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Excess of the duration of the day to 86400 s and angular velocity of the earth's rotation, since 1623

This table gives mean annual values of the duration of the day D, 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. 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
(years)
D
(ms)
[[omega]]
(prad/s)
DATE
(years)
D
(ms)
[[omega]]
(prad/s)
DATE
(years)
D
(ms)
[[omega]]
(prad/s)




1623.5
1624.5
1625.5
1626.5
1627.5
1628.5
1629.5
1630.5




-11.
-11.
-10.
-10.
-9.
-9.
-8.
-8.
72 921..



161.
161.
160.
160.
159.
159.
158.
158.


1671.5
1672.5
1673.5
1674.5
1675.5
1676.5
1677.5
1678.5
1679.5
1680.5


-3.
-3.
-3.
-3.
-3.
-3.
-3.
-3.
-2.
-2.
72 921..

154.
154.
154.
154.
154.
154.
154.
154.
153.
153.


1721.5
1722.5
1723.5
1724.5
1725.5
1726.5
1727.5
1728.5
1729.5
1730.5


0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
72 921..

151.3
151.3
151.4
151.4
151.4
151.4
151.4
151.3
151.3
151.3
1631.5
1632.5
1633.5
1634.5
1635.5
1636.5
1637.5
1638.5
1639.5
1640.5
-8.
-7.
-7.
-7.
-6.
-6.
-6.
-5.
-5.
-5.
158.
157.
157.
157.
157.
157.
157.
156.
156.
156.
1681.5
1682.5
1683.5
1684.5
1685.5
1686.5
1687.5
1688.5
1689.5
1690.5
-2.
-2.
-2.
-2.
-2.
-1.
-1.
-1.
-1.
-1.
153.
153.
153.
153.
153.
152.
152.
152.
152.
152.
1731.5
1732.5
1733.5
1734.5
1735.5
1736.5
1737.5
1738.5
1739.5
1740.5
0.2
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.3
151.3
151.3
151.3
151.3
151.3
151.2
151.2
151.2
151.2
151.2
1641.5
1642.5
1643.5
1644.5
1645.5
1646.5
1647.5
1648.5
1649.5
1650.5
-4.
-4.
-4.
-4.
-4.
-3.
-3.
-3.
-3.
-3.
155.
155.
155.
155.
155.
154.
154.
154.
154.
154.
1691.5
1692.5
1693.5
1694.5
1695.5
1696.5
1697.5
1698.5
1699.5
1700.5
-1.
-1.
0.
0.
0.
0.
0.
0.
0.
0.1
152.
152.
151.
151.
151.
151.
151.
151.
151.
151.4
1741.5
1742.5
1743.5
1744.5
1745.5
1746.5
1747.5
1748.5
1749.5
1750.5
0.3
0.3
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
151.2
151.2
151.1
151.1
151.1
151.1
151.1
151.1
151.1
151.1
1651.5
1652.5
1653.5
1654.5
1655.5
1656.5
1657.5
1658.5
1659.5
1660.5
-3.
-3.
-3.
-3.
-3.
-3.
-3.
-3.
-3.
-3.
154.
154.
154.
154.
154.
154.
154.
154.
154.
154.
1701.5
1702.5
1703.5
1704.5
1705.5
1706.5
1707.5
1708.5
1709.5
1710.5
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.4
0.3
0.3
151.3
151.3
151.2
151.2
151.2
151.2
151.2
151.1
151.2
151.2
1751.5
1752.5
1753.5
1754.5
1755.5
1756.5
1757.5
1758.5
1759.5
1760.5
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
151.1
151.1
151.1
151.1
151.1
151.1
151.1
151.1
151.1
151.1
1661.5
1662.5
1663.5
1664.5
1665.5
1666.5
1667.5
1668.5
1669.5
1670.5
