diff options
Diffstat (limited to 'ast/erfa/plan94.c')
| -rw-r--r-- | ast/erfa/plan94.c | 523 |
1 files changed, 523 insertions, 0 deletions
diff --git a/ast/erfa/plan94.c b/ast/erfa/plan94.c new file mode 100644 index 0000000..7191204 --- /dev/null +++ b/ast/erfa/plan94.c @@ -0,0 +1,523 @@ +#include "erfa.h" + +int eraPlan94(double date1, double date2, int np, double pv[2][3]) +/* +** - - - - - - - - - - +** e r a P l a n 9 4 +** - - - - - - - - - - +** +** Approximate heliocentric position and velocity of a nominated major +** planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or +** Neptune (but not the Earth itself). +** +** Given: +** date1 double TDB date part A (Note 1) +** date2 double TDB date part B (Note 1) +** np int planet (1=Mercury, 2=Venus, 3=EMB, 4=Mars, +** 5=Jupiter, 6=Saturn, 7=Uranus, 8=Neptune) +** +** Returned (argument): +** pv double[2][3] planet p,v (heliocentric, J2000.0, AU,AU/d) +** +** Returned (function value): +** int status: -1 = illegal NP (outside 1-8) +** 0 = OK +** +1 = warning: year outside 1000-3000 +** +2 = warning: failed to converge +** +** Notes: +** +** 1) The date date1+date2 is in the TDB time scale (in practice TT can +** be used) and is a Julian Date, apportioned in any convenient way +** between the two arguments. For example, JD(TDB)=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. The limited +** accuracy of the present algorithm is such that any of the methods +** is satisfactory. +** +** 2) If an np value outside the range 1-8 is supplied, an error status +** (function value -1) is returned and the pv vector set to zeroes. +** +** 3) For np=3 the result is for the Earth-Moon Barycenter. To obtain +** the heliocentric position and velocity of the Earth, use instead +** the ERFA function eraEpv00. +** +** 4) On successful return, the array pv contains the following: +** +** pv[0][0] x } +** pv[0][1] y } heliocentric position, AU +** pv[0][2] z } +** +** pv[1][0] xdot } +** pv[1][1] ydot } heliocentric velocity, AU/d +** pv[1][2] zdot } +** +** The reference frame is equatorial and is with respect to the +** mean equator and equinox of epoch J2000.0. +** +** 5) The algorithm is due to J.L. Simon, P. Bretagnon, J. Chapront, +** M. Chapront-Touze, G. Francou and J. Laskar (Bureau des +** Longitudes, Paris, France). From comparisons with JPL +** ephemeris DE102, they quote the following maximum errors +** over the interval 1800-2050: +** +** L (arcsec) B (arcsec) R (km) +** +** Mercury 4 1 300 +** Venus 5 1 800 +** EMB 6 1 1000 +** Mars 17 1 7700 +** Jupiter 71 5 76000 +** Saturn 81 13 267000 +** Uranus 86 7 712000 +** Neptune 11 1 253000 +** +** Over the interval 1000-3000, they report that the accuracy is no +** worse than 1.5 times that over 1800-2050. Outside 1000-3000 the +** accuracy declines. +** +** Comparisons of the present function with the JPL DE200 ephemeris +** give the following RMS errors over the interval 1960-2025: +** +** position (km) velocity (m/s) +** +** Mercury 334 