path: root/ast/erfa/dtdb.c

#include "erfa.h"

double eraDtdb(double date1, double date2,
               double ut, double elong, double u, double v)
/*
**  - - - - - - - -
**   e r a D t d b
**  - - - - - - - -
**
**  An approximation to TDB-TT, the difference between barycentric
**  dynamical time and terrestrial time, for an observer on the Earth.
**
**  The different time scales - proper, coordinate and realized - are
**  related to each other:
**
**            TAI             <-  physically realized
**             :
**          offset            <-  observed (nominally +32.184s)
**             :
**            TT              <-  terrestrial time
**             :
**    rate adjustment (L_G)   <-  definition of TT
**             :
**            TCG             <-  time scale for GCRS
**             :
**      "periodic" terms      <-  eraDtdb  is an implementation
**             :
**    rate adjustment (L_C)   <-  function of solar-system ephemeris
**             :
**            TCB             <-  time scale for BCRS
**             :
**    rate adjustment (-L_B)  <-  definition of TDB
**             :
**            TDB             <-  TCB scaled to track TT
**             :
**      "periodic" terms      <-  -eraDtdb is an approximation
**             :
**            TT              <-  terrestrial time
**
**  Adopted values for the various constants can be found in the IERS
**  Conventions (McCarthy & Petit 2003).
**
**  Given:
**     date1,date2   double  date, TDB (Notes 1-3)
**     ut            double  universal time (UT1, fraction of one day)
**     elong         double  longitude (east positive, radians)
**     u             double  distance from Earth spin axis (km)
**     v             double  distance north of equatorial plane (km)
**
**  Returned (function value):
**                   double  TDB-TT (seconds)
**
**  Notes:
**
**  1) The 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.
**
**     Although the date is, formally, barycentric dynamical time (TDB),
**     the terrestrial dynamical time (TT) can be used with no practical
**     effect on the accuracy of the prediction.
**
**  2) TT can be regarded as a coordinate time that is realized as an
**     offset of 32.184s from International Atomic Time, TAI.  TT is a
**     specific linear transformation of geocentric coordinate time TCG,
**     which is the time scale for the Geocentric Celestial Reference
**     System, GCRS.
**
**  3) TDB is a coordinate time, and is a specific linear transformation
**     of barycentric coordinate time TCB, which is the time scale for
**     the Barycentric Celestial Reference System, BCRS.
**
**  4) The difference TCG-TCB depends on the masses and positions of the
**     bodies of the solar system and the velocity of the Earth.  It is
**     dominated by a rate difference, the residual being of a periodic
**     character.  The latter, which is modeled by the present function,
**     comprises a main (annual) sinusoidal term of amplitude
**     approximately 0.00166 seconds, plus planetary terms up to about
**     20 microseconds, and lunar and diurnal terms up to 2 microseconds.
**     These effects come from the changing transverse Doppler effect
**     and gravitational red-shift as the observer (on the Earth's
**     surface) experiences variations in speed (with respect to the
**     BCRS) and gravitational potential.
**
**  5) TDB can be regarded as the same as TCB but with a rate adjustment
**     to keep it close to TT, which is convenient for many applications.
**     The history of successive attempts to define TDB is set out in
**     Resolution 3 adopted by the IAU General Assembly in 2006, which
**     defines a fixed TDB(TCB) transformation that is consistent with
**     contemporary solar-system ephemerides.  