ΔT (timekeeping)

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TT-UT1 2000+
ΔT vs. time from 1657 to 2022[1][2]

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 International Atomic Time (86,400 seconds). Formally, ΔT is the time difference ΔT = TT − UT between Universal Time (UT, defined by Earth's rotation) and Terrestrial Time (TT, independent of Earth's rotation). The value of ΔT for the start of 1902 was approximately zero; for 2002 it was about 64 seconds. So Earth's rotations over that century took about 64 seconds longer than would be required for days of atomic time. As well as this long-term drift in the length of the day there are short-term fluctuations in the length of day (Δτ) which are dealt with separately.

Since early 2017, the length of the day has happened to be very close to the conventional value, and ΔT has remained within half a second of 69 seconds.[3][4]

Calculation

Earth's rotational speed is ν = 1//dt, and a day corresponds to one period P = 1/ν. A rotational acceleration /dt gives a rate of change of the period of dP/dt = −1/ν2/dt, which is usually expressed as α = νdP/dt = −1/ν/dt. This has units of 1/time, and is commonly quoted as milliseconds-per-day per century (written as ms/day/cy, understood as (ms/day)/cy). Integrating α gives an expression for ΔT against time.

Universal time

Universal Time is a time scale based on the

last glacial period. This removed their tremendous weight, allowing the land under them to begin to rebound upward in the polar regions, an effect that is still occurring today and will continue until isostatic equilibrium is reached. This "post-glacial rebound" brings mass closer to the rotational axis of the Earth, which makes the Earth spin faster, according to the law of conservation of angular momentum, similar to an ice skater pulling their arms in to spin faster. Models estimate this effect to contribute about −0.6 ms/day/cy. Combining these two effects, the net acceleration (actually a deceleration) of the rotation of the Earth, or the change in the length of the mean solar day (LOD), is +1.7 ms/day/cy or +62 s/cy2 or +46.5 ns/day2. This matches the average rate derived from astronomical records over the past 27 centuries.[5][6][7]

Terrestrial time

Terrestrial Time is a theoretical uniform time scale, defined to provide continuity with the former

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

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

BC
), Earth's faster rotation would cause a total solar eclipse to occur 71.625° to the east of the location calculated using the uniform TT.

Values prior to 1955

All values of ΔT before 1955 depend on observations of the Moon, either via eclipses or occultations. The angular momentum lost by the Earth due to friction induced by the Moon's tidal effect is transferred to the Moon, increasing its angular momentum, which means that its moment arm (approximately its distance from the Earth, i.e. precisely the semi-major axis of the Moon's orbit) is increased (for the time being about +3.8 cm/year), which via Kepler's laws of planetary motion causes the Moon to revolve around the Earth at a slower rate. The cited values of ΔT assume that the lunar acceleration (actually a deceleration, that is a negative acceleration) due to this effect is dn/dt = −26″/cy2, where n is the mean sidereal angular motion of the Moon. This is close to the best estimate for dn/dt as of 2002 of −25.858 ± 0.003″/cy2,[19] so ΔT need not be recalculated given the uncertainties and smoothing applied to its current values. Nowadays, UT is the observed orientation of the Earth relative to an inertial reference frame formed by extra-galactic radio sources, modified by an adopted ratio between sidereal time and solar time. Its measurement by several observatories is coordinated by the International Earth Rotation and Reference Systems Service (IERS).

Current values

Recall ΔT = TT − UT1 by definition. While TT is only theoretical, it is commonly realized as TAI + 32.184 seconds where TAI is UTC plus the current leap seconds (TAI − UTC is 37 seconds as of 2024[20]), so ΔT = UTC − UT1 + (leap seconds) + 32.184 s.

This can be rewritten as ΔT = (leap seconds) + 32.184 s − DUT1, where

time signal services
, and by extension serve as a source of the current ΔT.

Geological evidence

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.[23]

Notes

  1. ^ IERS Rapid Service/Prediction Center (c. 1986). Historic Delta T and LOD. Source attributed data to McCarthy and Babcock (1986). Retrieved April 2022.
  2. ^ IERS Rapid Service/Prediction Center. Delta T determinations. Retrieved April 2022.
  3. ^ "deltat.data". urs.earthdata.nasa.gov. Retrieved September 19, 2022.
  4. ^ "Current values and short term predictions of Delta T (2000 to 2024)" (PDF).(diagram constructed by the UK Hydrographic Office).
  5. ^ McCarthy & Seidelmann 2009, 88–89.
  6. ^ Naval Oceanography Portal "Long-term Delta T"
  7. ^ 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
  8. ^ 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.
  9. ^ 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.
  10. ^ 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
  11. ^ 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".
  12. ^ 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.
  13. ^ See especially F R Stephenson (1997), and Stephenson & Morrison (1995), book and papers cited below.
  14. ^ A similar parabola is plotted on p. 54 of McCarthy & Seidelmann (2009).
  15. ^ "NASA.gov".
  16. ^ "Long-term Delta T — Naval Oceanography Portal". c. 2018. Retrieved September 29, 2018.
  17. ^ 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."
  18. ^ 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".
  19. ^ 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.
  20. ^ https://datacenter.iers.org/data/latestVersion/bulletinC.txt
  21. ^ "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.
  22. ISSN 2572-4525
    .
  23. .

References

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