0.437 +** Venus 1060 0.855 +** EMB 2010 0.815 +** Mars 7690 1.98 +** Jupiter 71700 7.70 +** Saturn 199000 19.4 +** Uranus 564000 16.4 +** Neptune 158000 14.4 +** +** Comparisons against DE200 over the interval 1800-2100 gave the +** following maximum absolute differences. (The results using +** DE406 were essentially the same.) +** +** L (arcsec) B (arcsec) R (km) Rdot (m/s) +** +** Mercury 7 1 500 0.7 +** Venus 7 1 1100 0.9 +** EMB 9 1 1300 1.0 +** Mars 26 1 9000 2.5 +** Jupiter 78 6 82000 8.2 +** Saturn 87 14 263000 24.6 +** Uranus 86 7 661000 27.4 +** Neptune 11 2 248000 21.4 +** +** 6) The present ERFA re-implementation of the original Simon et al. +** Fortran code differs from the original in the following respects: +** +** * C instead of Fortran. +** +** * The date is supplied in two parts. +** +** * The result is returned only in equatorial Cartesian form; +** the ecliptic longitude, latitude and radius vector are not +** returned. +** +** * The result is in the J2000.0 equatorial frame, not ecliptic. +** +** * More is done in-line: there are fewer calls to subroutines. +** +** * Different error/warning status values are used. +** +** * A different Kepler's-equation-solver is used (avoiding +** use of double precision complex). +** +** * Polynomials in t are nested to minimize rounding errors. +** +** * Explicit double constants are used to avoid mixed-mode +** expressions. +** +** None of the above changes affects the result significantly. +** +** 7) The returned status indicates the most serious condition +** encountered during execution of the function. Illegal np is +** considered the most serious, overriding failure to converge, +** which in turn takes precedence over the remote date warning. +** +** Called: +** eraAnp normalize angle into range 0 to 2pi +** +** Reference: Simon, J.L, Bretagnon, P., Chapront, J., +** Chapront-Touze, M., Francou, G., and Laskar, J., +** Astron. Astrophys. 282, 663 (1994). +** +** Copyright (C) 2013-2014, NumFOCUS Foundation. +** Derived, with permission, from the SOFA library. See notes at end of file. +*/ +{ +/* Gaussian constant */ + static const double GK = 0.017202098950; + +/* Sin and cos of J2000.0 mean obliquity (IAU 1976) */ + static const double SINEPS = 0.3977771559319137; + static const double COSEPS = 0.9174820620691818; + +/* Maximum number of iterations allowed to solve Kepler's equation */ + static const int KMAX = 10; + + int jstat, i, k; + double t, da, dl, de, dp, di, dom, dmu, arga, argl, am, + ae, dae, ae2, at, r, v, si2, xq, xp, tl, xsw, + xcw, xm2, xf, ci2, xms, xmc, xpxq2, x, y, z; + +/* Planetary inverse masses */ + static const double amas[] = { 6023600.0, /* Mercury */ + 408523.5, /* Venus */ + 328900.5, /* EMB */ + 3098710.0, /* Mars */ + 1047.355, /* Jupiter */ + 3498.5, /* Saturn */ + 22869.0, /* Uranus */ + 19314.0 }; /* Neptune */ + +/* +** Tables giving the mean Keplerian elements, limited to t^2 terms: +** +** a semi-major axis (AU) +** dlm mean longitude (degree and arcsecond) +** e