#include "erfa.h" void eraNut00b(double date1, double date2, double *dpsi, double *deps) /* ** - - - - - - - - - - ** e r a N u t 0 0 b ** - - - - - - - - - - ** ** Nutation, IAU 2000B model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation, luni-solar + planetary (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components in longitude and obliquity are in radians ** and with respect to the equinox and ecliptic of date. The ** obliquity at J2000.0 is assumed to be the Lieske et al. (1977) ** value of 84381.448 arcsec. (The errors that result from using ** this function with the IAU 2006 value of 84381.406 arcsec can be ** neglected.) ** ** The nutation model consists only of luni-solar terms, but ** includes also a fixed offset which compensates for certain long- ** period planetary terms (Note 7). ** ** 3) This function is an implementation of the IAU 2000B abridged ** nutation model formally adopted by the IAU General Assembly in ** 2000. The function computes the MHB_2000_SHORT luni-solar ** nutation series (Luzum 2001), but without the associated ** corrections for the precession rate adjustments and the offset ** between the GCRS and J2000.0 mean poles. ** ** 4) The full IAU 2000A (MHB2000) nutation model contains nearly 1400 ** terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only ** 77 terms, plus additional simplifications, yet still delivers ** results of 1 mas accuracy at present epochs. This combination of ** accuracy and size makes the IAU 2000B abridged nutation model ** suitable for most practical applications. ** ** The function delivers a pole accurate to 1 mas from 1900 to 2100 ** (usually better than 1 mas, very occasionally just outside ** 1 mas). The full IAU 2000A model, which is implemented in the ** function eraNut00a (q.v.), delivers considerably greater accuracy ** at current dates; however, to realize this improved accuracy, ** corrections for the essentially unpredictable free-core-nutation ** (FCN) must also be included. ** ** 5) The present function provides classical nutation. The ** MHB_2000_SHORT algorithm, from which it is adapted, deals also ** with (i) the offsets between the GCRS and mean poles and (ii) the ** adjustments in longitude and obliquity due to the changed ** precession rates. These additional functions, namely frame bias ** and precession adjustments, are supported by the ERFA functions ** eraBi00 and eraPr00. ** ** 6) The MHB_2000_SHORT algorithm also provides "total" nutations, ** comprising the arithmetic sum of the frame bias, precession ** adjustments, and nutation (luni-solar + planetary). These total ** nutations can be used in combination with an existing IAU 1976 ** precession implementation, such as eraPmat76, to deliver GCRS- ** to-true predictions of mas accuracy at current epochs. However, ** for symmetry with the eraNut00a function (q.v. for the reasons), ** the ERFA functions do not generate the "total nutations" ** directly. Should they be required, they could of course easily ** be generated by calling eraBi00, eraPr00 and the present function ** and adding the results. ** ** 7) The IAU 2000B model includes "planetary bias" terms that are ** fixed in size but compensate for long-period nutations. The ** amplitudes quoted in McCarthy & Luzum (2003), namely ** Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for ** the "total nutations" method described in Note 6. The Luzum ** (2001) values used in this ERFA implementation, namely -0.135 mas ** and +0.388 mas, are optimized for the "rigorous" method, where ** frame bias, precession and nutation are applied separately and in ** that order. During the interval 1995-2050, the ERFA ** implementation delivers a maximum error of 1.001 mas (not ** including FCN). ** ** References: ** ** Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions ** for the precession quantities based upon the IAU /1976/ system of ** astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977) ** ** Luzum, B., private communication, 2001 (Fortran code ** MHB_2000_SHORT) ** ** McCarthy, D.D. & Luzum, B.J., "An abridged model of the ** precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron. ** 85, 37-49 (2003) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994) ** ** Copyright (C) 2013-2017, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { double t, el, elp, f, d, om, arg, dp, de, sarg, carg, dpsils, depsls, dpsipl, depspl; int i; /* Units of 0.1 microarcsecond to radians */ static const double U2R = ERFA_DAS2R / 1e7; /* ---------------------------------------- */ /* Fixed offsets in lieu of planetary terms */ /* ---------------------------------------- */ static const double DPPLAN = -0.135 * ERFA_DMAS2R; static const double DEPLAN = 0.388 * ERFA_DMAS2R; /* --------------------------------------------------- */ /* Luni-solar nutation: argument and term coefficients */ /* --------------------------------------------------- */ /* The units for the sine and cosine coefficients are */ /* 0.1 microarcsec and the same per Julian century */ static const struct { int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */ double ps,pst,pc; /* longitude sin, t*sin, cos coefficients */ double ec,ect,es; /* obliquity cos, t*cos, sin coefficients */ } x[] = { /* 1-10 */ { 0, 0, 0, 0,1, -172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0}, { 0, 0, 2,-2,2, -13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0}, { 0, 0, 2, 0,2,-2276413.0,-234.0, 2796.0, 978459.0,-485.0,1374.0}, { 0, 0, 0, 0,2,2074554.0, 207.0, -698.0,-897492.0, 470.0,-291.0}, { 0, 1, 0, 0,0,1475877.0,-3633.0,11817.0, 73871.0,-184.0,-1924.0}, { 0, 1, 2,-2,2,-516821.0, 1226.0, -524.0, 224386.0,-677.0,-174.0}, { 1, 0, 0, 0,0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0}, { 0, 0, 2, 0,1,-387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0}, { 1, 0, 2, 0,2,-301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0}, { 0,-1, 2,-2,2, 215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0}, /* 11-20 */ { 0, 0, 2,-2,1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0}, {-1, 0, 2, 0,2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0}, {-1, 0, 0, 2,0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0}, { 1, 0, 0, 0,1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0}, {-1, 0, 0, 0,1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0}, {-1, 0, 2, 2,2, -59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0}, { 1, 0, 2, 0,1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0}, {-2, 0, 2, 0,1, 45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0}, { 0, 0, 0, 2,0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0}, { 0, 0, 2, 2,2, -38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0}, /* 21-30 */ { 0,-2, 2,-2,2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0}, {-2, 0, 0, 2,0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0}, { 2, 0, 2, 0,2, -31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0}, { 1, 0, 2,-2,2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0}, {-1, 0, 2, 0,1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0}, { 2, 0, 0, 0,0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0}, { 0, 0, 2, 0,0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0}, { 0, 1, 0, 0,1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0}, {-1, 0, 0, 2,1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0}, { 0, 2, 2,-2,2, -15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0}, /* 31-40 */ { 0, 0,-2, 2,0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0}, { 1, 0, 0,-2,1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0}, { 0,-1, 0, 0,1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0}, {-1, 0, 2, 2,1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0}, { 0, 2, 0, 0,0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0}, { 1, 0, 2, 2,2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0}, {-2, 0, 2, 0,0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0}, { 0, 1, 2, 0,2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0}, { 0, 0, 2, 2,1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0}, { 0,-1, 2, 0,2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0}, /* 41-50 */ { 0, 0, 0, 2,1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0}, { 1, 0, 2,-2,1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0}, { 2, 0, 2,-2,2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0}, {-2, 0, 0, 2,1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0}, { 2, 0, 2, 0,1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0}, { 0,-1, 2,-2,1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0}, { 0, 0, 0,-2,1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0}, {-1,-1, 0, 2,0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0}, { 2, 0, 0,-2,1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0}, { 1, 0, 0, 2,0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0}, /* 51-60 */ { 0, 1, 2,-2,1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0}, { 1,-1, 0, 0,0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0}, {-2, 0, 2, 0,2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0}, { 3, 0, 2, 0,2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0}, { 0,-1, 0, 2,0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0}, { 1,-1, 2, 0,2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0}, { 0, 0, 0, 1,0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0}, {-1,-1, 2, 2,2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0}, {-1, 0, 2, 0,0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0}, { 0,-1, 2, 2,2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0}, /* 61-70 */ {-2, 0, 0, 0,1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0}, { 1, 1, 2, 0,2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0}, { 2, 0, 0, 0,1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0}, {-1, 1, 0, 1,0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0}, { 1, 1, 0, 0,0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0}, { 