Δ T (timekeeping)
In precise timekeeping,
Since early 2017, the length of the day has happened to be very close to the conventional value, and
Calculation
[edit]Earth's rotational speed is
Universal time
[edit]Universal Time is a time scale based on the Earth's rotation, which is somewhat irregular over short periods (days up to a century), thus any time based on it cannot have an accuracy better than 1 in 108. However, a larger, more consistent effect has been observed over many centuries: Earth's rate of rotation is inexorably slowing down. This observed change in the rate of rotation is attributable to two primary forces, one decreasing and one increasing the Earth's rate of rotation. Over the long term, the dominating force is tidal friction, which is slowing the rate of rotation, contributing about
Terrestrial time
[edit]Terrestrial Time is a theoretical uniform time scale, defined to provide continuity with the former Ephemeris Time (ET). ET was an independent time-variable, proposed (and its adoption agreed) in the period 1948–1952[8] with the intent of forming a gravitationally uniform time scale as far as was feasible at that time, and depending for its definition on Simon Newcomb's Tables of the Sun (1895), interpreted in a new way to accommodate certain observed discrepancies.[9] Newcomb's tables formed the basis of all astronomical ephemerides of the Sun from 1900 through 1983: they were originally expressed (and published) in terms of Greenwich Mean Time and the mean solar day,[10][11] but later, in respect of the period 1960–1983, they were treated as expressed in terms of ET,[12] in accordance with the adopted ET proposal of 1948–52. ET, in turn, can now be seen (in light of modern results)[13] as close to the average mean solar time between 1750 and 1890 (centered on 1820), because that was the period during which the observations on which Newcomb's tables were based were performed. While TT is strictly uniform (being based on the SI second, every second is the same as every other second), it is in practice realised by International Atomic Time (TAI) with an accuracy of about 1 part in 1014.
Earth's rate of rotation
[edit]Earth's rate of rotation must be integrated to obtain time, which is Earth's angular position (specifically, the orientation of the meridian of Greenwich relative to the fictitious mean sun). Integrating +1.7 ms/d/cy and centering the resulting parabola on the year 1820 yields (to a first approximation) 32 × (year − 1820/100)2
- 20 seconds for
Values prior to 1955
[edit]All values of
Current values
[edit]Recall
This can be rewritten as
Geological evidence
[edit]Tidal deceleration rates have varied over the history of the Earth-Moon system. Analysis of layering in fossil mollusc shells from 70 million years ago, in the Late Cretaceous period, shows that there were 372 days a year, and thus that the day was about 23.5 hours long then.[20][21] Based on geological studies of tidal rhythmites, the day was 21.9±0.4 hours long 620 million years ago and there were 13.1±0.1 synodic months/year and 400±7 solar days/year. The average recession rate of the Moon between then and now has been 2.17±0.31 cm/year, which is about half the present rate. The present high rate may be due to near resonance between natural ocean frequencies and tidal frequencies.[22]
Notes
[edit]- ^ IERS Rapid Service/Prediction Center (c. 1986). Historic Delta T and LOD. Source attributed data to McCarthy and Babcock (1986). Retrieved April 2022.
- ^ IERS Rapid Service/Prediction Center. Delta T determinations. Retrieved April 2022.
- ^ "deltat.data". urs.earthdata.nasa.gov. Retrieved September 19, 2022.
- ^ "Current values and short term predictions of Delta T (2000 to 2024)" (PDF).(diagram constructed by the UK Hydrographic Office).
- ^ McCarthy & Seidelmann 2009, 88–89.
- ^ Naval Oceanography Portal "Long-term Delta T"
- ^ Naval Meteorology and Oceanography Command "Suggested Reading", Delta T information - McCarthy, D.D. and A.K. Babcock, Physics of the Earth and Planetary Interiors, Vol. 44, 1986, 281-292
- ^ Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, Nautical Almanac Offices of UK and US (1961), at pp. 9 and 71.
- ^ See G M Clemence's proposal of 1948, contained in his paper: "On the System of Astronomical Constants", Astronomical Journal (1948) vol.53 (6), issue #1170, pp 169–179; also G M Clemence (1971), "The Concept of Ephemeris Time", in Journal for the History of Astronomy v2 (1971), pp. 73–79 (giving details of the genesis and adoption of the ephemeris time proposal); also article Ephemeris time and references therein.