Future ephemerides will
**     imply slightly changed transformations between TCG and TCB, which
**     could introduce a linear drift between TDB and TT;  however, any
**     such drift is unlikely to exceed 1 nanosecond per century.
**
**  6) The geocentric TDB-TT model used in the present function is that of
**     Fairhead & Bretagnon (1990), in its full form.  It was originally
**     supplied by Fairhead (private communications with P.T.Wallace,
**     1990) as a Fortran subroutine.  The present C function contains an
**     adaptation of the Fairhead code.  The numerical results are
**     essentially unaffected by the changes, the differences with
**     respect to the Fairhead & Bretagnon original being at the 1e-20 s
**     level.
**
**     The topocentric part of the model is from Moyer (1981) and
**     Murray (1983), with fundamental arguments adapted from
**     Simon et al. 1994.  It is an approximation to the expression
**     ( v / c ) . ( r / c ), where v is the barycentric velocity of
**     the Earth, r is the geocentric position of the observer and
**     c is the speed of light.
**
**     By supplying zeroes for u and v, the topocentric part of the
**     model can be nullified, and the function will return the Fairhead
**     & Bretagnon result alone.
**
**  7) During the interval 1950-2050, the absolute accuracy is better
**     than +/- 3 nanoseconds relative to time ephemerides obtained by
**     direct numerical integrations based on the JPL DE405 solar system
**     ephemeris.
**
**  8) It must be stressed that the present function is merely a model,
**     and that numerical integration of solar-system ephemerides is the
**     definitive method for predicting the relationship between TCG and
**     TCB and hence between TT and TDB.
**
**  References:
**
**     Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247
**     (1990).
**
**     IAU 2006 Resolution 3.
**
**     McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
**     IERS Technical Note No. 32, BKG (2004)
**
**     Moyer, T.D., Cel.Mech., 23, 33 (1981).
**
**     Murray, C.A., Vectorial Astrometry, Adam Hilger (1983).
**
**     Seidelmann, P.K. et al., Explanatory Supplement to the
**     Astronomical Almanac, Chapter 2, University Science Books (1992).
**
**     Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
**     Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994).
**
**  Copyright (C) 2013-2016, NumFOCUS Foundation.
**  Derived, with permission, from the SOFA library.  See notes at end of file.
*/
{
   double t, tsol, w, elsun, emsun, d, elj, els, wt, w0, w1, w2, w3, w4,
          wf, wj;
   int j;

/*
** =====================
** Fairhead et al. model
** =====================
**
** 787 sets of three coefficients.
**
** Each set is
**    amplitude (microseconds)
**      frequency (radians per Julian millennium since J2000.0)
**      phase (radians)
**
** Sets   1-474 are the T**0 terms
**  "   475-679  "   "  T**1
**  "   680-764  "   "  T**2
**  "   765-784  "   "  T**3
**  "   785-787  "   "  T**4
*/

   static const double fairhd[787][3] = {
   /* 1, 10 */
      { 1656.674564e-6,     6283.075849991,  6.240054195 },
      {   22.417471e-6,     5753.384884897,  4.296977442 },
      {   13.839792e-6,    12566.151699983,  6.196904410 },
      {    4.770086e-6,      529.690965095,  0.444401603 },
      {    4.676740e-6,     6069.776754553,  4.021195093 },
      {    2.256707e-6,      213.299095438,  5.543113262 },
      {    1.694205e-6,      -3.523118349,   5.025132748 },
      {    1.554905e-6,    77713.771467920,  5.198467090 },
      {    1.276839e-6,     7860.419392439,  5.988822341 },
      {    1.193379e-6,     5223.693919802,  3.649823730 },
