EXCESS OF THE DURATION OF THE DAY TO 86400S AND ANGULAR VELOCITY OF THE EARTH'S ROTATION SINCE 1623

This table gives mean annual values of the duration of the day (its excess D to 86400 s), which are available for the last four centuries. For the interval 1623-1955, the data are those provided by L.V. Morrison, Royal Greenwich Observatory, interpolated for the middle of the year. The mean solar time has been referred to the dynamical time scale derived from the time argument of the lunar ephemeris. The duration of the day has been obtained :
  • from 1623 to 1860, by derivative of cubic splines fitted on individual values of the difference between mean solar time and dynamical time (13 knots), - from 1861 to 1955, by a 5-point quadratic convolute. More information on the computation of the duration of the day is available in Stephenson and Morrison (1984), with an estimation of the accuracy of these evaluations.

  • From 1956 up to present, the duration of the day has been obtained from the BIH/IERS values of UT1-TAI ; the table gives annual averages.

  • UT1-TT (Terrestrial Time) is computed by integration of D values.

At the level of precision of these values of the duration of the day, the unit of the dynamical time and the unit of TAI can be considered as having the same duration. Thus D is expressed in present SI units. The table gives also the values of the angular velocity of the Earth's rotation w derived from the listed values of D.

  DATE       D        w         UT1-(TT-32.184s) (from july 1955 : TT-32.184 s = TAI) 
  (years)   (ms)   (picorad/s)     (s)

