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Earth Rotation - the Change in the Length of Day and ΔT

Plot showing lod from -2000 to +2500

ΔT & lod from −2000 to +2500

This resource provides the results of the modern (updated in 2020) analysis of eclipse and occultation timings from ancient Babylonian, China, and the Arab and European worlds through early telescope observations to modern observations in the following papers:

and updated in

Download the file of FAQs to get some general information about the paper.

The analysis provides measurement of the rotation of the Earth and allows formation of the change in the length of day (lod), relative to the standard day of 86400 SI seconds, and ΔT(t), the difference (using current terminology) between TT and UT1, via a spline fit using a weighted least-squares analysis of the data.

The values of ΔT in the tables listed in the various sections should be used in conjunction with lunar ephemeris designated JPL DE430/LE430 in which the tidal acceleration of the Moon is −25.85"/cy2.

The menus below allows users to access all the data used in this Addendum 2020, which consists of both new and updated data as well the data from the original 2016 Royal Society paper.

Observational Data and Spline Polynomial Coefficients for ΔT - Version 2020

This section provides links of the various data files (ASCII) relevant to the paper. These files are also available from the data tab of the Royal Society Proceedings A website.

Tables 1-9, 12-14 are ASCII versions of the tables published in the 2016 paper, and Tables 10 v2020 and 11 v2020, are updated in the Addendum 2020, covering years BC 720 to 1605 AD. Each file table contains a few explanatory records at the end of each file.

The extract from the Lunar Occultation Archive VI/132B, (Herald+ 2012) held at by the Centre de Données Astronomiques de Strasbourg (CDS) archive covers years 1621 to 2015, and the format is described in the ReadMe file (see below).

The values of ΔT for the final three years, 2016.0 to 2019.0, are taken from the published values in The Astronomical Almanac which are from the IERS Bulletin B.

The spline approximation is provided via a set of polynomial coefficients (Table S15 v2020).

Link to FileNo. of data recordsContents
Table 01122Babylonian lunar eclipses.
Table 02 21Babylonian lunar eclipses, culmination of ziqpu star.
Table 03 25Babylonian solar eclipses.
Table 04 12Babylonian lunar eclipses in the Almagest.
Table 05 68Chinese timed lunar eclipses.
Table 06 42Chinese timed solar eclipses.
Table 07 11Greek timed lunar and solar eclipses.
Table 08 22Arab timed solar eclipses.
Table 09 32Arab timed lunar eclipses.
Table 10 v2020 48Untimed total and annular solar eclipses.
Table 11 v2020 20Untimed partial solar eclipses.
Table 12 3Untimed solar eclipses rose or set eclipsed.
Table 13 7Untimed lunar eclipses rose or set eclipsed.
Table 14 5Untimed lunar eclipses: estimates of degree of obscuration at rising or setting.
Lunar Occultations 1621-2015 201908 Extract of the lunar occultations from the CDS archive provided by Herald & Gault (2012, updated 2015 October).
ReadMe 168 ReadMe file describing the content and format of the file with the extracted lunar occultations data from the CDS file.
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Polynomials v202058Polynomial coefficients, a conversion from the spline coefficients. A pdf version of the file.
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2018 Files Updated files used in the analysis discussed in "Historical Changes in UT/lod from Eclipses, published Online in 2020 in the Proceedings of the Journees des Systemes de Reference et de la Rotation Terrestre, 2017, by Morrison, L.V., Stephenson, F.R. and Hohenkerk, C.Y..

ΔT and length of day (lod) from −2000 to −800

The values tabulated in the ΔT and lod tables have been extrapolated backwards by integration using the long term lod function

lod = +1.72 t − 3.5 sin(2π(t+0.75)/14)

between the years −800 to −2000, where t is the number of centuries from +1825.0.

Plot showing Delta T from -2000 to +1600

The resulting green-dashed line in the plot shows the extrapolated ΔT, while the continuous-black line shows the spline.

For ΔT the values are tabulated in hours every 100 years to the nearest 100 seconds.

