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time |
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package Astro::Montenbruck::Time::DeltaT; |
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137810
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use strict; |
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use warnings; |
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use Exporter qw/import/; |
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400
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use Readonly; |
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3138
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use Astro::Montenbruck::Time qw/cal2jd jd2cal/; |
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use Astro::Montenbruck::MathUtils qw/polynome/; |
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511
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our @EXPORT_OK = qw/delta_t/; |
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our $VERSION = 0.01; |
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Readonly::Hash our %HISTORICAL => ( |
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# From J.Meeus, Astronomical Algorithms, 2 edition |
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1620 => 121.0, |
18
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1622 => 112.0, |
19
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1624 => 103.0, |
20
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1626 => 95.0, |
21
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1628 => 88.0, |
22
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1630 => 82.0, |
23
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1632 => 77.0, |
24
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1634 => 72.0, |
25
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1636 => 68.0, |
26
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1638 => 63.0, |
27
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1640 => 60.0, |
28
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1642 => 56.0, |
29
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1644 => 53.0, |
30
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1646 => 51.0, |
31
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1648 => 48.0, |
32
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1650 => 46.0, |
33
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1652 => 44.0, |
34
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1654 => 42.0, |
35
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1656 => 40.0, |
36
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1658 => 38.0, |
37
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1660 => 35.0, |
38
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1662 => 33.0, |
39
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1664 => 31.0, |
40
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1666 => 29.0, |
41
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1668 => 26.0, |
42
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1670 => 24.0, |
43
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1672 => 22.0, |
44
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1674 => 20.0, |
45
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1676 => 19.0, |
46
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1678 => 16.0, |
47
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1680 => 14.0, |
48
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1682 => 12.0, |
49
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1684 => 11.0, |
50
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1686 => 10.0, |
51
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1688 => 9.0, |
52
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1690 => 8.0, |
53
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1692 => 7.0, |
54
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1694 => 7.0, |
55
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1696 => 7.0, |
56
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1698 => 7.0, |
57
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1700 => 7.0, |
58
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1702 => 7.0, |
59
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1704 => 8.0, |
60
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1706 => 8.0, |
61
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1708 => 9.0, |
62
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1710 => 9.0, |
63
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1712 => 9.0, |
64
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1714 => 9.0, |
65
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1716 => 9.0, |
66
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1718 => 10.0, |
67
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1720 => 10.0, |
68
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1722 => 10.0, |
69
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1724 => 10.0, |
70
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1726 => 10.0, |
71
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1728 => 10.0, |
72
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1730 => 10.0, |
73
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1732 => 10.0, |
74
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1734 => 11.0, |
75
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1736 => 11.0, |
76
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1738 => 11.0, |
77
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1740 => 11.0, |
78
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1742 => 11.0, |
79
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1744 => 12.0, |
80
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1746 => 12.0, |
81
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1748 => 12.0, |
82
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1750 => 12.0, |
83
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1752 => 13.0, |
84
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1754 => 13.0, |
85
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1756 => 13.0, |
86
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1758 => 14.0, |
87
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1760 => 14.0, |
88
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1762 => 14.0, |
89
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1764 => 14.0, |
90
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1766 => 15.0, |
91
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1768 => 15.0, |
92
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1770 => 15.0, |
93
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1772 => 15.0, |
94
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1774 => 15.0, |
95
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1776 => 16.0, |
96
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1778 => 16.0, |
97
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1780 => 16.0, |
98
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1782 => 16.0, |
99
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1784 => 16.0, |
100
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1786 => 16.0, |
101
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1788 => 16.0, |
102
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1790 => 16.0, |
103
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1792 => 15.0, |
104
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1794 => 15.0, |
105
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1796 => 14.0, |
106
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1798 => 13.0, |
107
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1800 => 13.1, |
108
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1802 => 12.5, |
109
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1804 => 12.2, |
110
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1806 => 12.0, |
111
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1808 => 12.0, |
112
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1810 => 12.0, |
113
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1812 => 12.0, |
114
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1814 => 12.0, |
115
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1816 => 12.0, |
116
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1818 => 11.9, |
117
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1820 => 11.6, |
118
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1822 => 11.0, |
119
