Delta T
Encyclopedia
ΔT, Delta T, delta-T, deltaT, or DT is the time difference obtained by subtracting Universal Time
(UT) from Terrestrial Time
(TT): ΔT=TT−UT.
Universal Time is a time scale based on the Earth's rotation, which is somewhat irregular over short periods (days up to 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 about 2.3 ms
/day
/cy
. However, there are other forces changing the rotation rate of the Earth. The most important one is believed to be a result of the melting of continental ice sheets at the end of the last glacial period. This removed their tremendous weight, allowing the land under them to begin to rebound upward in the polar regions, which has been continuing and will continue until isostatic equilibrium is reached. This "glacial rebound" brings mass closer to the rotation axis of the Earth, which makes the Earth spin faster (law of conservation of angular momentum
): the rate derived from models is about 0.6 ms/day/cy. So 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. This is indeed the average rate as observed over the past 27 centuries.
Terrestrial Time is a theoretical uniform time scale, defined to provide continuity with the former Ephemeris Time
(ET). ET was an independent time-variable, proposed (and its adoption agreed) in the period 1948–52 with the intent of forming a gravitationally uniform time scale as far as was feasible at that time, and depending for its definition on Simon Newcomb
's Tables of the Sun
(1895), interpreted in a new way to accommodate certain observed discrepancies. Newcomb's tables formed the basis of all astronomical ephemerides of the Sun from 1900 through 1983: they were originally expressed (and published) in terms of Greenwich Mean Time and the mean solar day, but later, in respect of the period 1960–1983, they were treated as expressed in terms of ET, in accordance with the adopted ET proposal of 1948–52. ET, in turn, can now be seen (in light of modern results) as close to the average mean solar time between 1750 and 1890 (centered on 1820), because that was the period during which the observations on which Newcomb's tables were based were performed. While TT is strictly uniform (being based on the 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 : 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 eclipse
s are about +16800 s at the year −500 (501 BC), +10600 s at 0 (1 BC), +5700 s at 500 (AD), +1600 s at 1000, and +180 s at 1500. After the invention of the telescope, measurements were made by observing occultations of stars by the Moon
, which allowed the derivation of more closely spaced and more accurate values for ΔT. 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. It will continue to increase at an ever faster (quadratic) rate in the future. This will require the addition of an ever greater number of leap second
s to UTC
as long as UTC is kept within one second of UT1. (The SI second as now used for UTC, when adopted, was already a little shorter than the current value of the second of mean solar time.) Physically, the meridian of Greenwich in Universal Time is almost always to the east of the meridian in Terrestrial Time, both in the past and in the future. +16800 s or 4⅔ h corresponds to 70°E. 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 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 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).
Universal Time
Universal Time is a time scale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC...
(UT) from Terrestrial Time
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....
(TT): ΔT=TT−UT.
Universal Time is a time scale based on the Earth's rotation, which is somewhat irregular over short periods (days up to 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
Tidal acceleration
Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite , and the primary planet that it orbits . The "acceleration" is usually negative, as it causes a gradual slowing and recession of a satellite in a prograde orbit away from the primary, and a corresponding...
inexorably slows Earth's rate of rotation by about 2.3 ms
Millisecond
A millisecond is a thousandth of a second.10 milliseconds are called a centisecond....
/day
Day
A day is a unit of time, commonly defined as an interval equal to 24 hours. It also can mean that portion of the full day during which a location is illuminated by the light of the sun...
/cy
Century
A century is one hundred consecutive years. Centuries are numbered ordinally in English and many other languages .-Start and end in the Gregorian Calendar:...
. However, there are other forces changing the rotation rate of the Earth. The most important one is believed to be a result of the melting of continental ice sheets at the end of the last glacial period. This removed their tremendous weight, allowing the land under them to begin to rebound upward in the polar regions, which has been continuing and will continue until isostatic equilibrium is reached. This "glacial rebound" brings mass closer to the rotation axis of the Earth, which makes the Earth spin faster (law of conservation of angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
): the rate derived from models is about 0.6 ms/day/cy. So 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. This is indeed the average rate as observed over the past 27 centuries.
Terrestrial Time is a theoretical uniform time scale, defined to provide continuity with the former Ephemeris Time
Ephemeris time
The term ephemeris time can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:...
(ET). ET was an independent time-variable, proposed (and its adoption agreed) in the period 1948–52 with the intent of forming a gravitationally uniform time scale as far as was feasible at that time, and depending for its definition on Simon Newcomb
Simon Newcomb
Simon Newcomb was a Canadian-American astronomer and mathematician. Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.-Early life:Simon Newcomb was born in the town of...
's Tables of the Sun
Newcomb's Tables of the Sun
Newcomb's Tables of the Sun is the short title and running head of a work by the American astronomer and mathematician Simon Newcomb entitled "Tables of the Motion of the Earth on its Axis and Around the Sun" on pages 1–169 of "Tables of the Four Inner Planets" , volume VI of the serial publication...
(1895), interpreted in a new way to accommodate certain observed discrepancies. Newcomb's tables formed the basis of all astronomical ephemerides of the Sun from 1900 through 1983: they were originally expressed (and published) in terms of Greenwich Mean Time and the mean solar day, but later, in respect of the period 1960–1983, they were treated as expressed in terms of ET, in accordance with the adopted ET proposal of 1948–52. ET, in turn, can now be seen (in light of modern results) as close to the average mean solar time between 1750 and 1890 (centered on 1820), because that was the period during which the observations on which Newcomb's tables were based were performed. While TT is strictly uniform (being based on the SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
, every second is the same as every other second), it is in practice realised by International Atomic Time
International Atomic Time
International Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...
(TAI) 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 eclipse
Solar eclipse
As seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...
s are about +16800 s at the year −500 (501 BC), +10600 s at 0 (1 BC), +5700 s at 500 (AD), +1600 s at 1000, and +180 s at 1500. After the invention of the telescope, measurements were made by observing occultations of stars by the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
, which allowed the derivation of more closely spaced and more accurate values for ΔT. 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. It will continue to increase at an ever faster (quadratic) rate in the future. This will require the addition of an ever greater number of leap second
Leap second
A leap second is a positive or negative one-second adjustment to the Coordinated Universal Time time scale that keeps it close to mean solar time. UTC, which is used as the basis for official time-of-day radio broadcasts for civil time, is maintained using extremely precise atomic clocks...
s to UTC
Coordinated Universal Time
Coordinated Universal Time is the primary time standard by which the world regulates clocks and time. It is one of several closely related successors to Greenwich Mean Time. Computer servers, online services and other entities that rely on having a universally accepted time use UTC for that purpose...
as long as UTC is kept within one second of UT1. (The SI second as now used for UTC, when adopted, was already a little shorter than the current value of the second of mean solar time.) Physically, the meridian of Greenwich in Universal Time is almost always to the east of the meridian in Terrestrial Time, both in the past and in the future. +16800 s or 4⅔ h corresponds to 70°E. 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
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....
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 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 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
Sidereal time
Sidereal time is a time-keeping system astronomers use to keep track of the direction to point their telescopes to view a given star in the night sky...
and solar time. Its measurement by several observatories is coordinated by the International Earth Rotation and Reference Systems Service
International Earth Rotation and Reference Systems Service
The International Earth Rotation and Reference Systems Service , formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Parameter and International Celestial Reference System ...
(IERS).