| 1 | #include "erfa.h"
|
|---|
| 2 |
|
|---|
| 3 | double eraEect00(double date1, double date2)
|
|---|
| 4 | /*
|
|---|
| 5 | ** - - - - - - - - - -
|
|---|
| 6 | ** e r a E e c t 0 0
|
|---|
| 7 | ** - - - - - - - - - -
|
|---|
| 8 | **
|
|---|
| 9 | ** Equation of the equinoxes complementary terms, consistent with
|
|---|
| 10 | ** IAU 2000 resolutions.
|
|---|
| 11 | **
|
|---|
| 12 | ** Given:
|
|---|
| 13 | ** date1,date2 double TT as a 2-part Julian Date (Note 1)
|
|---|
| 14 | **
|
|---|
| 15 | ** Returned (function value):
|
|---|
| 16 | ** double complementary terms (Note 2)
|
|---|
| 17 | **
|
|---|
| 18 | ** Notes:
|
|---|
| 19 | **
|
|---|
| 20 | ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
|
|---|
| 21 | ** convenient way between the two arguments. For example,
|
|---|
| 22 | ** JD(TT)=2450123.7 could be expressed in any of these ways,
|
|---|
| 23 | ** among others:
|
|---|
| 24 | **
|
|---|
| 25 | ** date1 date2
|
|---|
| 26 | **
|
|---|
| 27 | ** 2450123.7 0.0 (JD method)
|
|---|
| 28 | ** 2451545.0 -1421.3 (J2000 method)
|
|---|
| 29 | ** 2400000.5 50123.2 (MJD method)
|
|---|
| 30 | ** 2450123.5 0.2 (date & time method)
|
|---|
| 31 | **
|
|---|
| 32 | ** The JD method is the most natural and convenient to use in
|
|---|
| 33 | ** cases where the loss of several decimal digits of resolution
|
|---|
| 34 | ** is acceptable. The J2000 method is best matched to the way
|
|---|
| 35 | ** the argument is handled internally and will deliver the
|
|---|
| 36 | ** optimum resolution. The MJD method and the date & time methods
|
|---|
| 37 | ** are both good compromises between resolution and convenience.
|
|---|
| 38 | **
|
|---|
| 39 | ** 2) The "complementary terms" are part of the equation of the
|
|---|
| 40 | ** equinoxes (EE), classically the difference between apparent and
|
|---|
| 41 | ** mean Sidereal Time:
|
|---|
| 42 | **
|
|---|
| 43 | ** GAST = GMST + EE
|
|---|
| 44 | **
|
|---|
| 45 | ** with:
|
|---|
| 46 | **
|
|---|
| 47 | ** EE = dpsi * cos(eps)
|
|---|
| 48 | **
|
|---|
| 49 | ** where dpsi is the nutation in longitude and eps is the obliquity
|
|---|
| 50 | ** of date. However, if the rotation of the Earth were constant in
|
|---|
| 51 | ** an inertial frame the classical formulation would lead to
|
|---|
| 52 | ** apparent irregularities in the UT1 timescale traceable to side-
|
|---|
| 53 | ** effects of precession-nutation. In order to eliminate these
|
|---|
| 54 | ** effects from UT1, "complementary terms" were introduced in 1994
|
|---|
| 55 | ** (IAU, 1994) and took effect from 1997 (Capitaine and Gontier,
|
|---|
| 56 | ** 1993):
|
|---|
| 57 | **
|
|---|
| 58 | ** GAST = GMST + CT + EE
|
|---|
| 59 | **
|
|---|
| 60 | ** By convention, the complementary terms are included as part of
|
|---|
| 61 | ** the equation of the equinoxes rather than as part of the mean
|
|---|
| 62 | ** Sidereal Time. This slightly compromises the "geometrical"
|
|---|
| 63 | ** interpretation of mean sidereal time but is otherwise
|
|---|
| 64 | ** inconsequential.
|
|---|
| 65 | **
|
|---|
| 66 | ** The present function computes CT in the above expression,
|
|---|
| 67 | ** compatible with IAU 2000 resolutions (Capitaine et al., 2002, and
|
|---|
| 68 | ** IERS Conventions 2003).
