Benjamin Greiner
29e266d2f7
- 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
90 lines
5.8 KiB
Plaintext
90 lines
5.8 KiB
Plaintext
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Table S15: The Polynomial Coefficients for DT -720.0 to 2019.0 v. 2020
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Row Years Polynomial Coefficients
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i K_i K_{i+1} a_0 a_1 a_2 a_3
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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1 -720.0 -100.0 20371.848 -9999.586 776.247 409.160
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2 -100.0 400.0 11557.668 -5822.270 1303.151 -503.433
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3 400.0 1000.0 6535.116 -5671.519 -298.291 1085.087
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4 1000.0 1150.0 1650.393 -753.210 184.811 -25.346
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5 1150.0 1300.0 1056.647 -459.628 108.771 -24.641
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6 1300.0 1500.0 681.149 -421.345 61.953 -29.414
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7 1500.0 1600.0 292.343 -192.841 -6.572 16.197
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8 1600.0 1650.0 109.127 -78.697 10.505 3.018
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9 1650.0 1720.0 43.952 -68.089 38.333 -2.127
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10 1720.0 1800.0 12.068 2.507 41.731 -37.939
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11 1800.0 1810.0 18.367 -3.481 -1.126 1.918
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12 1810.0 1820.0 15.678 0.021 4.629 -3.812
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13 1820.0 1830.0 16.516 -2.157 -6.806 3.250
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14 1830.0 1840.0 10.804 -6.018 2.944 -0.096
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15 1840.0 1850.0 7.634 -0.416 2.658 -0.539
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16 1850.0 1855.0 9.338 1.642 0.261 -0.883
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17 1855.0 1860.0 10.357 -0.486 -2.389 1.558
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18 1860.0 1865.0 9.040 -0.591 2.284 -2.477
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19 1865.0 1870.0 8.255 -3.456 -5.148 2.720
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20 1870.0 1875.0 2.371 -5.593 3.011 -0.914
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21 1875.0 1880.0 -1.126 -2.314 0.269 -0.039
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22 1880.0 1885.0 -3.210 -1.893 0.152 0.563
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23 1885.0 1890.0 -4.388 0.101 1.842 -1.438
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24 1890.0 1895.0 -3.884 -0.531 -2.474 1.871
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25 1895.0 1900.0 -5.017 0.134 3.138 -0.232
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26 1900.0 1905.0 -1.977 5.715 2.443 -1.257
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27 1905.0 1910.0 4.923 6.828 -1.329 0.720
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28 1910.0 1915.0 11.142 6.330 0.831 -0.825
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29 1915.0 1920.0 17.479 5.518 -1.643 0.262
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30 1920.0 1925.0 21.617 3.020 -0.856 0.008
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31 1925.0 1930.0 23.789 1.333 -0.831 0.127
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32 1930.0 1935.0 24.418 0.052 -0.449 0.142
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33 1935.0 1940.0 24.164 -0.419 -0.022 0.702
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34 1940.0 1945.0 24.426 1.645 2.086 -1.106
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35 1945.0 1950.0 27.050 2.499 -1.232 0.614
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36 1950.0 1953.0 28.932 1.127 0.220 -0.277
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37 1953.0 1956.0 30.002 0.737 -0.610 0.631
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38 1956.0 1959.0 30.760 1.409 1.282 -0.799
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39 1959.0 1962.0 32.652 1.577 -1.115 0.507
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40 1962.0 1965.0 33.621 0.868 0.406 0.199
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41 1965.0 1968.0 35.093 2.275 1.002 -0.414
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42 1968.0 1971.0 37.956 3.035 -0.242 0.202
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43 1971.0 1974.0 40.951 3.157 0.364 -0.229
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44 1974.0 1977.0 44.244 3.199 -0.323 0.172
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45 1977.0 1980.0 47.291 3.069 0.193 -0.192
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46 1980.0 1983.0 50.361 2.878 -0.384 0.081
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47 1983.0 1986.0 52.936 2.354 -0.140 -0.165
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48 1986.0 1989.0 54.984 1.577 -0.637 0.448
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49 1989.0 1992.0 56.373 1.648 0.708 -0.276
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50 1992.0 1995.0 58.453 2.235 -0.121 0.110
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51 1995.0 1998.0 60.678 2.324 0.210 -0.313
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52 1998.0 2001.0 62.898 1.804 -0.729 0.109
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53 2001.0 2004.0 64.083 0.674 -0.402 0.199
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54 2004.0 2007.0 64.553 0.466 0.194 -0.017
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55 2007.0 2010.0 65.197 0.804 0.144 -0.084
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56 2010.0 2013.0 66.061 0.839 -0.109 0.128
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57 2013.0 2016.0 66.920 1.007 0.277 -0.095
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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
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seconds (s) and its derivative (the length of day lod) in milliseconds
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(ms) for any epoch between $-720$ and 2019. It is not valid outside the
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specified range of years.
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For the year and fraction Y, extract the coefficients a_0, a_1, a_2,
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a_3 from row i, where K_i <= Y <= K_{i+1} and form
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t = (Y - K_i)/(K_{i+1} - K_i), where 0 <= t < 1, and
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thus calculate
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DT = a_0 + a_1 t + a_2 t^2 + a_3 t^3 seconds
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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
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L.V. Morrison, F.R. Stephenson, C.Y. Hohenkerk and M. Zawilski, in
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their latest paper entitled ``Addendum 2020 to `Measurement of the
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Earth's Rotation: 720 BC to AD 2015'' published in the Royal Society
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Proceedings A, 478, 2021, see https://doi.org/10.1098/rspa.2020.0776.
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Details of the original analysis is published in Royal Society
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Proceedings A, 472, 2016, at https://doi.org/10.1098/rspa.2016.0404
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All the data is also available from the website of HM Nautical Almanac
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Office at http://astro.ukho.gov.uk/nao/lvm/.
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