| 1 | #include "slalib.h"
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| 2 | #include "slamac.h"
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| 3 | double slaDt ( double epoch )
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| 4 | /*
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| 5 | ** - - - - - -
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| 6 | ** s l a D t
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| 7 | ** - - - - - -
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| 8 | **
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| 9 | ** Estimate the offset between dynamical time and Universal Time
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| 10 | ** for a given historical epoch.
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| 11 | **
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| 12 | ** (double precision)
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| 13 | **
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| 14 | ** Given:
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| 15 | ** epoch double (Julian) epoch (e.g. 1850.0)
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| 16 | **
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| 17 | ** The result is a rough estimate of ET-UT (after 1984, TT-UT1) at
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| 18 | ** the given epoch, in seconds.
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| 19 | **
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| 20 | ** Notes:
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| 21 | **
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| 22 | ** 1 Depending on the epoch, one of three parabolic approximations
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| 23 | ** is used:
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| 24 | **
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| 25 | ** before 979 Stephenson & Morrison's 390 BC to AD 948 model
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| 26 | ** 979 to 1708 Stephenson & Morrison's 948 to 1600 model
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| 27 | ** after 1708 McCarthy & Babcock's post-1650 model
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| 28 | **
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| 29 | ** The breakpoints are chosen to ensure continuity: they occur
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| 30 | ** at places where the adjacent models give the same answer as
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| 31 | ** each other.
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| 32 | **
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| 33 | ** 2 The accuracy is modest, with errors of up to 20 sec during
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| 34 | ** the interval since 1650, rising to perhaps 30 min by 1000 BC.
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| 35 | ** Comparatively accurate values from AD 1600 are tabulated in
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| 36 | ** the Astronomical Almanac (see section K8 of the 1995 AA).
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| 37 | **
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| 38 | ** 3 The use of double-precision for both argument and result is
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| 39 | ** purely for compatibility with other SLALIB time routines.
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| 40 | **
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| 41 | ** 4 The models used are based on a lunar tidal acceleration value
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| 42 | ** of -26.00 arcsec per century.
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| 43 | **
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| 44 | ** Reference: Explanatory Supplement to the Astronomical Almanac,
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| 45 | ** ed P.K.Seidelmann, University Science Books (1992),
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| 46 | ** section 2.553, p83. This contains references to
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| 47 | ** the Stephenson & Morrison and McCarthy & Babcock
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| 48 | ** papers.
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| 49 | **
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| 50 | ** Last revision: 14 February 1995
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| 51 | **
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| 52 | ** Copyright P.T.Wallace. All rights reserved.
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| 53 | */
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| 54 | {
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| 55 | double t, w, s;
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| 56 |
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| 57 |
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| 58 | /* Centuries since 1800 */
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| 59 | t = ( epoch - 1800.0 ) / 100.0;
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| 60 |
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| 61 | /* Select model */
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| 62 | if ( epoch >= 1708.185161980887 ) {
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| 63 |
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| 64 | /* Post-1708: use McCarthy & Babcock */
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| 65 | w = t - 0.19;
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| 66 | s = 5.156 + 13.3066 * w * w;
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| 67 | } else {
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| 68 | if ( epoch >= 979.0258204760233 ) {
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| 69 |
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| 70 | /* 979-1708: use Stephenson & Morrison's 948-1600 model */
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| 71 | s = 25.5 * t * t;
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| 72 | } else {
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| 73 |
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| 74 | /* Pre-979: use Stephenson & Morrison's 390 BC to AD 948 model */
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| 75 | s = 1360.0 + ( 320.0 + 44.3 * t ) * t;
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| 76 | }
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| 77 | }
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| 78 |
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| 79 | /* Result */
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| 80 | return s;
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| 81 | }
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