 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 = 129 602 768.13 / (360×60×60×36 525×86 400).

Caesium 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 et al. (1958) determined that the ephemeris second corresponded to 9 192 631 770 ± 20 cycles of the chosen cesium resonance.[17]

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.[18]

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) or Terrestrial Time (TT) or its predecessor TDT.

The difference between ET and UT is called ΔT; it changes irregularly, but the long-term trend is parabolic, decreasing from ancient times until the nineteenth century,[22] and increasing since then at a rate corresponding to an increase in the solar day length of 1.7 ms per century (see leap seconds).

International Atomic Time (TAI) was set equal to UT2 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 1.000 3725 TT = 1977 January 1.000 0000 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.

## Notes and references

1. ^ 'ESAE 1961': 'Explanatory Supplement (1961), esp. p.9.
2. ^ 'ESAA (1992)': P K Seidelmann (ed)., especially at pp.41-42 and at p.79.
3. ^ B Guinot and P K Seidelmann (1988), at p.304-5.
4. ^ a b c
5. ^ a b
6. ^ For the components of the definition including its retrospective aspect, see G M Clemence (1948), esp. p.172, and 'ESAE 1961': 'Explanatory Supplement (1961), esp. pages 69 and 87.
7. ^ a b
8. ^
9. ^
10. ^ a b
11. ^ Clemence (1948), at p. 171.
12. ESAA (1992), see page 79.
13. ^ At the IAU meeting in Rome 1952: see ESAE (1961) at sect.1C, p. 9; also Clemence (1971).
14. ^ ESAA 1992, p. 79: citing decision of International Committee for Weights and Measures (CIPM), Sept 1954.
15. ^ ESAA (1992), see page 80, citing CIPM recommendation Oct 1956, adopted 1960 by the General Conference on Weights and Measures (CGPM).
16. ^ a b c ESAA (1992), at page 42.
17. ^ a b c W Markowitz, R G Hall, L Essen, J V L Parry (1958)
18. ^ a b
19. ^ The unit of _mean solar_ day is left implicit on p.9 but made explicit on p.20 of Newcomb (1895).
20. ^ a b Clemence (1948), p.172, following Spencer Jones (1939).
21. ^ ESAE (1961) at p.70.
22. ^ a b
23. ^ Clemence (1948), at pp.171-3.
24. ^
25. ^ a b B Guinot & P K Seidelmann (1988), at p.305.
26. ^ W G Melbourne & others, 1968, section II.E.4-5, pages 15-16, including footnote 7, noted that the Jet Propulsion Laboratory spacecraft tracking and data reduction programs of that time (including the Single Precision Orbit Determination Program) used, as ET, the current US atomic clock time A.1 offset by 32.25 seconds. The discussion also noted that the usage was "inaccurate" (the quantity indicated was not identical with any of the other realizations of ET such as ET0, ET1), and that while A.1 gave "certainly a closer approximation to uniform time than ET1" there were no grounds for considering either the atomic clocks or any other measures of ET as (perfectly) uniform. Section II.F, pages 18-19, indicates that an improved time measure of (A.1 + 32.15 seconds), applied in the JPL Double Precision Orbit Determination Program, was also designated ET.
27. ^
29. ^ IAU 2006 resolution 3
30. ^
31. ^ "Improved Lunar Ephemeris", US Government Printing Office, 1954.

## Bibliography

1972

1972 (MCMLXXII)

was a leap year starting on Saturday of the Gregorian calendar, the 1972nd year of the Common Era (CE) and Anno Domini (AD) designations, the 972nd year of the 2nd millennium, the 72nd year of the 20th century, and the 3rd year of the 1970s decade.

Within the context of Coordinated Universal Time (UTC) it was the longest year ever, as two leap seconds were added during this 366-day year, an event which has not since been repeated. (If its start and end are defined using mean solar time [the legal time scale], its duration was 31622401.141 seconds of Terrestrial Time (or Ephemeris Time), which is slightly shorter than 1908).

