Ephemeris time

In metrology, ephemeris time (ET) is time in association with any ephemeris (itinerary of the trajectory of an astronomical object). In practice it has been used more specifically to refer to:

a former standard astronomical time scale adopted in 1952 by the IAU,'ESAE 1961': 'Explanatory Supplement (1961), esp. p. 9. and superseded during the 1970s.'ESAA (1992)': P K Seidelmann (ed)., especially at pp. 41—42 and at p. 79. This time scale was proposed in 1948, to overcome the disadvantages 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.B Guinot and P K Seidelmann (1988), at p. 304—5. 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).E M Standish (1998).

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

An impression has sometimes arisen that ephemeris time has been in use since 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.S Newcomb (1895).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.

The ephemeris time of the 1952 standard leaves a continuing legacy, through its historical unit 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 the American astronomer Gerald Maurice Clemence.G M Clemence (1948).

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 the Dutch astronomer Willem de Sitter,W de Sitter (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 André-Louis 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.G M Clemence (1971).

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.

Clemence made a detailed proposal of this type based on the results of the English Astronomer Royal H Spencer Jones (1939).H 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".Clemence (1948), at p. 171.

De Sitter and Clemence both referred to the proposal as 'Newtonian' or 'uniform' time. D Brouwer suggested the name 'ephemeris time'.ESAA (1992), see page 79.

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.At the IAU meeting in Rome 1952: see ESAE (1961) at sect.1C, p. 9; also Clemence (1971). 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,ESAA 1992, p. 79: citing decision of International Committee for Weights and Measures (CIPM), Sept 1954. and then as the slightly modified fraction 1/31556925.9747 instead,ESAA (1992), see page 80, citing CIPM recommendation Oct 1956, adopted 1960 by the General Conference on Weights and Measures (CGPM). 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".ESAA (1992), at page 42. 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.Wm Markowitz (1988).

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 (but its practical implementation was usually achieved in another way, see below). Its detailed definition was based on Simon Newcomb's Tables of the Sun (1895), implemented 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 units of Julian centuries of 36525 mean solar daysThe unit of mean solar day is left implicit on p. 9 but made explicit on p. 20 of Newcomb (1895).), 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 differences between the observed positions of the Sun and the predicted positions given by Newcomb's formula demonstrated the need for the following correction to the formula:

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.Clemence (1948), p. 172, following Spencer Jones (1939).

Thus, a conventionally corrected form of Newcomb's formula, incorporating 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, however, did not adopt such a correction of mean solar time. Instead, the same numbers were used as in Newcomb's original uncorrected formula (1), but now applied somewhat prescriptively, to define a new 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)

With this reapplication, the time variable, now given as E, represents time in ephemeris centuries of 36525 ephemeris days of 86400 ephemeris seconds each. The 1961 official reference summarized the concept as such: "The origin and rate of ephemeris time are defined to make the Sun's mean longitude agree with Newcomb's expression"ESAE (1961) at p. 70.

From the comparison of formulae (2) and (3), both of which express the same real solar motion in the same real time but defined on separate 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)

with the 24.349 seconds of time corresponding to the 1.00" in ΔLs. Clemence's formula (today 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) units of ephemeris time have been, for the whole of the twentieth century, very slightly shorter than the corresponding (but not precisely constant) units of mean solar time (which, besides their irregular fluctuations, tend to lengthen gradually). This finding is consistent with the modern results of Morrison and StephensonL V Morrison & F R Stephenson (2004); also F R Stephenson, L V Morrison (1984), and F R Stephenson, L V Morrison (1995). (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,Clemence (1948), at pp. 171—3. it was usually measured in practice by the orbital motion of the Moon around the Earth.W Markowitz & others (1955); W Markowitz (1959); also W Markowitz, R G Hall, L Essen, J V L Parry (1958). 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.B Guinot & P K Seidelmann (1988), at p. 305.

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