- ^ Newcomb's Tables of the Sun (Washington, 1895), Introduction, I. Basis of the Tables, pp. 9 and 20, citing time units of Greenwich Mean Noon, Greenwich Mean Time, and mean solar day
- ^ W de Sitter, on p. 38 of Bulletin of the Astronomical Institutes of the Netherlands, v4 (1927), pp.21–38, "On the secular accelerations and the fluctuations of the moon, the sun, Mercury and Venus", which refers to "the 'astronomical time', given by the earth's rotation, and used in all practical astronomical computations", and states that it "differs from the 'uniform' or 'Newtonian' time".
- ^ See p. 612 in Explanatory Supplement to the Astronomical Almanac, ed. P K Seidelmann, 1992, confirming introduction of ET in the 1960 edition of the ephemerides.
- ^ See especially F R Stephenson (1997), and Stephenson & Morrison (1995), book and papers cited below.
- ^ A similar parabola is plotted on p. 54 of McCarthy & Seidelmann (2009).
- ^ "NASA.gov".
- ^ "Long-term Delta T — Naval Oceanography Portal". c. 2018. Retrieved September 29, 2018.
- ^ In "The Physical Basis of the Leap Second", by D D McCarthy, C Hackman and R A Nelson, in Astronomical Journal, vol.136 (2008), pages 1906–1908, it is stated (page 1908), that "the SI second is equivalent to an older measure of the second of UT1, which was too small to start with and further, as the duration of the UT1 second increases, the discrepancy widens."
- ^ In the late 1950s, the caesium standard was used to measure both the current mean length of the second of mean solar time (UT2) (result: 9192631830 cycles) and also the second of ephemeris time (ET) (result: 9192631770 ± 20 cycles), see "Time Scales", by L Essen, in Metrologia, vol.4 (1968), pp.161–165, on p.162. The ephemeris figure was chosen for the SI second. Essen in the same 1968 article (p.162) stated that this "seemed reasonable in view of the variations in UT2".
- ^ J.Chapront, M.Chapront-Touzé, G.Francou (2002): "A new determination of lunar orbital parameters, precession constant, and tidal acceleration from LLR measurements" (also in PDF). Astronomy & Astrophysics 387, 700–709.
- ^ "Ancient shell shows days were half-hour shorter 70 million years ago: Beer stein-shaped distant relative of modern clams captured snapshots of hot days in the late Cretaceous". ScienceDaily. Retrieved March 14, 2020.
- ^ Winter, Niels J. de; Goderis, Steven; Malderen, Stijn J. M. Van; Sinnesael, Matthias; Vansteenberge, Stef; Snoeck, Christophe; Belza, Joke; Vanhaecke, Frank; Claeys, Philippe (2020). "Subdaily-Scale Chemical Variability in a Torreites Sanchezi Rudist Shell: Implications for Rudist Paleobiology and the Cretaceous Day-Night Cycle". Paleoceanography and Paleoclimatology. 35 (2): e2019PA003723. doi:10.1029/2019PA003723. hdl:1854/LU-8685501. ISSN 2572-4525.
- ^ Williams, George E. (2000). "Geological constraints on the Precambrian history of Earth's rotation and the Moon's orbit". Reviews of Geophysics. 38 (1): 37–60. Bibcode:2000RvGeo..38...37W. CiteSeerX 10.1.1.597.6421. doi:10.1029/1999RG900016. S2CID 51948507.
References
[edit]- McCarthy, D.D. & Seidelmann, P.K. TIME: From Earth Rotation to Atomic Physics. Weinheim: Wiley-VCH. (2009). ISBN 978-3-527-40780-4
- Morrison, L.V. & Stephenson, F. R. "Historical values of the Earth's clock error
Δ T and the calculation of eclipses" (pdf, 862 KB), Journal for the History of Astronomy 35 (2004) 327–336. - Stephenson, F.R. Historical Eclipses and Earth's Rotation. Cambridge University Press, 1997. ISBN 0-521-46194-4
- Stephenson, F. R. & Morrison, L.V. "Long-term fluctuations in the Earth's rotation: 700 BC to AD 1990". Philosophical Transactions of the Royal Society of London, Series A 351 (1995) 165–202. JSTOR link. Includes evidence that the 'growth' in Delta-T is being modified by an oscillation with a wavelength around 1500 years; if that is true, then during the next few centuries Delta-T values will increase more slowly than is envisaged.
External links
[edit]- IERS Rapid Service-Prediction Center Values for Delta T.
- Delta T webpage by Robert van Gent
- Delta T webpage by Felix Verbelen (archived from the original dead URL)
- Eclipse Predictions and Earth's Rotation by Fred Espenak (archived from the original dead URL)
- Polynomial expressions for Delta T (
Δ T) Espenak and Meeus - Delta-T Charts and data software (archived from the original dead URL)