Atomic clock

An atomic clock is a clock device that uses an electron transition frequency in the microwave, optical, or ultraviolet region of the electromagnetic spectrum of atoms as a frequency standard for its timekeeping element. Atomic clocks are the most accurate time and frequency standards known, and are used as primary standards for international time distribution services, to control the wave frequency of television broadcasts, and in global navigation satellite systems such as GPS.

The principle of operation of an atomic clock is based on atomic physics; it measures the electromagnetic signal that electrons in atoms emit when they change energy levels. Early atomic clocks were based on masers at room temperature. Since 2004, more accurate atomic clocks first cool the atoms to near absolute zero temperature by slowing them with lasers and probing them in atomic fountains in a microwave-filled cavity. An example of this is the NIST-F1 atomic clock, one of the national primary time and frequency standards of the United States.

The accuracy of an atomic clock depends on two factors. The first factor is temperature of the sample atoms—colder atoms move much more slowly, allowing longer probe times. The second factor is the frequency and intrinsic width of the electronic transition. Higher frequencies and narrow lines increase the precision.

National standards agencies in many countries maintain a network of atomic clocks which are intercompared and kept synchronized to an accuracy of 10−9 seconds per day (approximately 1 part in 1014). These clocks collectively define a continuous and stable time scale, the International Atomic Time (TAI). For civil time, another time scale is disseminated, Coordinated Universal Time (UTC). UTC is derived from TAI, but has added leap seconds from UT1, to account for variations in the rotation of the Earth with respect to the solar time.

Barycentric Coordinate Time

Barycentric Coordinate Time (TCB, from the French Temps-coordonnée barycentrique) 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. It is equivalent to the proper time experienced by a clock at rest in a coordinate frame co-moving with the barycenter of the Solar system: that is, a clock that performs exactly the same movements as the Solar system but is outside the system's gravity well. It is therefore not influenced by the gravitational time dilation caused by the Sun and the rest of the system.

TCB was defined in 1991 by the International Astronomical Union, in Recommendation III of the XXIst General Assembly. It was intended as one of the replacements for the problematic 1976 definition of Barycentric Dynamical Time (TDB). Unlike former astronomical time scales, TCB is defined in the context of the general theory of relativity. The relationships between TCB and other relativistic time scales are defined with fully general relativistic metrics.

Because the reference frame for TCB is not influenced by the gravitational potential caused by the Solar system, TCB ticks faster than clocks on the surface of the Earth by 1.550505 × 10−8 (about 490 milliseconds per year). Consequently, the values of physical constants to be used with calculations using TCB differ from the traditional values of physical constants (The traditional values were in a sense wrong, incorporating corrections for the difference in time scales). Adapting the large body of existing software to change from TDB to TCB is an ongoing task, and as of 2002 many calculations continue to use TDB in some form.

Time coordinates on the TCB scale are conventionally specified using traditional means of specifying days, carried over from non-uniform time standards based on the rotation of the Earth. Specifically, both Julian Dates and the Gregorian calendar are used. For continuity with its predecessor Ephemeris Time, TCB was set to match ET at around Julian Date 2443144.5 (1977-01-01T00Z). More precisely, it was defined that TCB instant 1977-01-01T00:00:32.184 exactly corresponds to the International Atomic Time (TAI) instant 1977-01-01T00:00:00.000 exactly, at the geocenter. This is also the instant at which TAI introduced corrections for gravitational time dilation.

