FACT++  1.0
palDt.c
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1 /*
2 *+
3 * Name:
4 * palDt
5 
6 * Purpose:
7 * Estimate the offset between dynamical time and UT
8 
9 * Language:
10 * Starlink ANSI C
11 
12 * Type of Module:
13 * Library routine
14 
15 * Invocation:
16 * double palDt( double epoch );
17 
18 * Arguments:
19 * epoch = double (Given)
20 * Julian epoch (e.g. 1850.0)
21 
22 * Returned Value:
23 * palDt = double
24 * Rough estimate of ET-UT (after 1984, TT-UT) at the
25 * given epoch, in seconds.
26 
27 * Description:
28 * Estimate the offset between dynamical time and Universal Time
29 * for a given historical epoch.
30 
31 * Authors:
32 * TIMJ: Tim Jenness (JAC, Hawaii)
33 * PTW: Patrick T. Wallace
34 * {enter_new_authors_here}
35 
36 * Notes:
37 * - Depending on the epoch, one of three parabolic approximations
38 * is used:
39 *
40 * before 979 Stephenson & Morrison's 390 BC to AD 948 model
41 * 979 to 1708 Stephenson & Morrison's 948 to 1600 model
42 * after 1708 McCarthy & Babcock's post-1650 model
43 *
44 * The breakpoints are chosen to ensure continuity: they occur
45 * at places where the adjacent models give the same answer as
46 * each other.
47 * - The accuracy is modest, with errors of up to 20 sec during
48 * the interval since 1650, rising to perhaps 30 min by 1000 BC.
49 * Comparatively accurate values from AD 1600 are tabulated in
50 * the Astronomical Almanac (see section K8 of the 1995 AA).
51 * - The use of double-precision for both argument and result is
52 * purely for compatibility with other SLALIB time routines.
53 * - The models used are based on a lunar tidal acceleration value
54 * of -26.00 arcsec per century.
55 *
56 * See Also:
57 * Explanatory Supplement to the Astronomical Almanac,
58 * ed P.K.Seidelmann, University Science Books (1992),
59 * section 2.553, p83. This contains references to
60 * the Stephenson & Morrison and McCarthy & Babcock
61 * papers.
62 
63 * History:
64 * 2012-03-08 (TIMJ):
65 * Initial version with documentation from SLA/F.
66 * Adapted with permission from the Fortran SLALIB library.
67 * {enter_further_changes_here}
68 
69 * Copyright:
70 * Copyright (C) 1995 Rutherford Appleton Laboratory
71 * Copyright (C) 2012 Science and Technology Facilities Council.
72 * All Rights Reserved.
73 
74 * Licence:
75 * This program is free software; you can redistribute it and/or
76 * modify it under the terms of the GNU General Public License as
77 * published by the Free Software Foundation; either version 3 of
78 * the License, or (at your option) any later version.
79 *
80 * This program is distributed in the hope that it will be
81 * useful, but WITHOUT ANY WARRANTY; without even the implied
82 * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
83 * PURPOSE. See the GNU General Public License for more details.
84 *
85 * You should have received a copy of the GNU General Public License
86 * along with this program; if not, write to the Free Software
87 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
88 * MA 02110-1301, USA.
89 
90 * Bugs:
91 * {note_any_bugs_here}
92 *-
93 */
94 
95 #include "pal.h"
96 
97 double palDt ( double epoch ) {
98 
99  double t,w,s;
100 
101  /* Centuries since 1800 */
102  t = (epoch - 1800.0) / 100.0;
103 
104  /* Select model */
105  if ( epoch >= 1708.185161980887 ) {
106 
107  /* Post-1708: use McCarthy & Babcock */
108  w = t - 0.19;
109  s = 5.156 + 13.3066 * w * w;
110 
111  } else if ( epoch >= 979.0258204760233 ) {
112 
113  /* 978-1708: use Stephenson & Morrison's 948-1600 model */
114  s = 25.5 * t * t;
115 
116  } else {
117 
118  /* Pre-979: use Stephenson & Morrison's 390 BC to AD 948 model */
119  s = 1360.0 + (320.0 + 44.3*t) * t;
120 
121  }
122 
123  return s;
124 
125 }
palDt
double palDt(double epoch)
Definition: palDt.c:97
t
TT t
Definition: test_client.c:26