ΔT (timekeeping)
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 = 1/2π dθ/dt, and a day corresponds to one period P = 1/ν. A rotational acceleration dν/dt gives a rate of change of the period of dP/dt = −1/ν2 dν/dt, which is usually expressed as α = ν dP/dt = −1/ν dν/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
Terrestrial time
Terrestrial Time is a theoretical uniform time scale, defined to provide continuity with the former
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
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
Geological evidence
Notes
- ^ 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.
- ^ https://datacenter.iers.org/data/latestVersion/bulletinC.txt
- ^ "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.
- ISSN 2572-4525.
- S2CID 51948507.
References
- ISBN 978-3-527-40780-4
- Morrison, L.V. & Stephenson, F. R. "Historical values of the Earth's clock error ΔT 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
- 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 (ΔT) Espenak and Meeus
- Delta-T Charts and data software (archived from the original dead URL)