Barycentric Dynamical Time

Barycentric Dynamical Time (TDB, from the French Temps Dynamique Barycentrique) 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. TDB is now (since 2006) defined as a linear scaling of Barycentric Coordinate Time (TCB). A feature that distinguishes TDB from TCB is that TDB, when observed from the Earth's surface, has a difference from Terrestrial Time (TT) that is about as small as can be practically arranged with consistent definition: the differences are mainly periodic, and overall will remain at less than 2 milliseconds for several millennia.TDB applies to the Solar-System-barycentric reference frame, and was first defined in 1976 as a successor to the (non-relativistic) former standard of ephemeris time (adopted by the IAU in 1952 and superseded 1976). In 2006, after a history of multiple time-scale definitions and deprecation since the 1970s, a redefinition of TDB was approved by the IAU. The 2006 IAU redefinition of TDB as an international standard expressly acknowledged that the long-established JPL ephemeris time argument Teph, as implemented in JPL Development Ephemeris DE405, "is for practical purposes the same as TDB defined in this Resolution" (By 2006, ephemeris DE405 had already been in use for a few years as the official basis for planetary and lunar ephemerides in the Astronomical Almanac; it was the basis for editions for 2003 through 2014; in the edition for 2015 it is superseded by DE430).

Coordinated Universal Time

DUT1

The time correction DUT1 (sometimes also written DUT) is the difference between Universal Time (UT1), which is defined by Earth's rotation, and Coordinated Universal Time (UTC), which is defined by a network of precision atomic clocks.

DUT1 = UT1 − UTCUTC is maintained via leap seconds, such that DUT1 remains within the range −0.9 s < DUT1 < +0.9 s. The reason for this correction is partly that the rate of rotation of the Earth is not constant, due to tidal braking and the redistribution of mass within the Earth, including its oceans and atmosphere, and partly because the SI second (as now used for UTC) was already, when adopted, a little shorter than the current value of the second of mean solar time.Forecast values of DUT1 are published by IERS Bulletin A.

Weekly updated values of DUT1 with 0.1 s precision are broadcast by several time signal services, including WWV and MSF. These services transmit one pulse per second of some sort. To represent positive DUT1 values from +0.1 to +0.8 seconds, the pulses sent during seconds 1 through 8 are "emphasized" in some way, generally by transmitting a double pulse. The number of emphasized pulses gives the value of DUT1. Negative DUT1 values, from −0.1 to −0.8 seconds, are similarly represented by emphasizing pulses 9 through 16. For example, a DUT1 value of −0.4 would be transmitted by emphasizing pulses 9 through 12.

The Russian time signal RWM transmits an additional correction dUT1 in 0.02 s increments. Positive values of dUT1 from +0.02 to +0.08 s are encoded by emphasizing pulses 21 through 24; negative values are encoded by emphasizing pulses 31 through 34. The actual value of DUT1 is approximated by the sum of the transmitted DUT1 + dUT1.

The longwave RBU time signal also transmits dUT1.

Dynamical time scale

In time standards, dynamical time is the time-like argument of a dynamical theory; and a dynamical time scale in this sense is the realization of a time-like argument based on a dynamical theory: that is, the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via a theory of its motion. A first application of this concept of dynamical time was the definition of the ephemeris time scale (ET).In the late 19th century it was suspected, and in the early 20th century it was established, that the rotation of the Earth (i.e. the length of the day) was both irregular on short time scales, and was slowing down on longer time scales. The suggestion was made, that observation of the position of the Moon, Sun and planets and comparison of the observations with their gravitational ephemerides would be a better way to determine a uniform time scale. A detailed proposal of this kind was published in 1948 and adopted by the IAU in 1952 (see Ephemeris time - history).

Using data from Newcomb's Tables of the Sun (based on the theory of the apparent motion of the Sun by Simon Newcomb, 1895, as retrospectively used in the definition of ephemeris time), the SI second was defined in 1960 as:

the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.Caesium atomic clocks became operational in 1955, and their use provided further confirmation that the rotation of the earth fluctuated randomly. This confirmed the unsuitability of the mean solar second of Universal Time as a precision measure of time interval. After three years of comparisons with lunar observations it was determined that the ephemeris second corresponded to 9,192,631,770 ± 20 cycles of the caesium resonance. In 1967/68 the length of the SI second was redefined to be 9,192,631,770 cycles of the caesium resonance, equal to the previous measurement result for the ephemeris second (see Ephemeris time - redefinition of the second).

