Ephemeris time

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The term ephemeris time is in itself apt to refer to time in connection with any astronomical ephemeris. It has been used more specifically to refer:-

(1) to a (former standard) astronomical time scale, officially ephemeris time, sometimes designated ET. This was adopted in 1952 by IAU,^[1] and superseded in the 1970s.^[2] This time scale was proposed in 1948, to overcome the drawbacks of irregularly fluctuating mean solar time.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 Definition of ephemeris time (1952)).

also

(2) (sometimes in past, but with risk of confusion with (1)) to a modern relativistic coordinate time scale, implemented by the JPL ephemeris time argument T_eph, in a series of numerically integrated Development Ephemerides. Among them is the DE405 ephemeris in widespread current use. The time scale represented by T_eph 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 JPL ephemeris time argument Teph).^[3]

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.^[4]

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 Redefinition of the second).

Contents 1 History of ephemeris time (1952 standard) 2 Definition of ephemeris time (1952) 3 Use of ephemeris time in official almanacs and ephemerides 4 Revision of time scales 5 JPL ephemeris time argument Teph 6 Redefinition of the second 7 References

[edit] History of ephemeris time (1952 standard)

Ephemeris time (ET), adopted as standard in 1952, was originally designed "for the convenience of astronomers and other scientists", especially 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^[5]. The aim was to replace Universal Time (UT), and other mean solar time scales based on the rotation of the Earth around its axis, in astronomical and scientific uses which would otherwise suffer from the unpredictable irregularities of the mean solar time scale.

In the later nineteenth and early twentieth centuries it was first suspected, and eventually 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 evidence was compiled by W de Sitter (1927)^[6] 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.^[7]

G M Clemence (1948)^[5] made a detailed proposal of this type based on the results of H Spencer Jones (1939).^[8] 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".^[9]

De Sitter and Clemence both referred to the proposal as 'Newtonian' or 'uniform' time. D Brouwer suggested the name 'ephemeris time'.^[10]

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.^[1][11] Its practical introduction took some time (see #Use of ephemeris time in official almanacs and ephemerides); it 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^[13], and then as the slightly modified fraction 1/31556925.9747 instead,^[14] 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".^[15] ET was used for the calibration of atomic clocks in the 1950s,^[16] Close equality between the ET second with the later SI second (as defined with reference to the cesium atomic clock) has been verified.^[17]

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 in approximately in step with mean solar time.

[edit] Definition of ephemeris time (1952)

Ephemeris time was defined in principle by the orbital motion of the Earth around the Sun,^[2][18] but was usually measured in practice by the orbital motion of the Moon around the Earth.^[19]

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

In the introduction to Newcomb's Tables of the Sun (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^[20]) 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^[8] 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^[21]).

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"^[22]

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):

δt = + 24^s.349 + 72^s.3165T + 29^s.949T² + 1.821B.....(4)^[23]

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 (1984) and (1995) (see article ΔT).

[edit] 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, replacing UT in the main ephemerides in the issues for 1960 and after.^[24] (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^[25] (computed by W J Eckert from Brown's theory with modifications recommended by Clemence (1948)).

[edit] 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)^[26]. 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)^[27].

[edit] JPL ephemeris time argument Teph

High-precision ephemerides of sun, moon and planets were developed and calculated at the Jet Propulsion Laboratory 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 JPL ephemeris time argument T_eph had been in longstanding use at that institution since the 1960s. The time scale represented by T_eph 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 sec/yr) from the TCB time scale adopted in 1991 as a standard by the IAU. Thus for clocks on or near the geoid, T_eph (within 2 milliseconds), but not so closely TCB, can be used as approximations to Terrestrial Time, and via the standard ephemerides T_eph is in widespread use.^[3]

[edit] 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 = 129602768.13 / (360 x 60 x 60 x 36525 x 86400).

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.^[16]

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.^[17]

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, 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 1.0003725 TT = 1977 January 1.0000000 TAI, i.e.

ET - TAI = 32.184 seconds

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

[edit] References

1. ^ ^{a b} 'ESAE 1961': 'Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac' ('prepared jointly by the Nautical Almanac Offices of the United Kingdom and the United States of America', HMSO, London, 1961), esp. p.9
2. ^ ^{a b} 'ESAA (1992)': (ed) P K Seidelmann, 'Explanatory Supplement to the Astronomical Almanac', University Science Books, CA, 1992 ; ISBN 0-935702-68-7, esp. at pp.41-42.
3. ^ ^{a b} E M Standish, 'Time scales in the JPL and CfA ephemerides', Astron & Astrophys 336 (1998), 381-384.
4. ^ See ESAE (1961), e.g. pp.69 and 87, and Clemence (1948), at p.172
5. ^ ^{a b} 'Clemence (1948)': G M Clemence, 'On the System of Astronomical Constants', Astron J (1948) vol.53 (6), issue #1170, pp 169-179
6. ^ W de Sitter (1927), 'On the secular accelerations and the fluctuations of the longitudes of the moon, the sun, Mercury and Venus', Bull. Astron. Inst. Netherlands, v4 (1927) pp.21-38.
7. ^ 'Clemence (1971)': G M Clemence (1971), J Hist Astron v2 (1971) pp. 73-79.
8. ^ ^{a b} H Spencer Jones, "The Rotation of the Earth, and the Secular Accelerations of the Sun, Moon and Planets", in 'Monthly Notes of the Royal Astronomical Society', vol.99 (1939), pp 541-558.
9. ^ Clemence (1948), at p.171.
10. ^ ESAA (1992), p.79.
11. ^ at the IAU meeting in Rome 1952: see ESAE (1961) at sect.1C, p.9; ESAA (1992) at p.79; also Clemence (1971).
12. ^ ESAA (1992), at p.79
13. ^ ESAA 1992, p.79, citing decision of Intl. Committee on Weights and Measures (CIPM), Sept.1954
14. ^ ESAA 1992, at p.80, citing CIPM recommendation Oct 1956, adopted 1960 by general Conference on Weights and Measures (GCPM)
15. ^ See ESAA (1992), p.42
16. ^ ^{a b} W Markowitz, R G Hall, L Essen, J V L Parry (1958), 'Frequency of cesium in terms of ephemeris time', Phys Rev Letters v1 (1958), 105-107.
17. ^ ^{a b} 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 413-418.
18. ^ See ESAA (1992) esp. at pp.79-80.
19. ^ See Clemence (1948) at pp.171-3; also W Markowitz, 'Variations in the Rotation of the Earth, Results Obtained with the Dual-Rate Moon Camera and Photograhic Zenith Tubes', Astron J v64 (1959) 106-113; also W Markowitz, R G Hall, L Essen, J V L Parry (1958), 'Frequency of cesium in terms of ephemeris time', Phys Rev Letters v1 (1958), 105-107.
20. ^ The unit of _mean solar_ day is left implicit on p.9 but made explicit on p.20 of Newcomb's Tables (1895).
21. ^ Clemence 1948 at p.172, following Spencer Jones (1939)
22. ^ ESAE (1961) at p.70.
23. ^ Clemence (1948), at p.172.
24. ^ ESAA 1992, at p.612.
25. ^ 'Improved Lunar Ephemeris', US Government Printing Office, 1954.
26. ^ adopted by the IAU in 1976 at Grenoble, see ESAA (1992) at p.41
27. ^ see ESAA (1992) at p.42

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