   /* 11, 20 */
      {    1.115322e-6,     3930.209696220,  1.422745069 },
      {    0.794185e-6,    11506.769769794,  2.322313077 },
      {    0.447061e-6,       26.298319800,  3.615796498 },
      {    0.435206e-6,     -398.149003408,  4.349338347 },
      {    0.600309e-6,     1577.343542448,  2.678271909 },
      {    0.496817e-6,     6208.294251424,  5.696701824 },
      {    0.486306e-6,     5884.926846583,  0.520007179 },
      {    0.432392e-6,       74.781598567,  2.435898309 },
      {    0.468597e-6,     6244.942814354,  5.866398759 },
      {    0.375510e-6,     5507.553238667,  4.103476804 },
   /* 21, 30 */
      {    0.243085e-6,     -775.522611324,  3.651837925 },
      {    0.173435e-6,    18849.227549974,  6.153743485 },
      {    0.230685e-6,     5856.477659115,  4.773852582 },
      {    0.203747e-6,    12036.460734888,  4.333987818 },
      {    0.143935e-6,     -796.298006816,  5.957517795 },
      {    0.159080e-6,    10977.078804699,  1.890075226 },
      {    0.119979e-6,       38.133035638,  4.551585768 },
      {    0.118971e-6,     5486.777843175,  1.914547226 },
      {    0.116120e-6,     1059.381930189,  0.873504123 },
      {    0.137927e-6,    11790.629088659,  1.135934669 },
   /* 31, 40 */
      {    0.098358e-6,     2544.314419883,  0.092793886 },
      {    0.101868e-6,    -5573.142801634,  5.984503847 },
      {    0.080164e-6,      206.185548437,  2.095377709 },
      {    0.079645e-6,     4694.002954708,  2.949233637 },
      {    0.062617e-6,       20.775395492,  2.654394814 },
      {    0.075019e-6,     2942.463423292,  4.980931759 },
      {    0.064397e-6,     5746.271337896,  1.280308748 },
      {    0.063814e-6,     5760.498431898,  4.167901731 },
      {    0.048042e-6,     2146.165416475,  1.495846011 },
      {    0.048373e-6,      155.420399434,  2.251573730 },
   /* 41, 50 */
      {    0.058844e-6,      426.598190876,  4.839650148 },
      {    0.046551e-6,       -0.980321068,  0.921573539 },
      {    0.054139e-6,    17260.154654690,  3.411091093 },
      {    0.042411e-6,     6275.962302991,  2.869567043 },
      {    0.040184e-6,       -7.113547001,  3.565975565 },
      {    0.036564e-6,     5088.628839767,  3.324679049 },
      {    0.040759e-6,    12352.852604545,  3.981496998 },
      {    0.036507e-6,      801.820931124,  6.248866009 },
      {    0.036955e-6,     3154.687084896,  5.071801441 },
      {    0.042732e-6,      632.783739313,  5.720622217 },
   /* 51, 60 */
      {    0.042560e-6,   161000.685737473,  1.270837679 },
      {    0.040480e-6,    15720.838784878,  2.546610123 },
      {    0.028244e-6,    -6286.598968340,  5.069663519 },
      {    0.033477e-6,     6062.663207553,  4.144987272 },
      {    0.034867e-6,      522.577418094,  5.210064075 },
      {    0.032438e-6,     6076.890301554,  0.749317412 },
      {    0.030215e-6,     7084.896781115,  3.389610345 },
      {    0.029247e-6,   -71430.695617928,  4.183178762 },
      {    0.033529e-6,     9437.762934887,  2.404714239 },
      {    0.032423e-6,     8827.390269875,  5.541473556 },
   /* 61, 70 */
      {    0.027567e-6,     6279.552731642,  5.040846034 },
      {    0.029862e-6,    12139.553509107,  1.770181024 },
      {    0.022509e-6,    10447.387839604,  1.460726241 },
      {    0.020937e-6,     8429.241266467,  0.652303414 },
      {    0.020322e-6,      419.484643875,  3.735430632 },
      {    0.024816e-6,    -1194.447010225,  1.087136918 },
      {    0.025196e-6,     1748.016413067,  2.901883301 },
      {    0.021691e-6,    14143.495242431,  5.952658009 },
      {    0.017673e-6,     6812.766815086,  3.186129845 },
      {    0.022567e-6,     6133.512652857,  3.307984806 },
   /* 71, 80 */
      {    0.016155e-6,    10213.285546211,  1.331103168 },
