#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.
**
*/