ΔT (hours) : −2000 to −800
Error estimate ε hours
YearΔTε YearΔTε YearΔTε
−2000.0 12.8 ±0.3−1600.0 10.2 ±0.2−1200.0 8.1 ±0.2
−1900.0 12.1 ±0.3−1500.0 9.7 ±0.2−1100.0 7.6 ±0.2
−1800.0 11.4 ±0.3−1400.0 9.1 ±0.2−1000.0 7.1 ±0.2
−1700.0 10.8 ±0.3−1300.0 8.6 ±0.2− 900.0 6.6 ±0.1
−1600.0 10.2 ±0.2−1200.0 8.1 ±0.2− 800.0 6.1 ±0.1
Change in length of day (ms) : −2000 to −800
Error estimate ε = ±3 ms
Yearlod Yearlod Yearlod
−2000.0−69−1600.0−57−1200.0−50
−1900.0−66−1500.0−54−1100.0−50
−1800.0−63−1400.0−52−1000.0−49
−1700.0−60−1300.0−51− 900.0−49
−1600.0−57−1200.0−50− 800.0−48

ΔT and length of day (lod) from −720 to +1600

Plot showing observations and Delta T from -720 to +1600

The spline (continuous-black curve) that has been fitted to the observations has been tabulated, from the start at −720, then the following century years, giving both ΔT and the lod.

ΔT is given to the nearest 10 seconds together with an estimate of the errors (ε).

ΔT (s) : −720 to +1600
Error estimate ε (seconds)
YearΔTε YearΔTε YearΔTε
−720.0 +20370 ±180      0.0 +10440 ±90 +800.0 +2940 ±25
−700.0 +20050 ±170 +100.0 +9410 ±80 +900.0 +2230 ±20
−600.0 +18470 ±160 +200.0 +8420 ±70 +1000.0 +1650 ±15
−500.0 +16940 ±150 +300.0 +7480 ±60 +1100.0 +1220 ±15
−400.0 +15470 ±130 +400.0 +6540 ±50 +1200.0 +910 ±15
−300.0 +14080 ±120 +500.0 +5590 ±40 +1300.0 +680 ±15
−200.0 +12770 ±110 +600.0 +4650 ±40 +1400.0 +480 ±15
−100.0 +11560 ±100 +700.0 +3760 ±30 +1500.0 +290 ±15
      0.0 +10440 ±90 +800.0 +2940 ±25 +1600.0 +110 ±15
Change in length of day (ms) : −720 to +1600
Error estimate ε = ±3 ms
Yearlod Yearlod Yearlod
−720.0 −44.2       0.0 −29.4 +800.0 −21.1
−700.0 −43.9 +100.0 −27.5 +900.0 −17.8
−600.0 −42.6 +200.0 −26.3 +1000.0 −13.7
−500.0 −41.0 +300.0 −25.8 +1100.0 −9.9
−400.0 −39.2 +400.0 −25.9 +1200.0 −7.2
−300.0 −37.0 +500.0 −25.9 +1300.0 −5.8
−200.0 −34.6 +600.0 −25.1 +1400.0 −5.2
−100.0 −31.9 +700.0 −23.5 +1500.0 −5.3
       0.0 −29.4 +800.0 −21.1 +1600.0 −4.3

ΔT and length of day (lod) from +1600 to +1800

Plot showing observations and Delta T from 1550 to 2019

The spline (continuous-black curve) that has been fitted to the observations has been evaluated from 1600 to 1800 every 10 years, giving both ΔT and the lod.

ΔT is given to the nearest second and the lod to nearest 0.1 ms together with an estimate of their errors (ε).