eccentricity +** pi longitude of the perihelion (degree and arcsecond) +** dinc inclination (degree and arcsecond) +** omega longitude of the ascending node (degree and arcsecond) +*/ + + static const double a[][3] = { + { 0.3870983098, 0.0, 0.0 }, /* Mercury */ + { 0.7233298200, 0.0, 0.0 }, /* Venus */ + { 1.0000010178, 0.0, 0.0 }, /* EMB */ + { 1.5236793419, 3e-10, 0.0 }, /* Mars */ + { 5.2026032092, 19132e-10, -39e-10 }, /* Jupiter */ + { 9.5549091915, -0.0000213896, 444e-10 }, /* Saturn */ + { 19.2184460618, -3716e-10, 979e-10 }, /* Uranus */ + { 30.1103868694, -16635e-10, 686e-10 } /* Neptune */ + }; + + static const double dlm[][3] = { + { 252.25090552, 5381016286.88982, -1.92789 }, + { 181.97980085, 2106641364.33548, 0.59381 }, + { 100.46645683, 1295977422.83429, -2.04411 }, + { 355.43299958, 689050774.93988, 0.94264 }, + { 34.35151874, 109256603.77991, -30.60378 }, + { 50.07744430, 43996098.55732, 75.61614 }, + { 314.05500511, 15424811.93933, -1.75083 }, + { 304.34866548, 7865503.20744, 0.21103 } + }; + + static const double e[][3] = { + { 0.2056317526, 0.0002040653, -28349e-10 }, + { 0.0067719164, -0.0004776521, 98127e-10 }, + { 0.0167086342, -0.0004203654, -0.0000126734 }, + { 0.0934006477, 0.0009048438, -80641e-10 }, + { 0.0484979255, 0.0016322542, -0.0000471366 }, + { 0.0555481426, -0.0034664062, -0.0000643639 }, + { 0.0463812221, -0.0002729293, 0.0000078913 }, + { 0.0094557470, 0.0000603263, 0.0 } + }; + + static const double pi[][3] = { + { 77.45611904, 5719.11590, -4.83016 }, + { 131.56370300, 175.48640, -498.48184 }, + { 102.93734808, 11612.35290, 53.27577 }, + { 336.06023395, 15980.45908, -62.32800 }, + { 14.33120687, 7758.75163, 259.95938 }, + { 93.05723748, 20395.49439, 190.25952 }, + { 173.00529106, 3215.56238, -34.09288 }, + { 48.12027554, 1050.71912, 27.39717 } + }; + + static const double dinc[][3] = { + { 7.00498625, -214.25629, 0.28977 }, + { 3.39466189, -30.84437, -11.67836 }, + { 0.0, 469.97289, -3.35053 }, + { 1.84972648, -293.31722, -8.11830 }, + { 1.30326698, -71.55890, 11.95297 }, + { 2.48887878, 91.85195, -17.66225 }, + { 0.77319689, -60.72723, 1.25759 }, + { 1.76995259, 8.12333, 0.08135 } + }; + + static const double omega[][3] = { + { 48.33089304, -4515.21727, -31.79892 }, + { 76.67992019, -10008.48154, -51.32614 }, + { 174.87317577, -8679.27034, 15.34191 }, + { 49.55809321, -10620.90088, -230.57416 }, + { 100.46440702, 6362.03561, 326.52178 }, + { 113.66550252, -9240.19942, -66.23743 }, + { 74.00595701, 2669.15033, 145.93964 }, + { 131.78405702, -221.94322, -0.78728 } + }; + +/* Tables for trigonometric terms to be added to the mean elements of */ +/* the semi-major axes */ + + static const double kp[][9] = { + { 69613, 75645, 88306, 59899, 15746, 71087, 142173, 3086, 0 }, + { 21863, 32794, 26934, 10931, 26250, 43725, 53867, 28939, 0 }, + { 16002, 21863, 32004, 10931, 14529, 16368, 15318, 32794, 0 }, + { 6345, 7818, 15636, 7077, 8184, 14163, 1107, 4872, 0 }, + { 1760, 1454, 1167, 880, 287, 2640, 19, 2047, 