void iauPn00a(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - - ** i a u P n 0 0 a ** - - - - - - - - - ** ** Precession-nutation, IAU 2000A model: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based ** use indirectly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation (Note 2) ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Notes 8,9) ** ** 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 (luni-solar + planetary, IAU 2000A) in ** longitude and obliquity are in radians and with respect to the ** equinox and ecliptic of date. Free core nutation is omitted; ** for the utmost accuracy, use the iauPn00 function, where the ** nutation components are caller-specified. For faster but ** slightly less accurate results, use the iauPn00b function. ** ** 3) The mean obliquity is consistent with the IAU 2000 precession. ** ** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean ** equator and equinox by applying frame bias. ** ** 5) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean equator and equinox ** of date to true equator and equinox of date by applying the ** nutation (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true equator and ** equinox of date. It is the product rn x rbp, applying frame ** bias, precession and nutation in that order. ** ** 9) The X,Y,Z coordinates of the IAU 2000A Celestial Intermediate ** Pole are elements (3,1-3) of the GCRS-to-true matrix, ** i.e. rbpn[2][0-2]. ** ** 10) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the order given. ** ** Called: ** iauNut00a nutation, IAU 2000A ** iauPn00 bias/precession/nutation results, IAU 2000 ** ** Reference: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** This revision: 2013 November 14 ** ** SOFA release 2017-04-20 ** ** Copyright (C) 2017 IAU SOFA Board. See notes at end. */ { /* Nutation. */ iauNut00a(date1, date2, dpsi, deps); /* Remaining results. */ iauPn00(date1, date2, *dpsi, *deps, epsa, rb, rp, rbp, rn, rbpn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2017 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }
void iauPn00b(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - - ** i a u P n 0 0 b ** - - - - - - - - - ** ** Precession-nutation, IAU 2000B model: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based ** use indirectly. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation (Note 2) ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Notes 8,9) ** ** 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 (luni-solar + planetary, IAU 2000B) in ** longitude and obliquity are in radians and with respect to the ** equinox and ecliptic of date. For more accurate results, but ** at the cost of increased computation, use the iauPn00a function. ** For the utmost accuracy, use the iauPn00 function, where the ** nutation components are caller-specified. ** ** 3) The mean obliquity is consistent with the IAU 2000 precession. ** ** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean ** equator and equinox by applying frame bias. ** ** 5) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean equator and equinox ** of date to true equator and equinox of date by applying the ** nutation (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true equator and ** equinox of date. It is the product rn x rbp, applying frame ** bias, precession and nutation in that order. ** ** 9) The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate ** Pole are elements (3,1-3) of the matrix rbpn. ** ** 10) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the stated order. ** ** Called: ** iauNut00b nutation, IAU 2000B ** iauPn00 bias/precession/nutation results, IAU 2000 ** ** Reference: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003). ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** This revision: 2010 January 18 ** ** Original version 2012-03-01 ** ** Copyright (C) 2013 Naoki Arita. See notes at end. */ { /* Nutation. */ iauNut00b(date1, date2, dpsi, deps); /* Remaining results. */ iauPn00(date1, date2, *dpsi, *deps, epsa, rb, rp, rbp, rn, rbpn); return; /*---------------------------------------------------------------------- ** ** Celes is a wrapper of the SOFA Library for Ruby. ** ** This file is redistributed and relicensed in accordance with ** the SOFA Software License (http://www.iausofa.org/tandc.html). ** ** The original library is available from IAU Standards of ** Fundamental Astronomy (http://www.iausofa.org/). ** ** ** ** ** ** Copyright (C) 2013, Naoki Arita ** All rights reserved. ** ** 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. ** **--------------------------------------------------------------------*/ }
void iauC2tpe(double tta, double ttb, double uta, double utb, double dpsi, double deps, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - ** i a u C 2 t p e ** - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1, ** the nutation and the polar motion. IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** dpsi,deps double nutation (Note 2) ** xp,yp double coordinates of the pole (radians, Note 3) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 4) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any of ** these ways, among others: ** ** uta utb ** ** 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 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The caller is responsible for providing the nutation components; ** they are in longitude and obliquity, in radians and are with ** respect to the equinox and ecliptic of date. For high-accuracy ** applications, free core nutation should be included as well as ** any other relevant corrections to the position of the CIP. ** ** 3) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 4) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(GST) * RBPN * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), RBPN is the ** bias-precession-nutation matrix, GST is the Greenwich (apparent) ** Sidereal Time and RPOM is the polar motion matrix. ** ** 5) Although its name does not include "00", This function is in fact ** specific to the IAU 2000 models. ** ** Called: ** iauPn00 bias/precession/nutation results, IAU 2000 ** iauGmst00 Greenwich mean sidereal time, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauEe00 equation of the equinoxes, IAU 2000 ** iauPom00 polar motion matrix ** iauC2teqx form equinox-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2017-04-20 ** ** Copyright (C) 2017 IAU SOFA Board. See notes at end. */ { double epsa, rb[3][3], rp[3][3], rbp[3][3], rn[3][3], rbpn[3][3], gmst, ee, sp, rpom[3][3]; /* Form the celestial-to-true matrix for this TT. */ iauPn00(tta, ttb, dpsi, deps, &epsa, rb, rp, rbp, rn, rbpn); /* Predict the Greenwich Mean Sidereal Time for this UT1 and TT. */ gmst = iauGmst00(uta, utb, tta, ttb); /* Predict the equation of the equinoxes given TT and nutation. */ ee = iauEe00(tta, ttb, epsa, dpsi); /* Estimate s'. */ sp = iauSp00(tta, ttb); /* Form the polar motion matrix. */ iauPom00(xp, yp, sp, rpom); /* Combine to form the celestial-to-terrestrial matrix. */ iauC2teqx(rbpn, gmst + ee, rpom, rc2t); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2017 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }