Delta T

From Academic Kids


ΔT is the time difference obtained by subtracting Universal Time from Terrestrial Time.

Universal Time (UT) is a time scale based on the rotation of the Earth, which is somewhat irregular over the short term (less than a century), thus any time based on it cannot have an accuracy better than 1 : 108. But the principal effect is over the long term. Over many centuries tidal friction inexorably slows Earth's rate of rotation by 2.3 ms/day/cy. However, the melting of continental ice sheets at the end of the last ice age removed their tremendous weight, allowing the land under them to begin to isostatically rebound upward in the polar regions, which continues to this day, causing Earth's rate of rotation to speed up by 0.6 ms/day/cy. The net tidal acceleration or the change in the length of the mean solar day (LOD) is +1.7 ms/cy.

Terrestrial Time (TT) is a uniform time scale based on International Atomic Time (TAI), but corrected to equal the former Ephemeris Time (ET) by adding 32.184 s (TT = TAI + 32.184 s). ET is the independent variable of time in Simon Newcomb's Tables of the Sun, which formed the basis of all astronomical ephemerides from 1900 through 1983. ET, in turn, was actually the average mean solar time between 1750 and 1890 (centered on 1820), because that was the period during which the observations on which those tables were based were performed. TAI and hence TT is strictly uniform (every second is the same as every other second), with an accuracy of about 1 : 1014.

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) 31((Year − 1820)/100)² seconds for ΔT. Smoothed historical measurements of ΔT using total solar eclipses are about +16800 s at the year −500, +10600 s at 0, +5700 s at 500, +1600 s at 1000, and +180 s at 1500. During the telescopic era, measurements were made by observing occultations of stars by the Moon. ΔT continued to decrease until it reached a plateau of +11±6 s between 1680 and 1866. For about three decades immediately before 1902 it was negative, reaching −6.64 s. Then it increased to +63.83 s at 2000. Physically, this causes the meridian of Greenwich in Universal Time to be almost always to the east of the meridian in Terrestrial Time. +16800 s or 4 2/3 h corresponds to 70E. This means that at −500 Earth's faster rotation would cause a total solar eclipse to occur 70 to the east of its location calculated using the uniform TT.

All values of ΔT before 1955 depend on observations of the Moon, either via eclipses or occultations. Conservation of angular momentum in the Earth-Moon system requires that the angular momentum lost by the Earth due to tidal friction be transferred to the Moon, increasing its angular momentum, which means that its moment arm (its distance from the Earth) is increased, 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 due to this affect is Γ = −26"/cy². This is close to the best estimate for Γ as of 2002 of −25.858±0.003"/cy² 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 is performed by the International Earth Rotation and Reference Systems Service (IERS).


  • F.R. Stephenson, L.V. Morrison. "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.
  • F.R. Stephenson. Historical Eclipses and Earth's Rotation. Cambridge University Press, 1997. ISBN 0-521-46194-4

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