ΔT (s) : +1600 to +1800
Error estimate ε (seconds)
YearΔTε YearΔTε YearΔTε
+1600.0 +109 ±15 +1670.0 +28 ±10 +1740.0 +15 ±2
+1610.0 +94 ±15 +1680.0 +22 ±5 +1750.0 +17 ±2
+1620.0 +80 ±20 +1690.0 +17 ±5 +1760.0 +19 ±2
+1630.0 +66 ±20 +1700.0 +14 ±5 +1770.0 +21 ±1
+1640.0 +54 ±20 +1710.0 +12 ±5 +1780.0 +21 ±1
+1650.0 +44 ±20 +1720.0 +12 ±5 +1790.0 +21 ±1
+1660.0 +35 ±15 +1730.0 +13 ±2 +1800.0 +18 ±0.5
+1670.0 +28 ±10 +1740.0 +15 ±2 +1810.0 +16 ±0.5
Change in length of day (ms) : +1600 to +1800
Error estimate ε (ms)
Yearlodε Yearlodε Yearlodε
+1600.0 −4.3 ±3 +1670.0 −1.8 ±2.4 +1740.0 +0.6 ±1.0
+1610.0 −4.1 ±3 +1680.0 −1.4 ±2.2 +1750.0 +0.6 ±0.8
+1620.0 −3.8 ±3 +1690.0 −1.0 ±1.9 +1760.0 +0.5 ±0.7
+1630.0 −3.4 ±3 +1700.0 −0.6 ±1.6 +1770.0 +0.3 ±0.6
+1640.0 −3.1 ±3 +1710.0 −0.3 ±1.4 +1780.0  0.0 ±0.5
+1650.0 −2.7 ±3 +1720.0 +0.1 ±1.3 +1790.0 −0.4 ±0.4
+1660.0 −2.2 ±3 +1730.0 +0.4 ±1.1 +1800.0 −1.0 ±0.3
+1670.0 −1.8 ±2 +1740.0 +0.6 ±1.0 +1810.0  0.0 ±0.3

ΔT and length of day (lod) from +1800 to +1950

The spline that has been fitted to the observations has been evaluated every year from 1800 to 1950.

ΔT is given to the nearest 0.1 seconds from 1800 to 1850 and to 0.01 seconds to 1950. The lod is tabulated to nearest 0.1 ms.