                    72 921..                                                       
 1623.50   -11.00   161.00      -75.975
1624.50 -11.00 161.00 -71.957
1625.50 -10.00 160.00 -68.122
1626.50 -10.00 160.00 -64.470
1627.50 -9.00 159.00 -61.000
1628.50 -9.00 159.00 -57.712
1629.50 -8.00 158.00 -54.608
1630.50 -8.00 158.00 -51.686
1631.50 -8.00 158.00 -48.764
1632.50 -7.00 157.00 -46.024
1633.50 -7.00 157.00 -43.468
1634.50 -7.00 157.00 -40.911
1635.50 -6.00 157.00 -38.537
1636.50 -6.00 157.00 -36.345
1637.50 -6.00 157.00 -34.154
1638.50 -5.00 156.00 -32.145
1639.50 -5.00 156.00 -30.319
1640.50 -5.00 156.00 -28.492
1641.50 -4.00 155.00 -26.849
1642.50 -4.00 155.00 -25.388
1643.50 -4.00 155.00 -23.927
1644.50 -4.00 155.00 -22.466
1645.50 -4.00 155.00 -21.005
1646.50 -3.00 154.00 -19.726
1647.50 -3.00 154.00 -18.631
1648.50 -3.00 154.00 -17.535
1649.50 -3.00 154.00 -16.439
1650.50 -3.00 154.00 -15.343
1651.50 -3.00 154.00 -14.248
1652.50 -3.00 154.00 -13.152
1653.50 -3.00 154.00 -12.056
1654.50 -3.00 154.00 -10.960
1655.50 -3.00 154.00 -9.865
1656.50 -3.00 154.00 -8.769
1657.50 -3.00 154.00 -7.673
1658.50 -3.00 154.00 -6.577
1659.50 -3.00 154.00 -5.482
1660.50 -3.00 154.00 -4.386
1661.50 -3.00 154.00 -3.290
1662.50 -3.00 154.00 -2.194
1663.50 -3.00 154.00 -1.099
1664.50 -3.00 154.00 -0.003
1665.50 -3.00 154.00 1.093
1666.50 -3.00 154.00 2.189
1667.50 -3.00 154.00 3.284
1668.50 -3.00 154.00 4.380
1669.50 -3.00 154.00 5.476
1670.50 -3.00 154.00 6.572
1671.50 -3.00 154.00 7.667
1672.50 -3.00 154.00 8.763
1673.50 -3.00 154.00 9.859
1674.50 -3.00 154.00 10.955
1675.50 -3.00 154.00 12.050
1676.50 -3.00 154.00 13.146
1677.50 -3.00 154.00 14.242
1678.50 -3.00 154.00 15.338
1679.50 -2.00 153.00 16.251
1680.50 -2.00 153.00 16.981
1681.50 -2.00 153.00 17.712
1682.50 -2.00 153.00 18.442
1683.50 -2.00 153.00 19.173
1684.50 -2.00 153.00 19.903
1685.50 -2.00 153.00 20.634
1686.50 -1.00 152.00 21.182
1687.50 -1.00 152.00 21.547
1688.50 -1.00 152.00 21.912
1689.50 -1.00 152.00 22.277
1690.50 -1.00 152.00 22.643
1691.50 -1.00 152.00 23.008
1692.50 -1.00 152.00 23.373
1693.50 0.00 151.00 23.556
1694.50 0.00 151.00 23.556
1695.50 0.00 151.00 23.556
1696.50 0.00 151.00 23.556
1697.50 0.00 151.00 23.556
1698.50 0.00 151.00 23.556
1699.50 0.00 151.00 23.556
1700.50 0.10 151.40 23.537
1701.50 0.20 151.30 23.483
1702.50 0.20 151.30 23.410
1703.50 0.30 151.20 23.318
1704.50 0.30 151.20 23.209
1705.50 0.30 151.20 23.099
1706.50 0.30 151.20 22.989
1707.50 0.30 151.20 22.880
1708.50 0.40 151.10 22.752
1709.50 0.30 151.20 22.624
1710.50 0.30 151.20 22.515
1711.50 0.30 151.20 22.405
1712.50 0.30 151.20 22.296
1713.50 0.30 151.20 22.186
1714.50 0.30 151.20 22.076
1715.50 0.20 151.30 21.985
1716.50 0.20 151.30 21.912
1717.50 0.20 151.30 21.839
1718.50 0.20 151.30 21.766
1719.50 0.20 151.30 21.693
1720.50 0.20 151.30 21.620
1721.50 0.20 151.30 21.547
1722.50 0.20 151.30 21.474
1723.50 0.10 151.40 21.419
1724.50 0.10 151.40 21.382
1725.50 0.10 151.40 21.346
1726.50 0.10 151.40 21.309
1727.50 0.10 151.40 21.273
1728.50 0.20 151.30 21.218
1729.50 0.20 151.30 21.145
1730.50 0.20 151.30 21.072
1731.50 0.20 151.30 20.999
1732.50 0.20 151.30 20.926
1733.50 0.20 151.30 20.853
1734.50 0.20 151.30 20.780
1735.50 0.20 151.30 20.707
1736.50 0.30 151.20 20.615
1737.50 0.30 151.20 20.506
1738.50 0.30 151.20 20.396
1739.50 0.30 151.20 20.287
1740.50 0.30 151.20 20.177
1741.50 0.30 151.20 20.067
1742.50 0.30 151.20 19.958
1743.50 0.40 151.10 19.830
1744.50 0.40 151.10 19.684
1745.50 0.40 151.10 19.538
1746.50 0.40 151.10 19.392
1747.50 0.40 151.10 19.246