In 1976, however, the IAU resolved that the theoretical basis for ephemeris time was wholly non-relativistic, and therefore, beginning in 1984 ephemeris time would be replaced by two further time scales with allowance for relativistic corrections. Their names, assigned in 1979, emphasized their dynamical nature or origin, Barycentric Dynamical Time (TDB) and Terrestrial Dynamical Time (TDT). Both were defined for continuity with ET and were based on what had become the standard SI second, which in turn had been derived from the measured second of ET.

During the period 1991–2006, the TDB and TDT time scales were both redefined and replaced, owing to difficulties or inconsistencies in their original definitions. The current fundamental relativistic time scales are Geocentric Coordinate Time (TCG) and Barycentric Coordinate Time (TCB); both of these have rates that are based on the SI second in respective reference frames (and hypothetically outside the relevant gravity well), but on account of relativistic effects, their rates would appear slightly faster when observed at the Earth's surface, and therefore diverge from local earth-based time scales based on the SI second at the Earth's surface. Therefore, the currently defined IAU time scales also include Terrestrial Time (TT) (replacing TDT, and now defined as a re-scaling of TCG, chosen to give TT a rate that matches the SI second when observed at the Earth's surface), and a redefined Barycentric Dynamical Time (TDB), a re-scaling of TCB to give TDB a rate that matches the SI second at the Earth's surface.

Geocentric Coordinate Time

Geocentric Coordinate Time (TCG - Temps-coordonnée géocentrique) 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. It is equivalent to the proper time experienced by a clock at rest in a coordinate frame co-moving with the center of the Earth: that is, a clock that performs exactly the same movements as the Earth but is outside the Earth's gravity well. It is therefore not influenced by the gravitational time dilation caused by the Earth.

TCG was defined in 1991 by the International Astronomical Union, in Recommendation III of the XXIst General Assembly. It was intended as one of the replacements for the ill-defined Barycentric Dynamical Time (TDB). Unlike former astronomical time scales, TCG is defined in the context of the general theory of relativity. The relationships between TCG and other relativistic time scales are defined with fully general relativistic metrics.

Because the reference frame for TCG is not rotating with the surface of the Earth and not in the gravitational potential of the Earth, TCG ticks faster than clocks on the surface of the Earth by a factor of about 7.0 × 10−10 (about 22 milliseconds per year). Consequently, the values of physical constants to be used with calculations using TCG differ from the traditional values of physical constants. (The traditional values were in a sense wrong, incorporating corrections for the difference in time scales.) Adapting the large body of existing software to change from TDB to TCG is a formidable task, and as of 2002 many calculations continue to use TDB in some form.

Time coordinates on the TCG scale are conventionally specified using traditional means of specifying days, carried over from non-uniform time standards based on the rotation of the Earth. Specifically, both Julian Dates and the Gregorian calendar are used. For continuity with its predecessor Ephemeris Time, TCG was set to match ET at around Julian Date 2443144.5 (1977-01-01T00Z). More precisely, it was defined that TCG instant 1977-01-01T00:00:32.184 exactly corresponds to TAI instant 1977-01-01T00:00:00.000 exactly. This is also the instant at which TAI introduced corrections for gravitational time dilation.

TCG is a Platonic time scale: a theoretical ideal, not dependent on a particular realisation. For practical purposes, TCG must be realised by actual clocks in the Earth system. Because of the linear relationship between Terrestrial Time (TT) and TCG, the same clocks that realise TT also serve for TCG. See the article on TT for details of the relationship and how TT is realised.