ΔT (s) : +1800 to +1950
Error estimate ε (seconds)
YearΔTε YearΔTε YearΔTε
+1800.0 +18.4±0.5 +1850.0 +9.3±0.1 +1900.0 −1.98 ±0.05
+1801.0 +18.0±0.5 +1851.0 +9.67±0.1 +1901.0 −0.75 ±0.05
+1802.0 +17.6±0.4 +1852.0 +9.98±0.1 +1902.0 +0.62 ±0.05
+1803.0 +17.3±0.4 +1853.0 +10.23±0.1 +1903.0 +2.06 ±0.05
+1804.0 +16.9±0.4 +1854.0 +10.37±0.1 +1904.0 +3.51 ±0.05
+1805.0 +16.6±0.3 +1855.0 +10.36±0.1 +1905.0 +4.92 ±0.05
+1806.0 +16.3±0.3 +1856.0 +10.18±0.1 +1906.0 +6.24 ±0.05
+1807.0 +16.0±0.3 +1857.0 +9.88±0.1 +1907.0 +7.49 ±0.05
+1808.0 +15.8±0.3 +1858.0 +9.54±0.1 +1908.0 +8.70 ±0.05
+1809.0 +15.7±0.2 +1859.0 +9.24±0.1 +1909.0 +9.90 ±0.05
+1810.0 +15.7±0.2 +1860.0 +9.04±0.1 +1910.0 +11.14 ±0.05
+1811.0 +15.7±0.2 +1861.0 +8.99±0.1 +1911.0 +12.43 ±0.05
+1812.0 +15.8±0.2 +1862.0 +9.01±0.1 +1912.0 +13.75 ±0.05
+1813.0 +16.0±0.2 +1863.0 +8.97±0.1 +1913.0 +15.06 ±0.05
+1814.0 +16.2±0.2 +1864.0 +8.76±0.1 +1914.0 +16.32 ±0.05
+1815.0 +16.4±0.2 +1865.0 +8.25±0.1 +1915.0 +17.48 ±0.05
+1816.0 +16.5±0.2 +1866.0 +7.38±0.1 +1916.0 +18.52 ±0.05
+1817.0 +16.7±0.2 +1867.0 +6.22±0.1 +1917.0 +19.44 ±0.05
+1818.0 +16.7±0.2 +1868.0 +4.92±0.1 +1918.0 +20.25 ±0.05
+1819.0 +16.7±0.2 +1869.0 +3.59±0.1 +1919.0 +20.98 ±0.05
+1820.0 +16.5±0.2 +1870.0 +2.37±0.05 +1920.0 +21.62 ±0.05
+1821.0 +16.2±0.2 +1871.0 +1.36±0.05 +1921.0 +22.19 ±0.05
+1822.0 +15.8±0.2 +1872.0 +0.56±0.05 +1922.0 +22.69 ±0.05
+1823.0 +15.3±0.2 +1873.0 −0.10±0.05 +1923.0 +23.12 ±0.05
+1824.0 +14.8±0.2 +1874.0 −0.65±0.05 +1924.0 +23.49 ±0.05
+1825.0 +14.1±0.2 +1875.0 −1.13±0.05 +1925.0 +23.79 ±0.05
+1826.0 +13.5±0.2 +1876.0 −1.58±0.05 +1926.0 +24.02 ±0.05
+1827.0 +12.8±0.2 +1877.0 −2.01±0.05 +1927.0 +24.20 ±0.05
+1828.0 +12.1±0.2 +1878.0 −2.43±0.05 +1928.0 +24.32 ±0.05
+1829.0 +11.4±0.2 +1879.0 −2.83±0.05 +1929.0 +24.39 ±0.05
+1830.0 +10.8±0.2 +1880.0 −3.21±0.05 +1930.0 +24.42 ±0.05
+1831.0 +10.2±0.1 +1881.0 −3.58±0.05 +1931.0 +24.41 ±0.05
+1832.0 +9.7±0.1 +1882.0 −3.91±0.05 +1932.0 +24.38 ±0.05
+1833.0 +9.3±0.1 +1883.0 −4.17±0.05 +1933.0 +24.32 ±0.05
+1834.0 +8.9±0.1 +1884.0 −4.34±0.05 +1934.0 +24.25 ±0.05
+1835.0 +8.5±0.1 +1885.0 −4.39±0.05 +1935.0 +24.16 ±0.05
+1836.0 +8.2±0.1 +1886.0 −4.31±0.05 +1936.0 +24.08 ±0.05
+1837.0 +8.0±0.1 +1887.0 −4.14±0.05 +1937.0 +24.04 ±0.05
+1838.0 +7.8±0.1 +1888.0 −3.97±0.05 +1938.0 +24.06 ±0.05
+1839.0 +7.7±0.1 +1889.0 −3.86±0.05 +1939.0 +24.17 ±0.05
+1840.0 +7.6±0.1 +1890.0 −3.88±0.05 +1940.0 +24.43 ±0.05
+1841.0 +7.6±0.1 +1891.0 −4.07±0.05 +1941.0 +24.83 ±0.05
+1842.0 +7.7±0.1 +1892.0 −4.37±0.05 +1942.0 +25.35 ±0.05
+1843.0 +7.7±0.1 +1893.0 −4.69±0.05 +1943.0 +25.92 ±0.05
+1844.0 +7.9±0.1 +1894.0 −4.93±0.05 +1944.0 +26.51 ±0.05
+1845.0 +8.0±0.1 +1895.0 −5.02±0.05 +1945.0 +27.05 ±0.05
+1846.0 +8.2±0.1 +1896.0 −4.87±0.05 +1946.0 +27.51 ±0.05
+1847.0 +8.5±0.1 +1897.0 −4.48±0.05 +1947.0 +27.89 ±0.05
+1848.0 +8.7±0.1 +1898.0 −3.86±0.05 +1948.0 +28.24 ±0.05
+1849.0 +9.0±0.1 +1899.0 −3.02±0.05 +1949.0 +28.58 ±0.05