-3.
-3.
-3.
-3.
-3.
-3.
-3.
-3.
-3.
-3.
154.
154.
154.
154.
154.
154.
154.
154.
154.
154.
1711.5
1712.5
1713.5
1714.5
1715.5
1716.5
1717.5
1718.5
1719.5
1720.5
0.3
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.2
151.2
151.2
151.2
151.2
151.3
151.3
151.3
151.3
151.3
151.3
1761.5
1762.5
1763.5
1764.5
1765.5
1766.5
1767.5
1768.5
1769.5
1770.5
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
151.1
151.2
151.2
151.2
151.2
151.2
151.2
151.2
151.2
151.2
1771.5
1772.5
1773.5
1774.5
1775.5
1776.5
1777.5
1778.5
1779.5
1780.5
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
151.2
151.3
151.3
151.3
151.3
151.3
151.3
151.3
151.3
151.3
1821.5
1822.5
1823.5
1824.5
1825.5
1826.5
1827.5
1828.5
1829.5
1830.5
-0.81
-0.99
-1.16
-1.32
-1.42
-1.49
-1.50
-1.48
-1.41
-1.30
152.15
152.30
152.45
152.58
152.67
152.72
152.73
152.72
152.66
152.56
1871.5
1872.5
1873.5
1874.5
1875.5
1876.5
1877.5
1878.5
1879.5
1880.5
-2.59
-2.55
-2.10
-2.03
-1.77
-1.37
-1.24
-0.90
-0.49
-0.23
153.65
153.62
153.24
153.18
152.96
152.62
152.51
152.23
151.88
151.66
1781.5
1782.5
1783.5
1784.5
1785.5
1786.5
1787.5
1788.5
1789.5
1790.5
0.2
0.1
0.1
0.1
0.0
0.0
-0.1
-0.2
-0.3
-0.5
151.3
151.4
151.4
151.4
151.5
151.5
151.6
151.6
151.7
151.9
1831.5
1832.5
1833.5
1834.5
1835.5
1836.5
1837.5
1838.5
1839.5
1840.5
-1.14
-0.94
-0.73
-0.52
-0.34
-0.18
-0.04
0.09
0.19
0.27
152.43
152.26
152.08
151.91
151.75
151.62
151.50
151.39
151.31
151.24
1881.5
1882.5
1883.5
1884.5
1885.5
1886.5
1887.5
1888.5
1889.5
1890.5
-0.06
-0.15
-0.33
-0.24
-0.15
-0.05
-0.04
-0.18
-0.25
-0.48
151.52
151.59
151.75
151.67
151.59
151.51
151.50
151.62
151.68
151.87
1791.5
1792.5
1793.5
1794.5
1795.5
1796.5
1797.5
1798.5
1799.5
1800.5
-0.6
-0.7
-0.9
-0.9
-1.0
-1.0
-1.0
-1.0
-1.0
-0.87
152.0
152.1
152.2
152.2
152.3
152.3
152.3
152.3
152.3
152.20
1841.5
1842.5
1843.5
1844.5
1845.5
1846.5
1847.5
1848.5
1849.5
1850.5
0.33
0.37
0.39
0.40
0.41
0.41
0.40
0.39
0.38
0.36
151.19
151.15
151.14
151.13
151.12
151.12
151.13
151.14
151.15
151.16
1891.5
1892.5
1893.5
1894.5
1895.5
1896.5
1897.5
1898.5
1899.5
1900.5
-0.58
-0.42
-0.13
0.33
0.86
1.53
2.16
2.64
3.00
3.31
151.96
151.82
151.58
151.19
150.74
150.18
149.64
149.24
148.94
148.67
1801.5
1802.5
1803.5
1804.5
1805.5
1806.5
1807.5
1808.5
1809.5
1810.5
-0.75
-0.61
-0.46
-0.34
-0.23
-0.14
-0.06
-0.01
0.03
0.05
152.10
151.98
151.86
151.75
151.66
151.59
151.52
151.48
151.44
151.42
1851.5
1852.5
1853.5
1854.5
1855.5
1856.5
1857.5
1858.5
1859.5
1860.5
0.33
0.30
0.26
0.23
0.20
0.17
0.15
0.11
-0.02
-0.34
151.19
151.21
151.25
151.27
151.30
151.32
151.34
151.37
151.48
151.75
1901.5
1902.5