1, 0, 2, 0,0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0}, {-1, 0, 2,-2,1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0}, { 1, 0, 0, 0,2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0}, {-1, 0, 0, 1,0, 4026.0, 0.0, -353.0, -553.0, 0.0,-139.0}, { 0, 0, 2, 1,2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0}, /* 71-77 */ {-1, 0, 2, 4,2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0}, {-1, 1, 0, 1,1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0}, { 0,-2, 2,-2,1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0}, { 1, 0, 2, 2,1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0}, {-2, 0, 2, 2,2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0}, {-1, 0, 0, 0,2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0}, { 1, 1, 2,-2,2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0} }; /* Number of terms in the series */ const int NLS = (int) (sizeof x / sizeof x[0]); /*--------------------------------------------------------------------*/ /* Interval between fundamental epoch J2000.0 and given date (JC). */ t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC; /* --------------------*/ /* LUNI-SOLAR NUTATION */ /* --------------------*/ /* Fundamental (Delaunay) arguments from Simon et al. (1994) */ /* Mean anomaly of the Moon. */ el = fmod(485868.249036 + (1717915923.2178) * t, ERFA_TURNAS) * ERFA_DAS2R; /* Mean anomaly of the Sun. */ elp = fmod(1287104.79305 + (129596581.0481) * t, ERFA_TURNAS) * ERFA_DAS2R; /* Mean argument of the latitude of the Moon. */ f = fmod(335779.526232 + (1739527262.8478) * t, ERFA_TURNAS) * ERFA_DAS2R; /* Mean elongation of the Moon from the Sun. */ d = fmod(1072260.70369 + (1602961601.2090) * t, ERFA_TURNAS) * ERFA_DAS2R; /* Mean longitude of the ascending node of the Moon. */ om = fmod(450160.398036 + (-6962890.5431) * t, ERFA_TURNAS) * ERFA_DAS2R; /* Initialize the nutation values. */ dp = 0.0; de = 0.0; /* Summation of luni-solar nutation series (smallest terms first). */ for (i = NLS-1; i >= 0; i--) { /* Argument and functions. */ arg = fmod( (double)x[i].nl * el + (double)x[i].nlp * elp + (double)x[i].nf * f + (double)x[i].nd * d + (double)x[i].nom * om, ERFA_D2PI ); sarg = sin(arg); carg = cos(arg); /* Term. */ dp += (x[i].ps + x[i].pst * t) * sarg + x[i].pc * carg; de += (x[i].ec + x[i].ect * t) * carg + x[i].es * sarg; } /* Convert from 0.1 microarcsec units to radians. */ dpsils = dp * U2R; depsls = de * U2R; /* ------------------------------*/ /* IN LIEU OF PLANETARY NUTATION */ /* ------------------------------*/ /* Fixed offset to correct for missing terms in truncated series. */ dpsipl = DPPLAN; depspl = DEPLAN; /* --------*/ /* RESULTS */ /* --------*/ /* Add luni-solar and planetary components. */ *dpsi = dpsils + dpsipl; *deps = depsls + depspl; return; } /*---------------------------------------------------------------------- ** ** ** Copyright (C) 2013-2017, NumFOCUS Foundation. ** All rights reserved. ** ** This library is derived, with permission, from the International ** Astronomical Union's "Standards of Fundamental Astronomy" library, ** available from http://www.iausofa.org. ** ** The ERFA version is intended to retain identical functionality to ** the SOFA library, but made distinct through different function and ** file names, as set out in the SOFA license conditions. The SOFA ** original has a role as a reference standard for the IAU and IERS, ** and consequently redistribution is permitted only in its unaltered ** state. The ERFA version is not subject to this restriction and ** therefore can be included in distributions which do not support the ** concept of "read only" software. ** ** Although the intent is to replicate the SOFA API (other than ** replacement of prefix names) and results (with the exception of ** bugs; any that are discovered will be fixed), SOFA is not ** responsible for any errors found in this version of the library. ** ** If you wish to acknowledge the SOFA heritage, please acknowledge ** that you are using a library derived from SOFA, rather than SOFA ** itself. ** ** ** TERMS AND CONDITIONS ** ** Redistribution and use in source and binary forms, with or without ** modification, are permitted provided that the following conditions ** are met: ** ** 1 Redistributions of source code must retain the above copyright ** notice, this list of conditions and the following disclaimer. ** ** 2 Redistributions in binary form must reproduce the above copyright ** notice, this list of conditions and the following disclaimer in ** the documentation and/or other materials provided with the ** distribution. ** ** 3 Neither the name of the Standards Of Fundamental Astronomy Board, ** the International Astronomical Union nor the names of its ** contributors may be used to endorse or promote products derived ** from this software without specific prior written permission. ** ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ** POSSIBILITY OF SUCH DAMAGE. ** */