+1850.0 +9.3±0.1 +1900.0 −1.98±0.05 +1950.0 +28.93 ±0.05
Change in length of day (ms) : +1800 to +1950
Error estimate ε (ms)
Yearlodε Yearlodε Yearlodε
+1800.0 −1.0 ±0.3 +1850.0 +0.9 ±0.2 +1900.0 +3.1 ±0.1
+1801.0 −1.0 ±0.3 +1851.0 +0.9 ±0.2 +1901.0 +3.6 ±0.1
+1802.0 −1.0 ±0.3 +1852.0 +0.8 ±0.2 +1902.0 +3.9 ±0.1
+1803.0 −1.0 ±0.3 +1853.0 +0.5 ±0.2 +1903.0 +4.0 ±0.1
+1804.0 −0.9 ±0.3 +1854.0 +0.2 ±0.2 +1904.0 +3.9 ±0.1
+1805.0 −0.9 ±0.3 +1855.0 −0.3 ±0.2 +1905.0 +3.7 ±0.1
+1806.0 −0.8 ±0.3 +1856.0 −0.7 ±0.2 +1906.0 +3.5 ±0.1
+1807.0 −0.6 ±0.3 +1857.0 −0.9 ±0.2 +1907.0 +3.3 ±0.1
+1808.0 −0.4 ±0.3 +1858.0 −0.9 ±0.2 +1908.0 +3.3 ±0.1
+1809.0 −0.2 ±0.3 +1859.0 −0.7 ±0.2 +1909.0 +3.3 ±0.1
+1810.0  +0.0 ±0.3 +1860.0 −0.3 ±0.2 +1910.0 +3.5 ±0.1
+1811.0 +0.2 ±0.3 +1861.0 0.0 ±0.2 +1911.0 +3.6 ±0.1
+1812.0 +0.4 ±0.3 +1862.0 0.0 ±0.2 +1912.0 +3.6 ±0.1
+1813.0 +0.5 ±0.3 +1863.0 −0.3 ±0.2 +1913.0 +3.5 ±0.1
+1814.0 +0.5 ±0.3 +1864.0 −0.9 ±0.2 +1914.0 +3.3 ±0.1
+1815.0 +0.5 ±0.3 +1865.0 −1.9 ±0.2 +1915.0 +3.0 ±0.1
+1816.0 +0.4 ±0.3 +1866.0 −2.8 ±0.2 +1916.0 +2.7 ±0.1
+1817.0 +0.2 ±0.3 +1867.0 −3.4 ±0.2 +1917.0 +2.4 ±0.1
+1818.0  0.0 ±0.3 +1868.0 −3.7 ±0.2 +1918.0 +2.1 ±0.1
+1819.0 −0.2 ±0.3 +1869.0 −3.5 ±0.2 +1919.0 +1.9 ±0.1
+1820.0 −0.6 ±0.3 +1870.0 −3.1 ±0.2 +1920.0 +1.7 ±0.1
+1821.0 −0.9 ±0.3 +1871.0 −2.5 ±0.2 +1921.0 +1.5 ±0.1
+1822.0 −1.2 ±0.3 +1872.0 −2.0 ±0.2 +1922.0 +1.3 ±0.1
+1823.0 −1.5 ±0.3 +1873.0 −1.6 ±0.2 +1923.0 +1.1 ±0.1
+1824.0 −1.7 ±0.3 +1874.0 −1.4 ±0.2 +1924.0 +0.9 ±0.1
+1825.0 −1.8 ±0.3 +1875.0 −1.3 ±0.2 +1925.0 +0.7 ±0.1
+1826.0 −1.9 ±0.3 +1876.0 −1.2 ±0.2 +1926.0 +0.6 ±0.1
+1827.0 −1.9 ±0.3 +1877.0 −1.2 ±0.2 +1927.0 +0.4 ±0.1
+1828.0 −1.9 ±0.3 +1878.0 −1.1 ±0.2 +1928.0 +0.3 ±0.1
+1829.0 −1.8 ±0.3 +1879.0 −1.1 ±0.2 +1929.0 +0.1 ±0.1
+1830.0 −1.6 ±0.2 +1880.0 −1.0 ±0.2 +1930.0  0.0 ±0.1
+1831.0 −1.5 ±0.2 +1881.0 −1.0 ±0.2 +1931.0 −0.1 ±0.1
+1832.0 −1.3 ±0.2 +1882.0 −0.8 ±0.2 +1932.0 −0.1 ±0.1
+1833.0 −1.2 ±0.2 +1883.0 −0.6 ±0.2 +1933.0 −0.2 ±0.1
+1834.0 −1.0 ±0.2 +1884.0 −0.3 ±0.2 +1934.0 −0.2 ±0.1
+1835.0 −0.9 ±0.2 +1885.0 +0.1 ±0.2 +1935.0 −0.2 ±0.1
+1836.0 −0.7 ±0.2 +1886.0 +0.4 ±0.2 +1936.0 −0.2 ±0.1
+1837.0 −0.6 ±0.2 +1887.0 +0.5 ±0.2 +1937.0 −0.1 ±0.1
+1838.0 −0.4 ±0.2 +1888.0 +0.4 ±0.2 +1938.0 +0.2 ±0.1
+1839.0 −0.3 ±0.2 +1889.0 +0.2 ±0.1 +1939.0 +0.5 ±0.1
+1840.0 −0.1 ±0.2 +1890.0 −0.3 ±0.1 +1940.0 +0.9 ±0.1
+1841.0  0.0 ±0.2 +1891.0 −0.7 ±0.1 +1941.0 +1.3 ±0.1
+1842.0 +0.2 ±0.2 +1892.0 −0.9 ±0.1 +1942.0 +1.5 ±0.1
+1843.0 +0.3 ±0.2 +1893.0 −0.8 ±0.1 +1943.0 +1.6 ±0.1
+1844.0 +0.4 ±0.2 +1894.0 −0.5 ±0.1 +1944.0 +1.6 ±0.1
+1845.0 +0.5 ±0.2 +1895.0 +0.1 ±0.1 +1945.0 +1.4 ±0.1
+1846.0 +0.6 ±0.2 +1896.0 +0.7 ±0.1 +1946.0 +1.1 ±0.1
+1847.0 +0.7 ±0.2 +1897.0 +1.4 ±0.1 +1947.0 +1.0 ±0.1
+1848.0 +0.8 ±0.2 +1898.0 +2.0 ±0.1 +1948.0 +0.9 ±0.05
+1849.0 +0.8 ±0.2 +1899.0 +2.6 ±0.1 +1949.0 +0.9 ±0.05
+1850.0 +0.9 ±0.2 +1900.0 +3.1 ±0.1 +1950.0 +1.0 ±0.05