1903.5
1904.5
1905.5
1906.5
1907.5
1908.5
1909.5
1910.5
3.60
3.70
3.69
3.55
3.40
3.48
3.57
3.65
3.71
3.77
148.43
148.34
148.35
148.47
148.60
148.53
148.45
148.39
148.34
148.29
1811.5
1812.5
1813.5
1814.5
1815.5
1816.5
1817.5
1818.5
1819.5
1820.5
0.05
0.04
0.01
-0.04
-0.11
-0.18
-0.28
-0.39
-0.51
-0.65
151.42
151.43
151.46
151.50
151.56
151.62
151.70
151.80
151.90
152.02
1861.5
1862.5
1863.5
1864.5
1865.5
1866.5
1867.5
1868.5
1869.5
1870.5
-0.81
-1.19
-1.35
-1.61
-2.13
-2.76
-2.89
-2.60
-2.59
-2.51
152.15
152.47
152.61
152.83
153.26
153.80
153.91
153.66
153.65
153.59
1911.5
1912.5
1913.5
1914.5
1915.5
1916.5
1917.5
1918.5
1919.5
1920.5
3.86
3.89
3.62
3.18
2.92
2.74
2.35
2.05
1.76
1.48
148.21
148.18
148.41
148.78
149.00
149.15
149.48
149.74
149.98
150.22
1921.5
1922.5
1923.5
1924.5
1925.5
1926.5
1927.5
1928.5
1929.5
1930.5
1.51
1.28
0.98
0.93
0.81
0.56
0.18
-0.22
-0.35
-0.19
150.19
150.39
150.64
150.68
150.78
150.99
151.32
151.65
151.76
151.63
1971.5
1972.5
1973.5
1974.5
1975.5
1976.5
1977.5
1978.5
1979.5
1980.5
2.90
3.13
3.05
2.72
2.69
2.91
2.77
2.88
2.61
2.30
149.02
148.83
148.89
149.17
149.20
149.01
149.13
149.04
149.26
149.53
1931.5
1932.5
1933.5
1934.5
1935.5
1936.5
1937.5
1938.5
1939.5
1940.5
-0.10
-0.07
-0.06
-0.08
0.00
0.08
0.22
0.47
0.78
1.09
151.55
151.53
151.52
151.53
151.47
151.40
151.28
151.07
150.81
150.55
1981.5
1982.5
1983.5
1984.5
1985.5
1986.5
1987.5
1988.5
1989.5
1990.5
2.16
2.16
2.28
1.52
1.45
1.23
1.36
1.32
1.53
1.94
149.64
149.64
149.54
150.18
150.24
150.43
150.32
150.35
150.18
149.83
1941.5
1942.5
1943.5
1944.5
1945.5
1946.5
1947.5
1948.5
1949.5
1950.5
1.25
1.31
1.35
1.41
1.41
1.35
1.30
1.25
1.20
1.15
150.41
150.36
150.33
150.28
150.28
150.33
150.37
150.41
150.45
150.50
1991.5
1992.5
1993.5
1994.5
1995.5
1996.5
1997.5
1998.5
1999.5
2000.5
2.04
2.22
2.37
2.17
2.31
1.83
1.84
1.37
0.99
0.72
149.75
149.59
149.47
149.64
149.52
149.92
149.91
150.31
150.63
150.86
1951.5
1952.5
1953.5
1954.5
1955.5
1956.5
1957.5
1958.5
1959.5
1960.5
1.10
1.05
0.99
0.92
0.86
0.89
1.34
1.37
1.31
1.19
150.54
150.58
150.63
150.69
150.74
150.72
150.34
150.31
150.36
150.46
2001.5
2002.5
2003.5
2004.5
2005.5
2006.5
2007.5
2008.5
0.57
0.47
0.27
0.32
0.43
0.82
0.85
0.87
151.52
151.60
151.77
151.20
151.64
151.31
151.28
151.27
1961.5
1962.5
1963.5
1964.5
1965.5
1966.5
1967.5
1968.5
1969.5
1970.5
1.09
1.30
1.54
1.92
2.21
2.41
2.37
2.48
2.67
2.71
150.55
150.37
150.17
149.85
149.60
149.43
149.47
149.37
149.21
149.18
Table provided by the IERS Earth Orientation Centre. The original table is available here.

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