# Delta T

Δ T in the period 1657 to 2018.

In astronomy, delta T ( ) is the difference between terrestrial time  (TT) and universal time  (UT), i.e. the difference between an absolutely even time scale  TT, which is realized by atomic clocks , and the time scale UT, which is determined by the actual rotation of the earth : ${\ displaystyle \ Delta T}$

${\ displaystyle \ Delta T = TT-UT}$

The current value for can be determined from the data provided by the International Earth Rotation and Reference Systems Service (IERS). At the beginning of the 21st century was about 64 seconds; by the end of this century the time difference could grow to about 204 seconds, according to other sources to about 80 seconds. Historical values ​​for can be roughly determined by comparing traditional observations with today's calculation results. There are also various polynomials derived from this data for approximate calculation. Such polynomials are also used to forecast future values. ${\ displaystyle \ Delta T}$${\ displaystyle \ Delta T}$${\ displaystyle \ Delta T}$

## background

Due to the irregularity of the earth's rotation , Universal Time (UT) is not a strictly uniform measure of time and is therefore unsuitable for calculating ephemeris , so it is not suitable, for example, for the long-term advance calculation of planetary constellations . The coordinated universal time ( Universal Time Coordinated , UTC), which is derived from atomic time , is also unsuitable, because leap seconds are inserted at irregular intervals in order to align them with Universal Time. This is why ephemeris time (ET) was introduced in 1960 , which was replaced by Terrestrial Dynamic Time (TDT) in 1984, and Terrestrial Time (TT) since 1991. In contrast to UT and UTC, TT is a strictly uniform time scale, the basic unit of TT is the second (of the International System of Units ) and a day is always exactly 86,400 seconds long.

The time of occurrence for astronomical events is therefore usually calculated in DD. In order to be able to specify the local conditions for the observation on the earth's surface, the precise current angle of rotation of the earth's rotation must be taken into account. This is necessary for solar eclipses , for example , in order to be able to indicate which places on earth are covered by the shadow. For this purpose, the calculation result in TT must be converted into UT or UTC, for which the value forecast at this point in time is to be used. ${\ displaystyle \ Delta T}$

## Current value and forecast future values

The current value for (as of July 2020) is about 69.4 s. It consists of three contributions that vary at different speeds, ${\ displaystyle \ Delta T}$

${\ displaystyle \ Delta T = (TT-TAI) + (TAI-UTC) - (UT1-UTC)}$.

The following approximation formula is used to calculate between 2015 and 3000: ${\ displaystyle \ Delta T}$

${\ displaystyle \ Delta T / \ mathrm {s} = 67 {,} 62 + 0 {,} 3645 \ cdot \ left (y-2015 \ right) +0 {,} 0039755 \ cdot \ left (y-2015 \ right) ^ {2}}$.

Here is the year of the observed date, possibly supplemented by the fraction of the year. For example, for values ​​that are accurate to the month ${\ displaystyle y}$

${\ displaystyle y = {\ text {year}} + {\ frac {{\ text {month number}} - 0 {,} 5} {12}}}$.

## Historical values

year ΔT (s) σ (s) year ΔT (s) σ (s) year ΔT (s) −1000 25400 640 1200 740 30th 1860 8th −800 22000 550 1400 320 20th 1880 −5 −600 18800 460 1600 120 20th 1900 −3 −400 15530 390 1700 9 5 1920 21st −200 12790 330 1720 11 3 1940 24 0 10580 260 1740 12 2 1960 33 +200 8640 210 1760 15th 2 1980 51 +400 6700 160 1780 17th 1 1990 57 +600 4740 120 1800 14th 1 2000 64 +800 2960 80 1820 12 1 2010 66 +1000 1570 55 1840 6th <1 2015 68

Historical values ​​for can be determined by comparing traditional observations with modern retrospective calculations. Useful observations go back to about the year −700. With the invention of the telescope at the beginning of the 17th century, the accuracy of observation increased significantly, so that from this point on it can be determined much more precisely. ${\ displaystyle \ Delta T}$${\ displaystyle \ Delta T}$

## literature

• P. Kenneth Seidelmann (Ed.): Explanatory Supplement to the Astronomical Almanac. University Science Books, Sausalito 2006, ISBN 1-891389-45-9
• F. Richard Stephenson: Historical Eclipses and Earth's Rotation. Cambridge University Press, Cambridge 1997, ISBN 0-521-46194-4