ΔT and length of day (lod) from +1950 to +2019

The most accurate results from 1962 onwards are those derived from VLBI and other high-accuracy observations. These are available from the International Earth Rotation and Reference System Service (IERS).

The less accurate ΔT and lod listed here are evaluated from a spline fit to the occultation observations, which has the effect of smoothing out the annual and sub-annual fluctuations in the raw data. The values are tabulated at half-yearly intervals to a precision of 0.01 seconds in ΔT and 0.1 ms in lod. They agree to within ±0.05 seconds with the IERS values of ΔT. Taken together with the occultation data before 1962, the results tabulated here show the long-term trends in these Earth's rotation parameters.

ΔT (s) : +1950 to +2019
Error estimate ε: ε = ±0.05 seconds
YearΔT YearΔT YearΔT
+1950.0 +28.93 +1973.0 +43.15 +1996.0 +61.46
+1950.5 +29.12 +1973.5 +43.70 +1996.5 +61.85
+1951.0 +29.32 +1974.0 +44.24 +1997.0 +62.23
+1951.5 +29.52 +1974.5 +44.77 +1997.5 +62.58
+1952.0 +29.70 +1975.0 +45.28 +1998.0 +62.90
+1952.5 +29.86 +1975.5 +45.78 +1998.5 +63.18
+1953.0 +30.00 +1976.0 +46.28 +1999.0 +63.42
+1953.5 +30.11 +1976.5 +46.78 +1999.5 +63.63
+1954.0 +30.20 +1977.0 +47.29 +2000.0 +63.81
+1954.5 +30.30 +1977.5 +47.81 +2000.5 +63.96
+1955.0 +30.41 +1978.0 +48.33 +2001.0 +64.08
+1955.5 +30.56 +1978.5 +48.85 +2001.5 +64.18
+1956.0 +30.76 +1979.0 +49.37 +2002.0 +64.27
+1956.5 +31.03 +1979.5 +49.87 +2002.5 +64.34
+1957.0 +31.34 +1980.0 +50.36 +2003.0 +64.41
+1957.5 +31.68 +1980.5 +50.83 +2003.5 +64.48
+1958.0 +32.03 +1981.0 +51.28 +2004.0 +64.55
+1958.5 +32.36 +1981.5 +51.71 +2004.5 +64.64
+1959.0 +32.65 +1982.0 +52.13 +2005.0 +64.73
+1959.5 +32.89 +1982.5 +52.54 +2005.5 +64.83
+1960.0 +33.07 +1983.0 +52.94 +2006.0 +64.95
+1960.5 +33.23 +1983.5 +53.32 +2006.5 +65.07
+1961.0 +33.36 +1984.0 +53.70 +2007.0 +65.20
+1961.5 +33.49 +1984.5 +54.06 +2007.5 +65.33
+1962.0 +33.62 +1985.0 +54.39 +2008.0 +65.48
+1962.5 +33.78 +1985.5 +54.70 +2008.5 +65.62
+1963.0 +33.96 +1986.0 +54.98 +2009.0 +65.77
+1963.5 +34.18 +1986.5 +55.23 +2009.5 +65.92
+1964.0 +34.44 +1987.0 +55.46 +2010.0 +66.06
+1964.5 +34.74 +1987.5 +55.67 +2010.5 +66.20
+1965.0 +35.09 +1988.0 +55.89 +2011.0 +66.33
+1965.5 +35.50 +1988.5 +56.12 +2011.5 +66.47
+1966.0 +35.95 +1989.0 +56.37 +2012.0 +66.61
+1966.5 +36.43 +1989.5 +56.67 +2012.5 +66.76
+1967.0 +36.93 +1990.0 +56.99 +2013.0 +66.92
+1967.5 +37.45 +1990.5 +57.34 +2013.5 +67.09