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1824 => 10.2, |
120
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1826 => 9.2, |
121
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1828 => 8.2, |
122
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1830 => 7.1, |
123
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1832 => 6.2, |
124
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1834 => 5.6, |
125
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1836 => 5.4, |
126
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1838 => 5.3, |
127
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1840 => 5.4, |
128
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1842 => 5.6, |
129
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1844 => 5.9, |
130
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1846 => 6.2, |
131
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1848 => 6.5, |
132
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1850 => 6.8, |
133
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1852 => 7.1, |
134
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1854 => 7.3, |
135
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1856 => 7.5, |
136
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1858 => 7.6, |
137
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1860 => 7.7, |
138
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1862 => 7.3, |
139
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1864 => 6.2, |
140
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1866 => 5.2, |
141
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1868 => 2.7, |
142
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1870 => 1.4, |
143
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1872 => -1.2, |
144
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1874 => -2.8, |
145
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1876 => -3.8, |
146
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1878 => -4.8, |
147
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1880 => -5.5, |
148
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1882 => -5.3, |
149
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1884 => -5.6, |
150
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1886 => -5.7, |
151
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1888 => -5.9, |
152
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1890 => -6.0, |
153
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1892 => -6.3, |
154
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1894 => -6.5, |
155
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1896 => -6.2, |
156
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1898 => -4.7, |
157
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1900 => -2.8, |
158
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1902 => -0.1, |
159
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1904 => 2.6, |
160
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1906 => 5.3, |
161
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1908 => 7.7, |
162
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1910 => 10.4, |
163
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1912 => 13.3, |
164
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1914 => 16.0, |
165
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1916 => 18.2, |
166
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1918 => 20.2, |
167
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1920 => 21.1, |
168
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1922 => 22.4, |
169
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1924 => 23.5, |
170
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1926 => 23.8, |
171
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1928 => 24.3, |
172
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1930 => 24.0, |
173
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1932 => 23.9, |
174
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1934 => 23.9, |
175
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1936 => 23.7, |
176
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1938 => 24.0, |
177
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1940 => 24.3, |
178
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1942 => 25.3, |
179
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1944 => 26.2, |
180
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1946 => 27.3, |
181
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1948 => 28.2, |
182
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1950 => 29.1, |
183
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1952 => 30.0, |
184
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1954 => 30.7, |
185
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1956 => 31.4, |
186
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1958 => 32.2, |
187
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1960 => 33.1, |
188
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1962 => 34.0, |
189
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1964 => 35.0, |
190
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1966 => 36.5, |
191
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1968 => 38.3, |
192
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1970 => 40.2, |
193
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1972 => 42.2, |
194
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1974 => 44.5, |
195
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1976 => 46.5, |
196
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1978 => 48.5, |
197
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1980 => 50.5, |
198
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1982 => 52.2, |
199
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1984 => 53.8, |
200
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1986 => 54.9, |
201
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1988 => 55.8, |
202
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1990 => 56.9, |
203
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1992 => 58.3, |
204
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1994 => 60.0, |
205
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1996 => 61.6, |
206
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1998 => 63.0, |
207
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208
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# From http://www.staff.science.uu.nl/~gent0113/deltat/deltat_modern.htm |
209
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2000 => 63.8, |
210
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2002 => 63.3, |
211
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2004 => 64.6, |
212
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2006 => 64.9, |
213
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2008 => 65.5, |
214
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2010 => 66.1, |
215
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2012 => 68.0, |
216
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2014 => 69.0, |
217
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2016 => 70.0 |
218
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); |
219
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220
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Readonly our $TAB_SINCE => 1620; |
221
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Readonly our $TAB_UNTIL => 2016; |
222
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223
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sub _interpolate { |
224
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1
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1
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19
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my ( $jd, $ye ) = @_; |
225
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226
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# For a historical range from 1620 to a recent year, we interpolate from a |
227
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# table of observed values. Outside that range we use formulae. |
228
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229
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# Last value in the table |
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1
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50
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3
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if ( $ye == $TAB_UNTIL ) { |
231