|
|---|
| 69 | **
|
|---|
| 70 | ** Called:
|
|---|
| 71 | ** eraFal03 mean anomaly of the Moon
|
|---|
| 72 | ** eraFalp03 mean anomaly of the Sun
|
|---|
| 73 | ** eraFaf03 mean argument of the latitude of the Moon
|
|---|
| 74 | ** eraFad03 mean elongation of the Moon from the Sun
|
|---|
| 75 | ** eraFaom03 mean longitude of the Moon's ascending node
|
|---|
| 76 | ** eraFave03 mean longitude of Venus
|
|---|
| 77 | ** eraFae03 mean longitude of Earth
|
|---|
| 78 | ** eraFapa03 general accumulated precession in longitude
|
|---|
| 79 | **
|
|---|
| 80 | ** References:
|
|---|
| 81 | **
|
|---|
| 82 | ** Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275,
|
|---|
| 83 | ** 645-650 (1993)
|
|---|
| 84 | **
|
|---|
| 85 | ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
|
|---|
| 86 | ** implement the IAU 2000 definition of UT1", Astronomy &
|
|---|
| 87 | ** Astrophysics, 406, 1135-1149 (2003)
|
|---|
| 88 | **
|
|---|
| 89 | ** IAU Resolution C7, Recommendation 3 (1994)
|
|---|
| 90 | **
|
|---|
| 91 | ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
|
|---|
| 92 | ** IERS Technical Note No. 32, BKG (2004)
|
|---|
| 93 | **
|
|---|
| 94 | ** Copyright (C) 2013-2015, NumFOCUS Foundation.
|
|---|
| 95 | ** Derived, with permission, from the SOFA library. See notes at end of file.
|
|---|
| 96 | */
|
|---|
| 97 | {
|
|---|
| 98 | /* Time since J2000.0, in Julian centuries */
|
|---|
| 99 | double t;
|
|---|
| 100 |
|
|---|
| 101 | /* Miscellaneous */
|
|---|
| 102 | int i, j;
|
|---|
| 103 | double a, s0, s1;
|
|---|
| 104 |
|
|---|
| 105 | /* Fundamental arguments */
|
|---|
| 106 | double fa[14];
|
|---|
| 107 |
|
|---|
| 108 | /* Returned value. */
|
|---|
| 109 | double eect;
|
|---|
| 110 |
|
|---|
| 111 | /* ----------------------------------------- */
|
|---|
| 112 | /* The series for the EE complementary terms */
|
|---|
| 113 | /* ----------------------------------------- */
|
|---|
| 114 |
|
|---|
| 115 | typedef struct {
|
|---|
| 116 | int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */
|
|---|
| 117 | double s, c; /* sine and cosine coefficients */
|
|---|
| 118 | } TERM;
|
|---|
| 119 |
|
|---|
| 120 | /* Terms of order t^0 */
|
|---|
| 121 | static const TERM e0[] = {
|
|---|
| 122 |
|
|---|
| 123 | /* 1-10 */
|
|---|
| 124 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, 2640.96e-6, -0.39e-6 },
|
|---|
| 125 | {{ 0, 0, 0, 0, 2, 0, 0, 0}, 63.52e-6, -0.02e-6 },
|
|---|
| 126 | {{ 0, 0, 2, -2, 3, 0, 0, 0}, 11.75e-6, 0.01e-6 },
|
|---|
| 127 | {{ 0, 0, 2, -2, 1, 0, 0, 0}, 11.21e-6, 0.01e-6 },
|
|---|
| 128 | {{ 0, 0, 2, -2, 2, 0, 0, 0}, -4.55e-6, 0.00e-6 },
|
|---|
| 129 | {{ 0, 0, 2, 0, 3, 0, 0, 0}, 2.02e-6, 0.00e-6 },
|
|---|
| 130 | {{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.98e-6, 0.00e-6 },
|
|---|
| 131 | {{ 0, 0, 0, 0, 3, 0, 0, 0}, -1.72e-6, 0.00e-6 },
|
|---|
| 132 | {{ 0, 1, 0, 0, 1, 0, 0, 0}, -1.41e-6, -0.01e-6 },
|
|---|
| 133 | {{ 0, 1, 0, 0, -1, 0, 0, 0}, -1.26e-6, -0.01e-6 },
|
|---|
| 134 |
|
|---|
| 135 | /* 11-20 */
|
|---|
| 136 | {{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.63e-6, 0.00e-6 },
|
|---|
| 137 | {{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.63e-6, 0.00e-6 },
|
|---|
| 138 | {{ 0, 1, 2, -2, 3, 0, 0, 0}, 0.46e-6, 0.00e-6 },
|
|---|
| 139 | {{ 0, 1, 2, -2, 1, 0, 0, 0}, 0.45e-6, 0.00e-6 },
|
|---|
| 140 | {{ 0, 0, 4, -4, 4, 0, 0, 0}, 0.36e-6, 0.00e-6 },
|
|---|
| 141 | {{ 0, 0, 1, -1, 1, -8, 12, 0}, -0.24e-6, -0.12e-6 },
|
|---|
| 142 | {{ 0, 0, 2, 0, 0, 0, 0, 0}, 0.32e-6, 0.00e-6 },
|
|---|
| 143 | {{ 0, 0, 2, 0, 2, 0, 0, 0}, 0.28e-6, 0.00e-6 },
|
|---|
| 144 | {{ 1, 0, 2, 0, 3, 0, 0, 0}, 0.27e-6, 0.00e-6 },
|
|---|
| 145 | {{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.26e-6, 0.00e-6 },
