#include "sofam.h" int iauPlan94(double date1, double date2, int np, double pv[2][3]) /* ** - - - - - - - - - - ** i a u P l a n 9 4 ** - - - - - - - - - - ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** 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[3][2] planet pos,vel (heliocentric, J2000, 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 SOFA function iauEpv00. ** ** 4) On successful return, the array pv contains the following: ** ** pv[0][0] x } ** pv[1][0] y } heliocentric position, AU ** pv[2][0] z } ** ** pv[0][1] xdot } ** pv[1][1] ydot } heliocentric velocity, AU/d ** pv[2][1] zdot } ** ** The reference frame is equatorial and is with respect to the ** mean equator and equinox of epoch J2000. ** ** 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 SOFA 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 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: ** iauAnp 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). ** ** This revision: 2008 May 27 ** ** Copyright (C) 2008 IAU SOFA Review Board. See notes at end. */ { /* Gaussian constant */ static const double GK = 0.017202098950; /* Sin and cos of J2000 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. */ t = ((date1 - DJ00) + date2) / 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) * DAS2R; de = e[np][0] + ( e[np][1] + e[np][2] * t) * t; dp = iauAnpm((3600.0 * pi[np][0] + (pi[np][1] + pi[np][2] * t) * t) * DAS2R); di = (3600.0 * dinc[np][0] + (dinc[np][1] + dinc[np][2] * t) * t) * DAS2R; dom = iauAnpm((3600.0 * omega[np][0] + (omega[np][1] + omega[np][2] * t) * t) * 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, 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 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 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) 2008 ** Standards Of Fundamental Astronomy Review Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS ** WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Review Board ("the Board"). ** ** 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 adapt the SOFA software and its ** algorithms for your own purposes and you may copy and distribute ** a resulting "derived work" to others on a world-wide, royalty-free ** basis, provided that the derived work complies 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 contain ** software provided by SOFA or software that has been distributed ** by or endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon and/or differs from the ** original SOFA software. ** ** c) The name(s) of all routine(s) that you distribute shall differ ** from the SOFA names, even when the SOFA content has not been ** otherwise changed. ** ** d) The routine-naming prefix "iau" shall not be used. ** ** e) 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. ** ** f) 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. ** ** 4. In any published work or commercial products which includes ** results achieved by using the SOFA software, you shall acknowledge ** that the SOFA software was used in obtaining those results. ** ** 5. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or by ** inappropriate modification. ** ** 6. The SOFA software is provided "as is" and the Board makes no ** warranty as to its use or performance. The Board does not and ** cannot warrant the performance or results which the user may obtain ** by using the SOFA software. The Board 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 the Board be liable to the user for any consequential, ** incidental, or special damages, including any lost profits or lost ** savings, even if a Board representative has been advised of such ** damages, or for any claim by any third party. ** ** 7. 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. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** Internet email: sofa@rl.ac.uk ** Postal address: IAU SOFA Center ** Rutherford Appleton Laboratory ** Chilton, Didcot, Oxon OX11 0QX ** United Kingdom ** **---------------------------------------------------------------------*/ }