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0
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0
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return $HISTORICAL{$TAB_UNTIL}; |
232
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} |
233
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234
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# 1620 - 20xx |
235
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1
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50
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10
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my $y0 = |
236
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$ye % 2 == 0 ? $ye : $ye - 1; # there are only even numbers in the table |
237
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1
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2
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my $y1 = $y0 + 2; |
238
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1
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6
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my $d0 = $HISTORICAL{$y0}; |
239
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1
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11
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my $d1 = $HISTORICAL{$y1}; |
240
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1
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8
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my $j0 = cal2jd( $y0, 1, 1 ); |
241
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1
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6
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my $j1 = cal2jd( $y1, 1, 1 ); |
242
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243
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# simple linear interpolation between two values |
244
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1
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5
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( ( $jd - $j0 ) * ( $d1 - $d0 ) / ( $j1 - $j0 ) ) + $d0; |
245
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} |
246
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247
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sub delta_t { |
248
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4
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4
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1
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1111
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my $jd = shift; |
249
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250
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4
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14
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my ($ye) = jd2cal($jd); |
251
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252
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4
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100
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100
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15
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return _interpolate($jd, $ye) if $ye >= $TAB_SINCE && $ye <= $TAB_UNTIL; |
253
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3
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25
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my $t = ($ye - 2000) / 100.0; |
254
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3
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50
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7
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return polynome( $t, 2177.0, 497.0, 44.1 ) if $ye < 948; |
255
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256
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3
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9
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my $dt = polynome( $t, 102.0, 102.0, 25.3 ); |
257
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3
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100
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100
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17
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$dt += 0.37 * ( $ye - 2100 ) if $ye > $TAB_UNTIL && $ye < 2100; |
258
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3
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21
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$dt |
259
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} |
260
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261
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1; |
262
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263
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__END__ |
264
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265
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=pod |
266
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267
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=encoding UTF-8 |
268
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269
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=head1 NAME |
270
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271
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Astro::Montenbruck::Time::DeltaT - difference between I<UT> and I<TDT>. |
272
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273
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=head1 VERSION |
274
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275
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Version 0.01 |
276
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277
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278
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|
=head1 DESCRIPTION |
279
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280
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B<Delta-T> indicates the difference between I<UT> and I<TDT> |
281
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(I<Terrestrial Dynamic Time>), which used to be called I<Ephemeris time> in the |
282
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|
|
last century. While I<UT> is not a uniform time scale (it is occasionally |
283
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|
|
adjusted, due to irregularities in the Earth's rotation), I<TDT> is a uniform |
284
|
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|
|
time scale which is needed as an argument for mathematical theories of celestial |
285
|
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|
|
movements. |
286
|
|
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|
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287
|
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|
|
Formulae used by L</delta_t( $jd )> subroutine, are based on NASA Technical |
288
|
|
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|
|
Publication I<"Five Millennium Canon of Solar Eclipses: -1999 to +3000">. |
289
|
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|
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|
|
They are valid for any time during the interval 2000 B.C. to 3000 A.D. See |
290
|
|
|
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|
|
L<NASA Eclipse web site|http://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html">. |
291
|
|
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|
|
292
|
|
|
|
|
|
|
=head1 EXPORT |
293
|
|
|
|
|
|
|
|
294
|
|
|
|
|
|
|
=over |
295
|
|
|
|
|
|
|
|
296
|
|
|
|
|
|
|
=item * L</delta_t( $jd )> |
297
|
|
|
|
|
|
|
|
298
|
|
|
|
|
|
|
=back |
299
|
|
|
|
|
|
|
|
300
|
|
|
|
|
|
|
=head1 SUBROUTINES |
301
|
|
|
|
|
|
|
|
302
|
|
|
|
|
|
|
=head2 delta_t( $jd ) |
303
|
|
|
|
|
|
|
|
304
|
|
|
|
|
|
|
Returns approximate Delta-T in seconds for a given Julian Day. |
305
|
|
|
|
|
|
|
C<Delta-T = ET - UT> |
306
|
|
|
|
|
|
|
|
307
|
|
|
|
|
|
|
For a historical range from 1620 to recent years, we interpolate from a |
308
|
|
|
|
|
|
|
table of observed values. Outside that range we use formulae from |
309
|
|
|
|
|
|
|
I<Astronomical Algorithms> by I<J.Meeus>, second edition. |
310
|
|
|
|
|
|
|
|
311
|
|
|
|
|
|
|
=head3 Arguments |
312
|
|
|
|
|
|
|
|
313
|
|
|
|
|
|
|
=over |
314
|
|
|
|
|
|
|
|
315
|
|
|
|
|
|
|
=item * B<$jd> â Standard Julian Date. |
316
|
|
|
|
|
|
|
|
317
|
|
|
|
|
|
|
=back |
318
|
|
|
|
|
|
|
|
319
|
|
|
|
|
|
|
=head3 Returns |
320
|
|
|
|
|
|
|
|
321
|
|
|
|
|
|
|
Delta-T in seconds |
322
|
|
|
|
|
|
|
|
323
|
|
|
|
|
|
|
=cut |