1748.50 0.40 151.10 19.100
1749.50 0.40 151.10 18.953
1750.50 0.40 151.10 18.807
1751.50 0.40 151.10 18.661
1752.50 0.40 151.10 18.515
1753.50 0.40 151.10 18.369
1754.50 0.40 151.10 18.223
1755.50 0.40 151.10 18.077
1756.50 0.40 151.10 17.931
1757.50 0.40 151.10 17.785
1758.50 0.40 151.10 17.639
1759.50 0.40 151.10 17.492
1760.50 0.40 151.10 17.346
1761.50 0.40 151.10 17.200
1762.50 0.30 151.20 17.072
1763.50 0.30 151.20 16.963
1764.50 0.30 151.20 16.853
1765.50 0.30 151.20 16.744
1766.50 0.30 151.20 16.634
1767.50 0.30 151.20 16.525
1768.50 0.30 151.20 16.415
1769.50 0.30 151.20 16.305
1770.50 0.30 151.20 16.196
1771.50 0.30 151.20 16.086
1772.50 0.20 151.30 15.995
1773.50 0.20 151.30 15.922
1774.50 0.20 151.30 15.849
1775.50 0.20 151.30 15.776
1776.50 0.20 151.30 15.703
1777.50 0.20 151.30 15.630
1778.50 0.20 151.30 15.557
1779.50 0.20 151.30 15.484
1780.50 0.20 151.30 15.411
1781.50 0.20 151.30 15.337
1782.50 0.10 151.40 15.283
1783.50 0.10 151.40 15.246
1784.50 0.10 151.40 15.210
1785.50 0.00 151.50 15.191
1786.50 0.00 151.50 15.191
1787.50 -0.10 151.60 15.210
1788.50 -0.20 151.60 15.264
1789.50 -0.30 151.70 15.356
1790.50 -0.50 151.90 15.502
1791.50 -0.60 152.00 15.703
1792.50 -0.70 152.10 15.940
1793.50 -0.90 152.20 16.232
1794.50 -0.90 152.20 16.561
1795.50 -1.00 152.30 16.908
1796.50 -1.00 152.30 17.273
1797.50 -1.00 152.30 17.639
1798.50 -1.00 152.30 18.004
1799.50 -1.00 152.30 18.369
1800.50 -0.87 152.20 18.711
1801.50 -0.75 152.10 19.006
1802.50 -0.61 151.98 19.255
1803.50 -0.46 151.86 19.450
1804.50 -0.34 151.75 19.596
1805.50 -0.23 151.66 19.700
1806.50 -0.14 151.59 19.768
1807.50 -0.06 151.52 19.805
1808.50 -0.01 151.48 19.817
1809.50 0.03 151.44 19.814
1810.50 0.05 151.42 19.799
1811.50 0.05 151.42 19.781
1812.50 0.04 151.43 19.764
1813.50 0.01 151.46 19.755
1814.50 -0.04 151.50 19.761
1815.50 -0.11 151.56 19.788
1816.50 -0.18 151.62 19.841
1817.50 -0.28 151.70 19.925
1818.50 -0.39 151.80 20.047
1819.50 -0.51 151.90 20.212
1820.50 -0.65 152.02 20.424
1821.50 -0.81 152.15 20.690
1822.50 -0.99 152.30 21.019
1823.50 -1.16 152.45 21.412
1824.50 -1.32 152.58 21.865
1825.50 -1.42 152.67 22.365
1826.50 -1.49 152.72 22.896
1827.50 -1.50 152.73 23.442
1828.50 -1.48 152.72 23.987
1829.50 -1.41 152.66 24.514
1830.50 -1.30 152.56 25.009
1831.50 -1.14 152.43 25.455
1832.50 -0.94 152.26 25.835
1833.50 -0.73 152.08 26.140
1834.50 -0.52 151.91 26.368
1835.50 -0.34 151.75 26.525
1836.50 -0.18 151.62 26.620
1837.50 -0.04 151.50 26.660
1838.50 0.09 151.39 26.651
1839.50 0.19 151.31 26.600
1840.50 0.27 151.24 26.516
1841.50 0.33 151.19 26.406
1842.50 0.37 151.15 26.279
1843.50 0.39 151.14 26.140
1844.50 0.40 151.13 25.995
1845.50 0.41 151.12 25.848
1846.50 0.41 151.12 25.698
1847.50 0.40 151.13 25.550
1848.50 0.39 151.14 25.406
1849.50 0.38 151.15 25.265
1850.50 0.36 151.16 25.130
1851.50 0.33 151.19 25.004
1852.50 0.30 151.21 24.889
1853.50 0.26 151.25 24.787
1854.50 0.23 151.27 24.697
1855.50 0.20 151.30 24.619
1856.50 0.17 151.32 24.551
1857.50 0.15 151.34 24.492
1858.50 0.11 151.37 24.445
1859.50 -0.02 151.48 24.429
1860.50 -0.34 151.75 24.494
1861.50 -0.81 152.15 24.704
1862.50 -1.19 152.47 25.070
1863.50 -1.35 152.61 25.533
1864.50 -1.61 152.83 26.074
1865.50 -2.13 153.26 26.757
1866.50 -2.76 153.80 27.650
1867.50 -2.89 153.91 28.682
1868.50 -2.60 153.66 29.685
1869.50 -2.59 153.65 30.632
1870.50 -2.51 153.59 31.564
1871.50 -2.59 153.65 32.495
1872.50 -2.55 153.62 33.434
1873.50 -2.10 153.24 34.283
1874.50 -2.03 153.18 35.037
1875.50 -1.77 152.96 35.731
1876.50 -1.37 152.62 36.305
1877.50 -1.24 152.51 36.781