|
|---|
| 146 |
|
|---|
| 147 | /* 21-30 */
|
|---|
| 148 | {{ 0, 0, 2, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 },
|
|---|
| 149 | {{ 0, 1, -2, 2, -3, 0, 0, 0}, 0.19e-6, 0.00e-6 },
|
|---|
| 150 | {{ 0, 1, -2, 2, -1, 0, 0, 0}, 0.18e-6, 0.00e-6 },
|
|---|
| 151 | {{ 0, 0, 0, 0, 0, 8,-13, -1}, -0.10e-6, 0.05e-6 },
|
|---|
| 152 | {{ 0, 0, 0, 2, 0, 0, 0, 0}, 0.15e-6, 0.00e-6 },
|
|---|
| 153 | {{ 2, 0, -2, 0, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 },
|
|---|
| 154 | {{ 1, 0, 0, -2, 1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
|
|---|
| 155 | {{ 0, 1, 2, -2, 2, 0, 0, 0}, -0.14e-6, 0.00e-6 },
|
|---|
| 156 | {{ 1, 0, 0, -2, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
|
|---|
| 157 | {{ 0, 0, 4, -2, 4, 0, 0, 0}, 0.13e-6, 0.00e-6 },
|
|---|
| 158 |
|
|---|
| 159 | /* 31-33 */
|
|---|
| 160 | {{ 0, 0, 2, -2, 4, 0, 0, 0}, -0.11e-6, 0.00e-6 },
|
|---|
| 161 | {{ 1, 0, -2, 0, -3, 0, 0, 0}, 0.11e-6, 0.00e-6 },
|
|---|
| 162 | {{ 1, 0, -2, 0, -1, 0, 0, 0}, 0.11e-6, 0.00e-6 }
|
|---|
| 163 | };
|
|---|
| 164 |
|
|---|
| 165 | /* Terms of order t^1 */
|
|---|
| 166 | static const TERM e1[] = {
|
|---|
| 167 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.87e-6, 0.00e-6 }
|
|---|
| 168 | };
|
|---|
| 169 |
|
|---|
| 170 | /* Number of terms in the series */
|
|---|
| 171 | const int NE0 = (int) (sizeof e0 / sizeof (TERM));
|
|---|
| 172 | const int NE1 = (int) (sizeof e1 / sizeof (TERM));
|
|---|
| 173 |
|
|---|
| 174 | /*--------------------------------------------------------------------*/
|
|---|
| 175 |
|
|---|
| 176 | /* Interval between fundamental epoch J2000.0 and current date (JC). */
|
|---|
| 177 | t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
|
|---|
| 178 |
|
|---|
| 179 | /* Fundamental Arguments (from IERS Conventions 2003) */
|
|---|
| 180 |
|
|---|
| 181 | /* Mean anomaly of the Moon. */
|
|---|
| 182 | fa[0] = eraFal03(t);
|
|---|
| 183 |
|
|---|
| 184 | /* Mean anomaly of the Sun. */
|
|---|
| 185 | fa[1] = eraFalp03(t);
|
|---|
| 186 |
|
|---|
| 187 | /* Mean longitude of the Moon minus that of the ascending node. */
|
|---|
| 188 | fa[2] = eraFaf03(t);
|
|---|
| 189 |
|
|---|
| 190 | /* Mean elongation of the Moon from the Sun. */
|
|---|
| 191 | fa[3] = eraFad03(t);
|
|---|
| 192 |
|
|---|
| 193 | /* Mean longitude of the ascending node of the Moon. */
|
|---|
| 194 | fa[4] = eraFaom03(t);
|
|---|
| 195 |
|
|---|
| 196 | /* Mean longitude of Venus. */
|
|---|
| 197 | fa[5] = eraFave03(t);
|
|---|
| 198 |
|
|---|
| 199 | /* Mean longitude of Earth. */
|
|---|
| 200 | fa[6] = eraFae03(t);
|
|---|
| 201 |
|
|---|
| 202 | /* General precession in longitude. */
|
|---|
| 203 | fa[7] = eraFapa03(t);
|
|---|
| 204 |
|
|---|
| 205 | /* Evaluate the EE complementary terms. */
|
|---|
| 206 | s0 = 0.0;
|
|---|
| 207 | s1 = 0.0;
|
|---|
| 208 |
|
|---|
| 209 | for (i = NE0-1; i >= 0; i--) {
|
|---|
| 210 | a = 0.0;
|
|---|
| 211 | for (j = 0; j < 8; j++) {
|
|---|
| 212 | a += (double)(e0[i].nfa[j]) * fa[j];
|
|---|
| 213 | }
|
|---|
| 214 | s0 += e0[i].s * sin(a) + e0[i].c * cos(a);
|
|---|
| 215 | }
|
|---|
| 216 |
|
|---|
| 217 | for (i = NE1-1; i >= 0; i--) {
|
|---|
| 218 | a = 0.0;
|
|---|
| 219 | for (j = 0; j < 8; j++) {
|
|---|
| 220 | a += (double)(e1[i].nfa[j]) * fa[j];
|
|---|
| 221 | }
|
|---|
| 222 | s1 += e1[i].s * sin(a) + e1[i].c * cos(a);
|
|---|
| 223 | }
|
|---|
| 224 |
|
|---|
| 225 | eect = (s0 + s1 * t ) * ERFA_DAS2R;
|
|---|
| 226 |
|
|---|
| 227 | return eect;
|
|---|
| 228 |
|
|---|
| 229 | }
|
|---|
| 230 | /*----------------------------------------------------------------------
|
|---|
| 231 | **
|
|---|
| 232 | **
|
|---|
| 233 | ** Copyright (C) 2013-2015, NumFOCUS Foundation.