1454 }, + { 574, 0, 880, 287, 19, 1760, 1167, 306, 574 }, + { 204, 0, 177, 1265, 4, 385, 200, 208, 204 }, + { 0, 102, 106, 4, 98, 1367, 487, 204, 0 } + }; + + static const double ca[][9] = { + { 4, -13, 11, -9, -9, -3, -1, 4, 0 }, + { -156, 59, -42, 6, 19, -20, -10, -12, 0 }, + { 64, -152, 62, -8, 32, -41, 19, -11, 0 }, + { 124, 621, -145, 208, 54, -57, 30, 15, 0 }, + { -23437, -2634, 6601, 6259, -1507,-1821, 2620, -2115, -1489 }, + { 62911,-119919, 79336,17814,-24241,12068, 8306, -4893, 8902 }, + { 389061,-262125,-44088, 8387,-22976,-2093, -615, -9720, 6633 }, + { -412235,-157046,-31430,37817, -9740, -13, -7449, 9644, 0 } + }; + + static const double sa[][9] = { + { -29, -1, 9, 6, -6, 5, 4, 0, 0 }, + { -48, -125, -26, -37, 18, -13, -20, -2, 0 }, + { -150, -46, 68, 54, 14, 24, -28, 22, 0 }, + { -621, 532, -694, -20, 192, -94, 71, -73, 0 }, + { -14614,-19828, -5869, 1881, -4372, -2255, 782, 930, 913 }, + { 139737, 0, 24667, 51123, -5102, 7429, -4095, -1976, -9566 }, + { -138081, 0, 37205,-49039,-41901,-33872,-27037,-12474, 18797 }, + { 0, 28492,133236, 69654, 52322,-49577,-26430, -3593, 0 } + }; + +/* Tables giving the trigonometric terms to be added to the mean */ +/* elements of the mean longitudes */ + + static const double kq[][10] = { + { 3086,15746,69613,59899,75645,88306, 12661, 2658, 0, 0 }, + { 21863,32794,10931, 73, 4387,26934, 1473, 2157, 0, 0 }, + { 10,16002,21863,10931, 1473,32004, 4387, 73, 0, 0 }, + { 10, 6345, 7818, 1107,15636, 7077, 8184, 532, 10, 0 }, + { 19, 1760, 1454, 287, 1167, 880, 574, 2640, 19, 1454 }, + { 19, 574, 287, 306, 1760, 12, 31, 38, 19, 574 }, + { 4, 204, 177, 8, 31, 200, 1265, 102, 4, 204 }, + { 4, 102, 106, 8, 98, 1367, 487, 204, 4, 102 } + }; + + static const double cl[][10] = { + { 21, -95, -157, 41, -5, 42, 23, 30, 0, 0 }, + { -160, -313, -235, 60, -74, -76, -27, 34, 0, 0 }, + { -325, -322, -79, 232, -52, 97, 55, -41, 0, 0 }, + { 2268, -979, 802, 602, -668, -33, 345, 201, -55, 0 }, + { 7610, -4997,-7689,-5841,-2617, 1115,-748,-607, 6074, 354 }, + { -18549, 30125,20012, -730, 824, 23,1289,-352, -14767, -2062 }, + { -135245,-14594, 4197,-4030,-5630,-2898,2540,-306, 2939, 1986 }, + { 89948, 2103, 8963, 2695, 3682, 1648, 866,-154, -1963, -283 } + }; + + static const double sl[][10] = { + { -342, 136, -23, 62, 66, -52, -33, 17, 0, 0 }, + { 524, -149, -35, 117, 151, 122, -71, -62, 0, 0 }, + { -105, -137, 258, 35, -116, -88,-112, -80, 0, 0 }, + { 854, -205, -936, -240, 140, -341, -97, -232, 536, 0 }, + { -56980, 8016, 1012, 1448,-3024,-3710, 318, 503, 3767, 577 }, + { 138606,-13478,-4964, 1441,-1319,-1482, 427, 1236, -9167, -1918 }, + { 71234,-41116, 5334,-4935,-1848, 66, 434, -1748, 3780, -701 }, + { -47645, 11647, 2166, 3194, 679, 0,-244, -419, -2531, 48 } + }; + +/*--------------------------------------------------------------------*/ + +/* Validate the planet number. */ + if ((np < 1) || (np > 8)) { + jstat = -1; + + /* Reset the result in case of failure. */ + for (k = 0; k < 2; k++) { + for (i = 0; i < 3; i++) { + pv[k][i] = 0.0; + } + } + + } else { + + /* Decrement the planet number to start at zero. */ + np--; + + /* Time: Julian millennia since J2000.0. */ + t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJM; + + /* OK status unless remote date. */ + jstat = fabs(t) <= 1.0 ? 