Delta T (ΔT) and Universal Time

Fred Espenak

For many centuries, the fundamental unit of time was the rotational period of the Earth with respect to the Sun. Universal Time or UT (colloquially called Greenwich Mean Time or GMT) is based on mean solar time from Greenwich, England. Unfortunately, Universal Time is not a uniform time scale because Earth's rotational period is gradually dinreasing.

As Earth rotates on its axis, tidal friction is imposed on it through the gravitational attraction with the Moon and, to a lesser extent, the Sun. This secular acceleration gradually transfers angular momentum from Earth to the Moon. As Earth loses energy and slows down, the Moon gains this energy and its orbital period and distance from Earth increase.

The secular acceleration of the Moon is very poorly known and may not be constant. Careful records for its derivation only go back as far as 100 years or so. Before then, spurious and often incomplete eclipse and occultation observations from medieval and ancient manuscripts comprise the data base. In any case, the current value implies an increase in the length of the day by about 0.002 seconds per day per century. Such a trivially small amount may seem insignificant, but it has very measurable cummulative effects. If we compare the rotation of the actual Earth with a fictional Earth turning at a constant rate, we would find that solar time on the real Earth would fall about one minute behind the fictional Earth after just one century.

Earth's rotation on its axis is also subject to short term fluctuations for periods of up to several decades. It is believed that these fluctuations may be due to fluid motions in Earth's core which interact with and disturb the rotation of the mantle. However, climatological changes and variations in sea-level may also play significant roles since they should alter Earth's moment of inertia. Whatever the mechanism is, it is clear that its effects cannot be predicted with the current state of knowledge. When combined, the long term secular changes and rapid multi-decade fluctuations can put Earth an hour or more "behind schedule" in the course of one millennium.

Terrestrial Dynamical Time (TDT) is an atomic time scale. It can be thought of as the time that would be kept by an ideal clock. Most astronomical calculations (including eclipses) use Terrestrial Dynamical Time since the orbits of all the planets can be accurately described with it.

Although solar eclipse predictions are based on Terrestrial Dynamical Time, the position of the central eclipse path still depends on Universal Time. To convert TDT predictions to UT, one must know the difference between Terrestrial Dynamical Time and Universal Time. This parameter is known as delta-T or ΔT (ΔT = TDT - UT).

Stephenson and collaborators have produced a number of seminal works in the field of Earth's rotation over the past several millennia. In particular, they have identified hundreds of eclipse and occultation observations in early European, Middle Eastern and Chinese annals, manuscripts, canons and records. In spite of their relatively low precision, these data represent our only record to the value of ΔT during the past several millennia.

Values of delta T before AD 1600 pre-date the telescope and are based on historic records of naked eye observations of eclipses and occultations. A number of researchers have made significant contributions in this area. In particular, Morrison and Stephenson (2004) have fit hundreds of records with simple polynomials to achieve a best fit for describing the value of ΔT from 700 BCE to 1600 CE. An abbreviated table of their results follows:

                     Year       ΔT                Longitude
                               (sec)                Shift

                     -500      17190 = 04h 47m       71.6°
                        0      10580 = 02h 56m       44.1°
                      500       5710 = 01h 35m       23.8°
                     1000       1570 = 00h 26m        6.5°
                     1500        200 = 00h 03m        0.8°

Recent observed values for ΔT are as follows:

                     Year        ΔT

                    1970.0      40.18
                    1975.0      45.48
                    1980.0      50.54
                    1985.0      54.34
                    1990.0      56.86
                    1995.0      60.79

                    2000.0      63.83
                    2001.0      64.09
                    2002.0      64.30
                    2003.0      64.47
                    2004.0      64.57
                    2005.0      64.69
                    2006.0      64.85
                    2007.0      65.15

Values for ΔT in the past and future are uncertain but may be approximated by extrapolating from known values. However, the further into the past or future that one extrapolates, the greater the uncertainty in ΔT. For more information, see: Historical Values of Delta T.

References for Delta T

Dickey, J.O., "Earth Rotation Variations from Hours to Centuries", in: I. Appenzeller (ed.), Highlights of Astronomy: Vol. 10 (Kluwer Academic Publishers, Dordrecht/Boston/London, 1995), pp. 17-44.

Meeus, J., "The Effect of Delta T on Astronomical Calculations", Journal of the British Astronomical Association, 108 (1998), 154-156.

Morrison, L.V. & Stephenson, F.R., "Historical Values of the Earth's Clock Error Delta T and the Calculation of Eclipses", Journal for the History of Astronomy, Vol. 35 Part 3, August 2004, No. 120 (2004), pages 327-336.

Morrison, L.V. and Ward, C. G., "An analysis of the transits of Mercury: 1677-1973", Mon. Not. Roy. Astron. Soc., 173, 183-206, 1975.

Spencer Jones, H., "The Rotation of the Earth, and the Secular Accelerations of the Sun, Moon and Planets", Monthly Notices of the Royal Astronomical Society, 99 (1939), 541-558.

Stephenson, F.R. & Morrison, L.V., "Long-Term Changes in the Rotation of the Earth: 700 BC to AD 1980", Philosophical Transactions of the Royal Society of London, Ser. A, 313 (1984), 47-70.

Stephenson F.R and Houlden M.A., Atlas of Historical Eclipse Maps: East Asia 1500 BD - AD 1900, Cambridge Univ.Press., 1986.

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, Ser. A, 351 (1995), 165-202.

Stephenson F.R., Historical Eclipses and Earth's Rotation , Cambridge Univ.Press, 1997.


2011 Dec 28