| 1 | /*
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| 2 | *+
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| 3 | * Name:
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| 4 | * palDt
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| 5 |
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| 6 | * Purpose:
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| 7 | * Estimate the offset between dynamical time and UT
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| 8 |
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| 9 | * Language:
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| 10 | * Starlink ANSI C
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| 11 |
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| 12 | * Type of Module:
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| 13 | * Library routine
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| 14 |
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| 15 | * Invocation:
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| 16 | * double palDt( double epoch );
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| 17 |
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| 18 | * Arguments:
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| 19 | * epoch = double (Given)
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| 20 | * Julian epoch (e.g. 1850.0)
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| 21 |
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| 22 | * Returned Value:
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| 23 | * palDt = double
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| 24 | * Rough estimate of ET-UT (after 1984, TT-UT) at the
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| 25 | * given epoch, in seconds.
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| 26 |
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| 27 | * Description:
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| 28 | * Estimate the offset between dynamical time and Universal Time
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| 29 | * for a given historical epoch.
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| 30 |
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| 31 | * Authors:
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| 32 | * TIMJ: Tim Jenness (JAC, Hawaii)
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| 33 | * PTW: Patrick T. Wallace
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| 34 | * {enter_new_authors_here}
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| 35 |
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| 36 | * Notes:
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| 37 | * - Depending on the epoch, one of three parabolic approximations
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| 38 | * is used:
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| 39 | *
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| 40 | * before 979 Stephenson & Morrison's 390 BC to AD 948 model
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| 41 | * 979 to 1708 Stephenson & Morrison's 948 to 1600 model
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| 42 | * after 1708 McCarthy & Babcock's post-1650 model
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| 43 | *
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| 44 | * The breakpoints are chosen to ensure continuity: they occur
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| 45 | * at places where the adjacent models give the same answer as
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| 46 | * each other.
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| 47 | * - The accuracy is modest, with errors of up to 20 sec during
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| 48 | * the interval since 1650, rising to perhaps 30 min by 1000 BC.
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| 49 | * Comparatively accurate values from AD 1600 are tabulated in
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| 50 | * the Astronomical Almanac (see section K8 of the 1995 AA).
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| 51 | * - The use of double-precision for both argument and result is
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| 52 | * purely for compatibility with other SLALIB time routines.
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| 53 | * - The models used are based on a lunar tidal acceleration value
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| 54 | * of -26.00 arcsec per century.
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| 55 | *
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| 56 | * See Also:
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| 57 | * Explanatory Supplement to the Astronomical Almanac,
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| 58 | * ed P.K.Seidelmann, University Science Books (1992),
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| 59 | * section 2.553, p83. This contains references to
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| 60 | * the Stephenson & Morrison and McCarthy & Babcock
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| 61 | * papers.
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| 62 |
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| 63 | * History:
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| 64 | * 2012-03-08 (TIMJ):
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| 65 | * Initial version with documentation from SLA/F.
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| 66 | * Adapted with permission from the Fortran SLALIB library.
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| 67 | * {enter_further_changes_here}
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| 68 |
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| 69 | * Copyright:
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| 70 | * Copyright (C) 1995 Rutherford Appleton Laboratory
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| 71 | * Copyright (C) 2012 Science and Technology Facilities Council.
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| 72 | * All Rights Reserved.
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| 73 |
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| 74 | * Licence:
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| 75 | * This program is free software; you can redistribute it and/or
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| 76 | * modify it under the terms of the GNU General Public License as
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| 77 | * published by the Free Software Foundation; either version 3 of
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| 78 | * the License, or (at your option) any later version.
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| 79 | *
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| 80 | * This program is distributed in the hope that it will be
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| 81 | * useful, but WITHOUT ANY WARRANTY; without even the implied
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| 82 | * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
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| 83 | * PURPOSE. See the GNU General Public License for more details.
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| 84 | *
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| 85 | * You should have received a copy of the GNU General Public License
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| 86 | * along with this program; if not, write to the Free Software
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| 87 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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| 88 | * MA 02110-1301, USA.
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| 89 |
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| 90 | * Bugs:
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| 91 | * {note_any_bugs_here}
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| 92 | *-
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| 93 | */
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| 94 |
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| 95 | #include "pal.h"
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| 96 |
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| 97 | double palDt ( double epoch ) {
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| 98 |
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| 99 | double t,w,s;
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| 100 |
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| 101 | /* Centuries since 1800 */
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| 102 | t = (epoch - 1800.0) / 100.0;
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| 103 |
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| 104 | /* Select model */
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| 105 | if ( epoch >= 1708.185161980887 ) {
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| 106 |
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| 107 | /* Post-1708: use McCarthy & Babcock */
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| 108 | w = t - 0.19;
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| 109 | s = 5.156 + 13.3066 * w * w;
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| 110 |
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| 111 | } else if ( epoch >= 979.0258204760233 ) {
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| 112 |
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| 113 | /* 978-1708: use Stephenson & Morrison's 948-1600 model */
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| 114 | s = 25.5 * t * t;
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| 115 |
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| 116 | } else {
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| 117 |
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| 118 | /* Pre-979: use Stephenson & Morrison's 390 BC to AD 948 model */
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| 119 | s = 1360.0 + (320.0 + 44.3*t) * t;
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| 120 |
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| 121 | }
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| 122 |
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| 123 | return s;
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| 124 |
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| 125 | }
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