0 : 1; + + /* Compute the mean elements. */ + da = a[np][0] + + (a[np][1] + + a[np][2] * t) * t; + dl = (3600.0 * dlm[np][0] + + (dlm[np][1] + + dlm[np][2] * t) * t) * ERFA_DAS2R; + de = e[np][0] + + ( e[np][1] + + e[np][2] * t) * t; + dp = eraAnpm((3600.0 * pi[np][0] + + (pi[np][1] + + pi[np][2] * t) * t) * ERFA_DAS2R); + di = (3600.0 * dinc[np][0] + + (dinc[np][1] + + dinc[np][2] * t) * t) * ERFA_DAS2R; + dom = eraAnpm((3600.0 * omega[np][0] + + (omega[np][1] + + omega[np][2] * t) * t) * ERFA_DAS2R); + + /* Apply the trigonometric terms. */ + dmu = 0.35953620 * t; + for (k = 0; k < 8; k++) { + arga = kp[np][k] * dmu; + argl = kq[np][k] * dmu; + da += (ca[np][k] * cos(arga) + + sa[np][k] * sin(arga)) * 1e-7; + dl += (cl[np][k] * cos(argl) + + sl[np][k] * sin(argl)) * 1e-7; + } + arga = kp[np][8] * dmu; + da += t * (ca[np][8] * cos(arga) + + sa[np][8] * sin(arga)) * 1e-7; + for (k = 8; k < 10; k++) { + argl = kq[np][k] * dmu; + dl += t * (cl[np][k] * cos(argl) + + sl[np][k] * sin(argl)) * 1e-7; + } + dl = fmod(dl, ERFA_D2PI); + + /* Iterative soln. of Kepler's equation to get eccentric anomaly. */ + am = dl - dp; + ae = am + de * sin(am); + k = 0; + dae = 1.0; + while (k < KMAX && fabs(dae) > 1e-12) { + dae = (am - ae + de * sin(ae)) / (1.0 - de * cos(ae)); + ae += dae; + k++; + if (k == KMAX-1) jstat = 2; + } + + /* True anomaly. */ + ae2 = ae / 2.0; + at = 2.0 * atan2(sqrt((1.0 + de) / (1.0 - de)) * sin(ae2), + cos(ae2)); + + /* Distance (AU) and speed (radians per day). */ + r = da * (1.0 - de * cos(ae)); + v = GK * sqrt((1.0 + 1.0 / amas[np]) / (da * da * da)); + + si2 = sin(di / 2.0); + xq = si2 * cos(dom); + xp = si2 * sin(dom); + tl = at + dp; + xsw = sin(tl); + xcw = cos(tl); + xm2 = 2.0 * (xp * xcw - xq * xsw); + xf = da / sqrt(1 - de * de); + ci2 = cos(di / 2.0); + xms = (de * sin(dp) + xsw) * xf; + xmc = (de * cos(dp) + xcw) * xf; + xpxq2 = 2 * xp * xq; + + /* Position (J2000.0 ecliptic x,y,z in AU). */ + x = r * (xcw - xm2 * xp); + y = r * (xsw + xm2 * xq); + z = r * (-xm2 * ci2); + + /* Rotate to equatorial. */ + pv[0][0] = x; + pv[0][1] = y * COSEPS - z * SINEPS; + pv[0][2] = y * SINEPS + z * COSEPS; + + /* Velocity (J2000.0 ecliptic xdot,ydot,zdot in AU/d). */ + x = v * (( -1.0 + 2.0 * xp * xp) * xms + xpxq2 * xmc); + y = v * (( 1.0 - 2.0 * xq * xq) * xmc - xpxq2 * xms); + z = v * (2.0 * ci2 * (xp * xms + xq * xmc)); + + /* Rotate to equatorial. */ + pv[1][0] = x; + pv[1][1] = y * COSEPS - z * SINEPS; + pv[1][2] = y * SINEPS + z * COSEPS; + + } + +/* Return the status. */ + return jstat; + +} +/*---------------------------------------------------------------------- +** +** +** Copyright (C) 2013-2014, 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. +** +*/ |