Barycentric Coordinate Time (TCB) is the analog of TCG, used for calculations relating to the solar system beyond Earth orbit. TCG is defined by a different reference frame from TCB, such that they are not linearly related. Over the long term, TCG ticks more slowly than TCB by about 1.6 × 10−8 (about 0.5 seconds per year). In addition there are periodic variations, as Earth moves within the Solar system. When the Earth is at perihelion in January, TCG ticks even more slowly than it does on average, due to gravitational time dilation from being deeper in the Sun's gravity well and also velocity time dilation from moving faster relative to the Sun. At aphelion in July the opposite holds, with TCG ticking faster than it does on average.

List of cycles

This is a list of recurring cycles. See also Index of wave articles, Time, and Pattern.

List of non-standard dates

There are several non-standard dates that are used in calendars. Some are used sarcastically, some for scientific or mathematical purposes, and some for exceptional or fictional calendars.

Lunar month

In lunar calendars, a lunar month is the time between two successive syzygies (new moons or full moons). The precise definition varies, especially for the beginning of the month.

This article deals with the definitions of a 'month' that are mainly of significance in astronomy. For other definitions, including a description of a month in the calendars of different cultures around the world, see: month.

National Physical Laboratory (United Kingdom)

The National Physical Laboratory (NPL) is the national measurement standards laboratory for the United Kingdom, based at Bushy Park in Teddington, London, England. It comes under the management of the Department for Business, Energy and Industrial Strategy.

Second

The second is the base unit of time in the International System of Units (SI), commonly understood and historically defined as ​1⁄86400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each. Analog clocks and watches often have sixty tick marks on their faces, representing seconds, and a "second hand" to mark the passage of time in seconds. Digital clocks and watches often have a two-digit seconds counter. The second is also part of several other units of measurement like meters per second for velocity, meters per second per second for acceleration, and per second for frequency.

Although the historical definition of the unit was based on this division of the Earth's rotation cycle, the formal definition in the International System of Units (SI) is a much steadier timekeeper: 1 second is defined to be exactly "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" (at a temperature of 0 K).

Because the Earth's rotation varies and is also slowing ever so slightly, a leap second is periodically added to clock time to keep clocks in sync with Earth's rotation.

Multiples of seconds are usually counted in hours and minutes. Fractions of a second are usually counted in tenths or hundredths. In scientific work, small fractions of a second are counted in milliseconds (thousandths), microseconds (millionths), nanoseconds (billionths), and sometimes smaller units of a second.

An everyday experience with small fractions of a second is a 1-gigahertz microprocessor which has a cycle time of 1 nanosecond. Camera shutter speeds usually range from ​1⁄60 second to ​1⁄250 second.

Sexagesimal divisions of the day from a calendar based on astronomical observation have existed since the third millennium BC, though they were not seconds as we know them today. Small divisions of time could not be counted back then, so such divisions were figurative. The first timekeepers that could count seconds accurately were pendulum clocks invented in the 17th century. Starting in the 1950s, atomic clocks became better timekeepers than earth's rotation, and they continue to set the standard today.

Solar time

Solar time is a calculation of the passage of time based on the position of the Sun 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).

Terrestrial Time

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

For example, the Astronomical Almanac uses TT for its tables of positions (ephemerides) of the Sun, Moon and planets as seen from Earth. In this role, TT continues Terrestrial Dynamical Time (TDT or TD), which in turn succeeded ephemeris time (ET). TT shares the original purpose for which ET was designed, to be free of the irregularities in the rotation of Earth.

The unit of TT is the SI second, the definition of which is currently based on the caesium atomic clock, but TT is not itself defined by atomic clocks. It is a theoretical ideal, and real clocks can only approximate it.

TT is distinct from the time scale often used as a basis for civil purposes, Coordinated Universal Time (UTC). TT indirectly underlies UTC, via International Atomic Time (TAI). Because of the historical difference between TAI and ET when TT was introduced, TT is approximately 32.184 s ahead of TAI.

Theoretical astronomy

Theoretical astronomy is the use of the analytical models of physics and chemistry to describe astronomical objects and astronomical phenomena.

