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 first contribution, the difference between TT and the International Atomic Time TAI, has a constant value of 32.184 seconds.
• The second contribution, the difference between TAI and Coordinated Universal Time UTC, corresponds to the number of leap seconds previously inserted at UTC (since January 1, 2017 37 seconds, as of July 2020).
• The last contribution, the difference between the UT1 variant of Universal Time and UTC, which takes into account the polar fluctuations , varies quickly, but its amount always remains less than 0.9 s. He is one of the Earth rotation parameters , by the International Earth Rotation and Reference Systems Service are published (IERS) in its bulletin A and B.

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 ${\displaystyle y}$

${\displaystyle y={\text{Jahreszahl}}+{\frac {{\text{Monatsnummer}}-0{,}5}{12}}}$.

Historical values

Historical values ​​of ΔT and their uncertainty σ

year	ΔT (s)	σ (s)		year	ΔT (s)	σ (s)		year	ΔT (s)	σ (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

Web links

• IERS bulletins. (English, Bulletin A contains, among other things, the value of TT − TAI, the current values ​​of TAI − UTC and UT1 − UTC as well as a forecast of UT1 − UTC for the next 12 months; is published weekly.). 
• Time scales. IERS (English, query of current and previous values ​​from UT1 − UTC). 
• F. Richard Stephenson: Historical eclipses and Earth's rotation. ( Memento from August 16, 2012) Harold Jeffreys Lecture 2002 (PDF; 243 kB)
• Fred Espenak: Delta T (ΔT) and Universal Time
• RH van Gent: Delta T: Terrestrial Time, Universal Time and Algorithms for Historical Periods
• FR Stephenson, LV Morrison, CY Hohenkerk: Measurement of the Earth's Rotation: 720 BC to AD 2015. Proceedings of the Royal Society A, volume 472, issue 2196 (Dec. 2016) ( HTML , PDF; 1.4 MB ), doi : 10.1098 / rspa.2016.0404

Individual evidence

1. ↑ NASA: Five Millennium Catalog of Solar Eclipses (2001 to 2100) and CalSky [1] there, note the links in the text deltaT values ​​used in CalSky: 1500–2300, -2000-3000, and length of day LOD values .
2. ^ Jean Meeus: The Effect of Delta T on Astronomical Calculations. In: Journal of the British Astronomical Association. 108: 154-156, 1998 ( bibcode : 1998JBAA..108..154M ).
3. ↑ Time scales. IERS , accessed on July 13, 2020 . 
4. ^ IERS Bulletins. Retrieved July 13, 2020 . 
5. ↑ Fred Espenak: polynomial expression for delta T .
6. ^ Morrison LV, Stephenson FR: Historical values ​​of the Earth's clock error ΔT and the calculation of eclipses. Journal for the History of Astronomy, Vol. 35, Part 3, No. 120, pp. 327-336 (2004) ( bibcode : 2004JHA .... 35..327M ); same: Addendum: Historical values ​​of the Earth's clock error. JHA, Vol. 36, Part 3, No. 124, p. 339 (2005) ( bibcode : 2005JHA .... 36..339M ).
7. ^ IERS Rapid Service / Prediction Center ( [2] ).