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'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) 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Clemence's formula, now superseded by more modern estimations, was included in the original conference decision on ephemeris time.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).
Read more about this topic: Ephemeris Time
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