Ptolemy's Almagest, although a brilliant treatise on theoretical astronomy combined with a practical handbook for computation, nevertheless includes many compromises to reconcile discordant observations. Theoretical astronomy is usually assumed to have begun with Johannes Kepler (1571–1630), and Kepler's laws. It is co-equal with observation. The general history of astronomy deals with the history of the descriptive and theoretical astronomy of the Solar System, from the late sixteenth century to the end of the nineteenth century. The major categories of works on the history of modern astronomy include general histories, national and institutional histories, instrumentation, descriptive astronomy, theoretical astronomy, positional astronomy, and astrophysics. Astronomy was early to adopt computational techniques to model stellar and galactic formation and celestial mechanics. From the point of view of theoretical astronomy, not only must the mathematical expression be reasonably accurate but it should preferably exist in a form which is amenable to further mathematical analysis when used in specific problems. Most of theoretical astronomy uses Newtonian theory of gravitation, considering that the effects of general relativity are weak for most celestial objects. The obvious fact is that theoretical astronomy cannot (and does not try to) predict the position, size and temperature of every star in the heavens. Theoretical astronomy by and large has concentrated upon analyzing the apparently complex but periodic motions of celestial objects.

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 time-of-day.

Standardized time measurements are made using a clock to count periods of some period changes, 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 18 century to the 19th century it was assumed that the Earth's daily rotational rate was constant. 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 small-scale irregularities, and this was confirmed in the early twentieth century. 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.

William Markowitz

William Markowitz (February 8, 1907 in Vítkov, Austrian Silesia – October 10, 1998 in Pompano Beach, Florida) was an American astronomer, principally known for his work on the standardization of time.

His mother was visiting Melč, Vítkov in Austrian Silesia (now cs:Melč, Czech Republic) when William was born. The Polish family emigrated to the U.S. in 1910 and settled in Chicago.

William earned his doctorate from the university in 1931, under W.D. MacMillan. He taught at Pennsylvania State College before joining the United States Naval Observatory in 1936, working under Paul Sollenberger and Gerald Clemence in the time service department.

After having married Rosalyn Shulemson in 1943, Markowitz eventually became director of the department. He developed the ephemeris time scale, which had been adopted by the IAU in 1952 on a proposal formulated by Clemence in 1948, as an international time standard. He subsequently worked with Louis Essen in England to calibrate the newly developed atomic clocks in terms of the ephemeris second. The fundamental frequency of caesium atomic clocks, which they determined as 9,192,631,770 ± 20 Hz, was used to define the second internationally since 1967. At the International Astronomical Union (IAU) meeting in Dublin in 1955, he had proposed the system of distinguishing between variants of Universal Time, as UT0 (UT as directly observed), UT1 (reduced to invariable meridian by correcting to remove effect of polar motion) and UT2 (further corrected to remove (extrapolated) seasonal variation in earth rotation rate), a system which remains in some use today.

He served as President of the IAU commission on time from 1955 to 1961, and was active in the International Union of Geodesy and Geophysics, the American Geophysical Union, and the International Consultative Committee for the Definition of the Second.

After retirement in 1966, Markowitz served as professor of physics at Marquette University until 1972, and also held a post at Nova Southeastern University.

ΔT

In precise timekeeping, ΔT (Delta T, delta-T, deltaT, or DT) is a measure of the cumulative effect of the departure of the Earth's rotation period from the fixed-length day of atomic time. Formally it is the time difference obtained by subtracting Universal Time (UT, defined by the Earth's rotation) from Terrestrial Time (TT, independent of the Earth's rotation): ΔT = TT − UT. The value of ΔT for the start of 1902 is approximately zero; for 2002 it is about 64 seconds. So the Earth's rotations over that century took about 64 seconds longer than would be required for days of atomic time.

International standards
Obsolete standards
Time in physics
Horology
Calendar
Archaeology and geology
Astronomical chronology
Other units of time
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