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python-skyfield/Table-S15.2020.txt

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Accepting request 886486 from home:bnavigator:branches:devel:languages:python:numeric - Update to 1.39 * The Angle.dstr() and Angle.hstr() methods now accept a format= argument that lets callers override Skyfield’s default angle formatting and supply their own; see Formatting angles. #513 * The prototype planetary_magnitude() function now works not only when given a single position, but when given a vector of several positions. - Release 1.38 * Replaced the old historic ∆T table from the United States Naval Observatory with up-to-date splines from the 2020 release of the extensive research by Morrison, Stephenson, Hohenkerk, and Zawilski and also adjusted the slope of Skyfield’s near-future ∆T estimates to make the slope of ∆T much less abrupt over the coming century. * Added a full reference frame object for the TEME reference frame used by SGP4 Earth satellite elements. - Release 1.37 * Added a frame_latlon_and_rates() method that can compute the rates at which angles like altitude and azimuth, or right ascension and declination, are changing. * Accepted a contributor’s helpful fix for a rounding error that had slightly shifted a few constellation boundaries. #548 * The Time tuple utc and method utc_strftime() are now backed by the same math, so they always advance to the next calendar day at the same moment. This makes it safe to mix values returned by one of them with values returned by the other. #542 * Vector subtraction now returns the position subclass specific to the resulting vector’s center. #549 - Release 1.36 OBS-URL: https://build.opensuse.org/request/show/886486 OBS-URL: https://build.opensuse.org/package/show/devel:languages:python:numeric/python-skyfield?expand=0&rev=35
2021-04-18 18:02:54 +00:00
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Table S15: The Polynomial Coefficients for DT -720.0 to 2019.0 v. 2020
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Row Years Polynomial Coefficients
i K_i K_{i+1} a_0 a_1 a_2 a_3
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1 -720.0 -100.0 20371.848 -9999.586 776.247 409.160
2 -100.0 400.0 11557.668 -5822.270 1303.151 -503.433
3 400.0 1000.0 6535.116 -5671.519 -298.291 1085.087
4 1000.0 1150.0 1650.393 -753.210 184.811 -25.346
5 1150.0 1300.0 1056.647 -459.628 108.771 -24.641
6 1300.0 1500.0 681.149 -421.345 61.953 -29.414
7 1500.0 1600.0 292.343 -192.841 -6.572 16.197
8 1600.0 1650.0 109.127 -78.697 10.505 3.018
9 1650.0 1720.0 43.952 -68.089 38.333 -2.127
10 1720.0 1800.0 12.068 2.507 41.731 -37.939
11 1800.0 1810.0 18.367 -3.481 -1.126 1.918
12 1810.0 1820.0 15.678 0.021 4.629 -3.812
13 1820.0 1830.0 16.516 -2.157 -6.806 3.250
14 1830.0 1840.0 10.804 -6.018 2.944 -0.096
15 1840.0 1850.0 7.634 -0.416 2.658 -0.539
16 1850.0 1855.0 9.338 1.642 0.261 -0.883
17 1855.0 1860.0 10.357 -0.486 -2.389 1.558
18 1860.0 1865.0 9.040 -0.591 2.284 -2.477
19 1865.0 1870.0 8.255 -3.456 -5.148 2.720
20 1870.0 1875.0 2.371 -5.593 3.011 -0.914
21 1875.0 1880.0 -1.126 -2.314 0.269 -0.039
22 1880.0 1885.0 -3.210 -1.893 0.152 0.563
23 1885.0 1890.0 -4.388 0.101 1.842 -1.438
24 1890.0 1895.0 -3.884 -0.531 -2.474 1.871
25 1895.0 1900.0 -5.017 0.134 3.138 -0.232
26 1900.0 1905.0 -1.977 5.715 2.443 -1.257
27 1905.0 1910.0 4.923 6.828 -1.329 0.720
28 1910.0 1915.0 11.142 6.330 0.831 -0.825
29 1915.0 1920.0 17.479 5.518 -1.643 0.262
30 1920.0 1925.0 21.617 3.020 -0.856 0.008
31 1925.0 1930.0 23.789 1.333 -0.831 0.127
32 1930.0 1935.0 24.418 0.052 -0.449 0.142
33 1935.0 1940.0 24.164 -0.419 -0.022 0.702
34 1940.0 1945.0 24.426 1.645 2.086 -1.106
35 1945.0 1950.0 27.050 2.499 -1.232 0.614
36 1950.0 1953.0 28.932 1.127 0.220 -0.277
37 1953.0 1956.0 30.002 0.737 -0.610 0.631
38 1956.0 1959.0 30.760 1.409 1.282 -0.799
39 1959.0 1962.0 32.652 1.577 -1.115 0.507
40 1962.0 1965.0 33.621 0.868 0.406 0.199
41 1965.0 1968.0 35.093 2.275 1.002 -0.414
42 1968.0 1971.0 37.956 3.035 -0.242 0.202
43 1971.0 1974.0 40.951 3.157 0.364 -0.229
44 1974.0 1977.0 44.244 3.199 -0.323 0.172
45 1977.0 1980.0 47.291 3.069 0.193 -0.192
46 1980.0 1983.0 50.361 2.878 -0.384 0.081
47 1983.0 1986.0 52.936 2.354 -0.140 -0.165
48 1986.0 1989.0 54.984 1.577 -0.637 0.448
49 1989.0 1992.0 56.373 1.648 0.708 -0.276
50 1992.0 1995.0 58.453 2.235 -0.121 0.110
51 1995.0 1998.0 60.678 2.324 0.210 -0.313
52 1998.0 2001.0 62.898 1.804 -0.729 0.109
53 2001.0 2004.0 64.083 0.674 -0.402 0.199
54 2004.0 2007.0 64.553 0.466 0.194 -0.017
55 2007.0 2010.0 65.197 0.804 0.144 -0.084
56 2010.0 2013.0 66.061 0.839 -0.109 0.128
57 2013.0 2016.0 66.920 1.007 0.277 -0.095
58 2016.0 2019.0 68.109 1.277 -0.007 -0.139
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The above table of polynomial coefficients enables evaluation of DT in
seconds (s) and its derivative (the length of day lod) in milliseconds
(ms) for any epoch between $-720$ and 2019. It is not valid outside the
specified range of years.
For the year and fraction Y, extract the coefficients a_0, a_1, a_2,
a_3 from row i, where K_i <= Y <= K_{i+1} and form
t = (Y - K_i)/(K_{i+1} - K_i), where 0 <= t < 1, and
thus calculate
DT = a_0 + a_1 t + a_2 t^2 + a_3 t^3 seconds
lod = (a_1 + 2 a_2 t + 3 a_3 t^2) / (K_{i+1}-K_i) / 0.36525 ms
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These coefficients reproduce the spline approximation discussed by
L.V. Morrison, F.R. Stephenson, C.Y. Hohenkerk and M. Zawilski, in
their latest paper entitled ``Addendum 2020 to `Measurement of the
Earth's Rotation: 720 BC to AD 2015'' published in the Royal Society
Proceedings A, 478, 2021, see https://doi.org/10.1098/rspa.2020.0776.
Details of the original analysis is published in Royal Society
Proceedings A, 472, 2016, at https://doi.org/10.1098/rspa.2016.0404
All the data is also available from the website of HM Nautical Almanac
Office at http://astro.ukho.gov.uk/nao/lvm/.
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