+1968.0 +37.96 +1991.0 +57.70 +2014.0 +67.28
+1968.5 +38.46 +1991.5 +58.08 +2014.5 +67.48
+1969.0 +38.95 +1992.0 +58.45 +2015.0 +67.69
+1969.5 +39.44 +1992.5 +58.82 +2015.5 +67.90
+1970.0 +39.93 +1993.0 +59.19 +2016.0 +68.11
+1970.5 +40.43 +1993.5 +59.55 +2016.5 +68.32
+1971.0 +40.95 +1994.0 +59.92 +2017.0 +68.53
+1971.5 +41.49 +1994.5 +60.30 +2017.5 +68.73
+1972.0 +42.04 +1995.0 +60.68 +2018.0 +68.92
+1972.5 +42.59 +1995.5 +61.07 +2018.5 +69.09
+1973.0 +43.15 +1996.0 +61.46 +2019.0 +69.24
Change in length of day (ms) : +1950 to +2019
Error estimate ε = ±0.05 ms
Yearlod Yearlod Yearlod
+1950.0 +1.0 +1973.0 +3.0 +1996.0 +2.2
+1950.5 +1.1 +1973.5 +3.0 +1996.5 +2.1
+1951.0 +1.1 +1974.0 +2.9 +1997.0 +2.0
+1951.5 +1.0 +1974.5 +2.8 +1997.5 +1.8
+1952.0 +1.0 +1975.0 +2.8 +1998.0 +1.6
+1952.5 +0.8 +1975.5 +2.7 +1998.5 +1.4
+1953.0 +0.7 +1976.0 +2.7 +1999.0 +1.2
+1953.5 +0.5 +1976.5 +2.8 +1999.5 +1.1
+1954.0 +0.5 +1977.0 +2.8 +2000.0 +0.9
+1954.5 +0.5 +1977.5 +2.8 +2000.5 +0.7
+1955.0 +0.7 +1978.0 +2.9 +2001.0 +0.6
+1955.5 +0.9 +1978.5 +2.8 +2001.5 +0.5
+1956.0 +1.3 +1979.0 +2.8 +2002.0 +0.4
+1956.5 +1.6 +1979.5 +2.7 +2002.5 +0.4
+1957.0 +1.8 +1980.0 +2.6 +2003.0 +0.4
+1957.5 +1.9 +1980.5 +2.5 +2003.5 +0.4
+1958.0 +1.9 +1981.0 +2.4 +2004.0 +0.4
+1958.5 +1.7 +1981.5 +2.3 +2004.5 +0.5
+1959.0 +1.4 +1982.0 +2.3 +2005.0 +0.5
+1959.5 +1.1 +1982.5 +2.2 +2005.5 +0.6
+1960.0 +0.9 +1983.0 +2.1 +2006.0 +0.6
+1960.5 +0.8 +1983.5 +2.1 +2006.5 +0.7
+1961.0 +0.7 +1984.0 +2.0 +2007.0 +0.7
+1961.5 +0.7 +1984.5 +1.9 +2007.5 +0.8
+1962.0 +0.8 +1985.0 +1.8 +2008.0 +0.8
+1962.5 +0.9 +1985.5 +1.6 +2008.5 +0.8
+1963.0 +1.1 +1986.0 +1.4 +2009.0 +0.8
+1963.5 +1.3 +1986.5 +1.3 +2009.5 +0.8
+1964.0 +1.5 +1987.0 +1.2 +2010.0 +0.8
+1964.5 +1.8 +1987.5 +1.2 +2010.5 +0.7
+1965.0 +2.1 +1988.0 +1.2 +2011.0 +0.7
+1965.5 +2.3 +1988.5 +1.3 +2011.5 +0.8
+1966.0 +2.6 +1989.0 +1.5 +2012.0 +0.8
+1966.5 +2.7 +1989.5 +1.7 +2012.5 +0.8
+1967.0 +2.8 +1990.0 +1.9 +2013.0 +0.9
+1967.5 +2.8 +1990.5 +2.0 +2013.5 +1.0
+1968.0 +2.8 +1991.0 +2.0 +2014.0 +1.1
+1968.5 +2.7 +1991.5 +2.1 +2014.5 +1.1
+1969.0 +2.7 +1992.0 +2.0 +2015.0 +1.1
+1969.5 +2.7 +1992.5 +2.0 +2015.5 +1.2
+1970.0 +2.7 +1993.0 +2.0 +2016.0 +1.2
+1970.5 +2.8 +1993.5 +2.0 +2016.5 +1.2
+1971.0 +2.9 +1994.0 +2.0 +2017.0 +1.1
+1971.5 +3.0 +1994.5 +2.1 +2017.5 +1.1
+1972.0 +3.0 +1995.0 +2.1 +2018.0 +1.0
+1972.5 +3.1 +1995.5 +2.2 +2018.5 +0.9
+1973.0 +3.0 +1996.0 +2.2 +2019.0 +0.8