1878.50 -0.90 152.23 37.172
1879.50 -0.49 151.88 37.426
1880.50 -0.23 151.66 37.557
1881.50 -0.06 151.52 37.610
1882.50 -0.15 151.59 37.649
1883.50 -0.33 151.75 37.736
1884.50 -0.24 151.67 37.841
1885.50 -0.15 151.59 37.912
1886.50 -0.05 151.51 37.948
1887.50 -0.04 151.50 37.965
1888.50 -0.18 151.62 38.005
1889.50 -0.25 151.68 38.083
1890.50 -0.48 151.87 38.217
1891.50 -0.58 151.96 38.410
1892.50 -0.42 151.82 38.593
1893.50 -0.13 151.58 38.693
1894.50 0.33 151.19 38.657
1895.50 0.86 150.74 38.440
1896.50 1.53 150.18 38.003
1897.50 2.16 149.64 37.329
1898.50 2.64 149.24 36.453
1899.50 3.00 148.94 35.423
1900.50 3.31 148.67 34.270
1901.50 3.60 148.43 33.008
1902.50 3.70 148.34 31.675
1903.50 3.69 148.35 30.326
1904.50 3.55 148.47 29.003
1905.50 3.40 148.60 27.734
1906.50 3.48 148.53 26.478
1907.50 3.57 148.45 25.190
1908.50 3.65 148.39 23.872
1909.50 3.71 148.34 22.527
1910.50 3.77 148.29 21.161
1911.50 3.86 148.21 19.768
1912.50 3.89 148.18 18.353
1913.50 3.62 148.41 16.981
1914.50 3.18 148.78 15.739
1915.50 2.92 149.00 14.625
1916.50 2.74 149.15 13.592
1917.50 2.35 149.48 12.662
1918.50 2.05 149.74 11.858
1919.50 1.76 149.98 11.163
1920.50 1.48 150.22 10.571
1921.50 1.51 150.19 10.025
1922.50 1.28 150.39 9.515
1923.50 0.98 150.64 9.103
1924.50 0.93 150.68 8.754
1925.50 0.81 150.78 8.436
1926.50 0.56 150.99 8.186
1927.50 0.18 151.32 8.051
1928.50 -0.22 151.65 8.058
1929.50 -0.35 151.76 8.162
1930.50 -0.19 151.63 8.261
1931.50 -0.10 151.55 8.314
1932.50 -0.07 151.53 8.345
1933.50 -0.06 151.52 8.369
1934.50 -0.08 151.53 8.394
1935.50 0.00 151.47 8.409
1936.50 0.08 151.40 8.394
1937.50 0.22 151.28 8.339
1938.50 0.47 151.07 8.213
1939.50 0.78 150.81 7.985
1940.50 1.09 150.55 7.644
1941.50 1.25 150.41 7.216
1942.50 1.31 150.36 6.749
1943.50 1.35 150.33 6.263
1944.50 1.41 150.28 5.759
1945.50 1.41 150.28 5.244
1946.50 1.35 150.33 4.740
1947.50 1.30 150.37 4.256
1948.50 1.25 150.41 3.790
1949.50 1.20 150.45 3.343
1950.50 1.15 150.50 2.914
1951.50 1.10 150.54 2.503
1952.50 1.05 150.58 2.110
1953.50 0.99 150.63 1.737
1954.50 0.92 150.69 1.389
1955.50 0.86 150.74 1.064
1956.50 0.89 150.72 0.744
1957.50 1.34 150.34 0.337
1958.50 1.37 150.31 -0.158
1959.50 1.31 150.36 -0.648
1960.50 1.19 150.46 -1.104
1961.50 1.09 150.55 -1.521
1962.50 1.30 150.37 -1.957
1963.50 1.54 150.17 -2.476
1964.50 1.92 149.85 -3.108
1965.50 2.21 149.60 -3.862
1966.50 2.41 149.43 -4.706
1967.50 2.37 149.47 -5.579
1968.50 2.48 149.37 -6.464
1969.50 2.67 149.21 -7.405
1970.50 2.71 149.18 -8.387
1971.50 2.90 149.02 -9.412
1972.50 3.13 148.83 -10.513
1973.50 3.05 148.89 -11.642
1974.50 2.72 149.17 -12.695
1975.50 2.69 149.20 -13.683
1976.50 2.91 149.01 -14.706
1977.50 2.77 149.13 -15.743
1978.50 2.88 149.04 -16.775
1979.50 2.61 149.26 -17.778
1980.50 2.30 149.53 -18.675
1981.50 2.16 149.64 -19.489
1982.50 2.16 149.64 -20.278
1983.50 2.28 149.54 -21.089
1984.50 1.52 150.18 -21.783
1985.50 1.45 150.24 -22.325
1986.50 1.23 150.43 -22.815
1987.50 1.36 150.32 -23.288
1988.50 1.32 150.35 -23.777
1989.50 1.53 150.18 -24.298
1990.50 1.94 149.83 -24.931
1991.50 2.04 149.75 -25.658
1992.50 2.22 149.59 -26.436
1993.50 2.37 149.47 -27.274
1994.50 2.17 149.64 -28.104
1995.50 2.31 149.52 -28.922
1996.50 1.83 149.92 -29.678
1997.50 1.84 149.91 -30.348
1998.50 1.37 150.31 -30.934
1999.50 0.99 150.63 -31.365
2000.50 0.72 150.86 -31.796 2001.50 0.57 150.99 -32.028 2002.50 0.47 151.07 -32.230 2003.50 0.27 151.24 -32.366 2004.50 0.32 151.20 -32.469 2005.50 0.43 151.10 -32.615

Longterm variation in lenght of day from 1623 to 2000 
(reference value is 86400s TAI)