Five Millennium Canon of Lunar Eclipses [Espenak and Meeus]

Greenwich Mean Time

For thousands of years, time has been measured using the length of the solar day. This is the interval between two successive returns of the Sun to an observer's local meridian. Unfortunately, the length of the apparent solar day can vary by tens of seconds over the course of a year. Earth's elliptical orbit around the Sun and the 23.5° inclination of Earth's axis of rotation are responsible for these variations. Apparent solar time was eventually replaced by mean solar time because it provides for a uniform time scale. The key to mean solar time is the mean solar day, which has a constant length of 24 hours throughout the year.

Mean solar time on the 0° longitude meridian in Greenwich, England is known as Greenwich Mean Time (GMT). At the International Meridian Conference of 1884, GMT[1] was adopted as the reference time for all clocks around the world. It was also agreed that all longitudes would be measured east or west with respect to the Greenwich meridian. In 1972, GMT was replaced by Coordinated Universal Time (UTC) as the international time reference. Nevertheless, UTC is colloquially referred to as GMT although this is technically not correct.

Ephemeris Time

During the 20th century, it was found that the rotational period of Earth (length of the day) was gradually slowing down. For the purposes of orbital calculations, time using Earth's rotation was abandoned for a more uniform time scale based on Earth's orbit about the Sun. In 1952, the International Astronomical Union (IAU) introduced Ephemeris Time (ET) to address this problem. The ephemeris second was defined as a fraction of the tropical year for 1900 Jan 01, as calculated from Newcomb's tables of the Sun (1895). Ephemeris Time was used for Solar System ephemeris calculations until it was replaced by TD in 1979.

Terrestrial Dynamical Time

TD was introduced by the IAU in 1979 as the coordinate time scale for an observer on the surface of Earth. It takes into account relativistic effects and is based on International Atomic Time (TAI), which is a high-precision standard using several hundred atomic clocks worldwide. As such, TD is the atomic time equivalent to its predecessor ET and is used in the theories of motion for bodies in the solar system. To ensure continuity with ET, TD was defined to match ET for the date 1977 Jan 01. In 1991, the IAU refined the definition of TD to make it more precise. It was also renamed Terrestrial Time (TT), although on this Web site, the older name Terrestrial Dynamical Time is preferred and used.

Universal Time

For many centuries, the fundamental unit of time was the rotational period of Earth with respect to the Sun. GMT was the standard time reference based on the mean solar time on the 0° longitude meridian in Greenwich, England. Universal Time (UT) is the modern counterpart to GMT and is determined from Very Long Baseline Interferometry (VLBI) observations of the diurnal motion of quasars. Unfortunately, UT is not a uniform time scale because Earth's rotational period is (on average) gradually increasing.

The change is primarily due to tidal friction between Earth's oceans and its rocky mantle through the gravitational attraction of 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. Shorter period fluctuations in terrestrial rotation also exist, which can produce an accumulated clock error of 20 s in one or more decades. These decade variations are attributed to several geophysical mechanisms including fluid interactions between the core and mantle of Earth. Climatological changes and variations in sea-level may also play significant roles because they alter Earth's moment of inertia.

The secular acceleration of the Moon implies an increase in the length of day (LOD) of about 2.3 milliseconds per century. Such a small amount may seem insignificant, but it has very measurable cumulative effects. At this rate, time as measured through Earth's rotation is losing about 84 seconds per century squared when compared to atomic time.

Coordinated Universal Time

Coordinated Universal Time (UTC) is the present day basis of all civilian time throughout the world. Derived from TAI, the length of the UTC second is defined in terms of an atomic transition of the element cesium and is accurate to approximately 1 ns (billionth of a second) per day. Because most daily life is still organized around the solar day, UTC was defined to closely parallel Universal Time. The two time systems are intrinsically incompatible, however, because UTC is uniform while UT is based on Earth's rotation, which is gradually slowing. In order to keep the two times within 0.9 s of each other, a leap second is added to UTC about once every 12 to 18 months.

Delta T (ΔT)

The orbital positions of the Sun and Moon required by eclipse predictions, are calculated using TD because it is a uniform time scale. World time zones and daily life, however, are based on UT[2]. In order to convert eclipse predictions from TD to UT, the difference between these two time scales must be known. The parameter delta-T (ΔT) is the arithmetic difference, in seconds, between the two as:

                                         ΔT = TD - UT

Past values of ΔT can be deduced from the historical records. In particular, hundreds of eclipse observations (both solar and lunar) were recorded in early European, Middle Eastern, and Chinese annals, manuscripts, and canons. In spite of their relatively low precision, these data represent the only evidence for the value of ΔT prior to 1600 CE. In the centuries following the introduction of the telescope (circa 1609 CE), thousands of high quality observations have been made of lunar occultations of stars. The number and accuracy of these timings increase from the 17th through the 20th century, affording valuable data in the determination of ΔT.

For more information, visit the ΔT page.

A series of polynomial expressions have been derived to simplify the evaluation of ΔT for any time during the interval -1999 to +3000. The uncertainty in ΔT over this period can be estimated from scatter in the measurements.

The information above was previously published in:

Five Millennium Canon of Lunar Eclipses: -1999 to +3000 (NASA TP-2009-214172)
Five Millennium Catalog of Lunar Eclipses: -1999 to +3000 (NASA TP-2009-214173)

Return to main index for:

Five Millennium Catalog of Lunar Eclipses


    [1] GMT was originally reckoned from noon to noon. In 1925, some countries shifted GMT by 12 h so that it would begin at Greenwich midnight. This new definition is the one in common usage for world time and in the navigational publications of English-speaking countries. The designation Greenwich Mean Astronomical Time (GMAT) is reserved for the reckoning of time from noon (and previously called GMT).

    [2] World time zones are actually based on Coordinated Universal Time (UTC). It is an atomic time synchronized and adjusted to stay within 0.9 seconds of astronomically determined Universal Time (UT). Occasionally, a "leap second" is added to UTC to keep it in sync with UT (which changes due to variations in Earth's rotation rate).

2009 Jan 30