|
|---|
| 234 | ** All rights reserved.
|
|---|
| 235 | **
|
|---|
| 236 | ** This library is derived, with permission, from the International
|
|---|
| 237 | ** Astronomical Union's "Standards of Fundamental Astronomy" library,
|
|---|
| 238 | ** available from http://www.iausofa.org.
|
|---|
| 239 | **
|
|---|
| 240 | ** The ERFA version is intended to retain identical functionality to
|
|---|
| 241 | ** the SOFA library, but made distinct through different function and
|
|---|
| 242 | ** file names, as set out in the SOFA license conditions. The SOFA
|
|---|
| 243 | ** original has a role as a reference standard for the IAU and IERS,
|
|---|
| 244 | ** and consequently redistribution is permitted only in its unaltered
|
|---|
| 245 | ** state. The ERFA version is not subject to this restriction and
|
|---|
| 246 | ** therefore can be included in distributions which do not support the
|
|---|
| 247 | ** concept of "read only" software.
|
|---|
| 248 | **
|
|---|
| 249 | ** Although the intent is to replicate the SOFA API (other than
|
|---|
| 250 | ** replacement of prefix names) and results (with the exception of
|
|---|
| 251 | ** bugs; any that are discovered will be fixed), SOFA is not
|
|---|
| 252 | ** responsible for any errors found in this version of the library.
|
|---|
| 253 | **
|
|---|
| 254 | ** If you wish to acknowledge the SOFA heritage, please acknowledge
|
|---|
| 255 | ** that you are using a library derived from SOFA, rather than SOFA
|
|---|
| 256 | ** itself.
|
|---|
| 257 | **
|
|---|
| 258 | **
|
|---|
| 259 | ** TERMS AND CONDITIONS
|
|---|
| 260 | **
|
|---|
| 261 | ** Redistribution and use in source and binary forms, with or without
|
|---|
| 262 | ** modification, are permitted provided that the following conditions
|
|---|
| 263 | ** are met:
|
|---|
| 264 | **
|
|---|
| 265 | ** 1 Redistributions of source code must retain the above copyright
|
|---|
| 266 | ** notice, this list of conditions and the following disclaimer.
|
|---|
| 267 | **
|
|---|
| 268 | ** 2 Redistributions in binary form must reproduce the above copyright
|
|---|
| 269 | ** notice, this list of conditions and the following disclaimer in
|
|---|
| 270 | ** the documentation and/or other materials provided with the
|
|---|
| 271 | ** distribution.
|
|---|
| 272 | **
|
|---|
| 273 | ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
|
|---|
| 274 | ** the International Astronomical Union nor the names of its
|
|---|
| 275 | ** contributors may be used to endorse or promote products derived
|
|---|
| 276 | ** from this software without specific prior written permission.
|
|---|
| 277 | **
|
|---|
| 278 | ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
|---|
| 279 | ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
|---|
| 280 | ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
|---|
| 281 | ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
|---|
| 282 | ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
|---|
| 283 | ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
|
|---|
| 284 | ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|---|
| 285 | ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
|
|---|
| 286 | ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|---|
| 287 | ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
|
|---|
| 288 | ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
|---|
| 289 | ** POSSIBILITY OF SUCH DAMAGE.
|
|---|
| 290 | **
|
|---|
| 291 | */
|
|---|