ΔT and length of day (lod) from +2020 to +2500

Plot showing Delta T from -700 to +2500

The values tabulated in the ΔT and lod tables have been extrapolated forwards (green-dashed curve). The extrapolated values for ΔT are obtained by integrating the long-term lod function

lod = +1.72 t − 3.5 sin(2π(t+0.75)/14)

where t is the number of centuries from +1825.0. This extrapolated representation of ΔT in seconds is plotted as the green-dashed curve between 2010 and 2200 in the plot below. The continuous-black curve shows the spline fit.

Plot showing Delta T from 1500 to 2200

ΔT (seconds) : +2020 to +2500
Error estimate ε (seconds)
YearΔTε YearΔTε
+2030.0 +67± 2+2200.0 +160 ±20
+2040.0 +68± 4+2300.0 +330 ±30
+2050.0 +70± 6+2400.0 +610 ±50
+2100.0 +80±10+2500.0+1000 ±100
Change in length of day (ms) : +2020 to +2500
Error estimate ε (ms)
Yearlodε Yearlodε Yearlodε
+2020.0+0.1 ±0.05+2030.0+0.2 ±1+2100.0 +1 ±2
+2040.0+0.3 ±1+2200.0 +3 ±3
+2050.0+0.5 ±1+2300.0 +6 ±3
+2400.0 +9 ±3
+2500.0+12 ±3

Evaluate ΔT and length of day (lod) from −720 to +2019.0

To be provided.

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Last modified: 2021 March 5.