      {    0.014751e-6,     1349.867409659,  4.308933301 },
      {    0.015949e-6,     -220.412642439,  4.005298270 },
      {    0.015974e-6,    -2352.866153772,  6.145309371 },
      {    0.014223e-6,    17789.845619785,  2.104551349 },
      {    0.017806e-6,       73.297125859,  3.475975097 },
      {    0.013671e-6,     -536.804512095,  5.971672571 },
      {    0.011942e-6,     8031.092263058,  2.053414715 },
      {    0.014318e-6,    16730.463689596,  3.016058075 },
      {    0.012462e-6,      103.092774219,  1.737438797 },
   /* 81, 90 */
      {    0.010962e-6,        3.590428652,  2.196567739 },
      {    0.015078e-6,    19651.048481098,  3.969480770 },
      {    0.010396e-6,      951.718406251,  5.717799605 },
      {    0.011707e-6,    -4705.732307544,  2.654125618 },
      {    0.010453e-6,     5863.591206116,  1.913704550 },
      {    0.012420e-6,     4690.479836359,  4.734090399 },
      {    0.011847e-6,     5643.178563677,  5.489005403 },
      {    0.008610e-6,     3340.612426700,  3.661698944 },
      {    0.011622e-6,     5120.601145584,  4.863931876 },
      {    0.010825e-6,      553.569402842,  0.842715011 },
   /* 91, 100 */
      {    0.008666e-6,     -135.065080035,  3.293406547 },
      {    0.009963e-6,      149.563197135,  4.870690598 },
      {    0.009858e-6,     6309.374169791,  1.061816410 },
      {    0.007959e-6,      316.391869657,  2.465042647 },
      {    0.010099e-6,      283.859318865,  1.942176992 },
      {    0.007147e-6,     -242.728603974,  3.661486981 },
      {    0.007505e-6,     5230.807466803,  4.920937029 },
      {    0.008323e-6,    11769.853693166,  1.229392026 },
      {    0.007490e-6,    -6256.777530192,  3.658444681 },
      {    0.009370e-6,   149854.400134205,  0.673880395 },
   /* 101, 110 */
      {    0.007117e-6,       38.027672636,  5.294249518 },
      {    0.007857e-6,    12168.002696575,  0.525733528 },
      {    0.007019e-6,     6206.809778716,  0.837688810 },
      {    0.006056e-6,      955.599741609,  4.194535082 },
      {    0.008107e-6,    13367.972631107,  3.793235253 },
      {    0.006731e-6,     5650.292110678,  5.639906583 },
      {    0.007332e-6,       36.648562930,  0.114858677 },
      {    0.006366e-6,     4164.311989613,  2.262081818 },
      {    0.006858e-6,     5216.580372801,  0.642063318 },
      {    0.006919e-6,     6681.224853400,  6.018501522 },
   /* 111, 120 */
      {    0.006826e-6,     7632.943259650,  3.458654112 },
      {    0.005308e-6,    -1592.596013633,  2.500382359 },
      {    0.005096e-6,    11371.704689758,  2.547107806 },
      {    0.004841e-6,     5333.900241022,  0.437078094 },
      {    0.005582e-6,     5966.683980335,  2.246174308 },
      {    0.006304e-6,    11926.254413669,  2.512929171 },
      {    0.006603e-6,    23581.258177318,  5.393136889 },
      {    0.005123e-6,       -1.484472708,  2.999641028 },
      {    0.004648e-6,     1589.072895284,  1.275847090 },
      {    0.005119e-6,     6438.496249426,  1.486539246 },
   /* 121, 130 */
      {    0.004521e-6,     4292.330832950,  6.140635794 },
      {    0.005680e-6,    23013.539539587,  4.557814849 },
      {    0.005488e-6,       -3.455808046,  0.090675389 },
      {    0.004193e-6,     7234.794256242,  4.869091389 },
      {    0.003742e-6,     7238.675591600,  4.691976180 },
      {    0.004148e-6,     -110.206321219,  3.016173439 },
      {    0.004553e-6,    11499.656222793,  5.554998314 },
      {    0.004892e-6,     5436.993015240,  1.475415597 },
      {    0.004044e-6,     4732.030627343,  1.398784824 },
      {    0.004164e-6,    12491.370101415,  5.650931916 },
   /* 131, 140 */
      {    0.004349e-6,    11513.883316794,  2.181745369 },
      {    0.003919e-6,    12528.018664345,  5.823319737 },
      {    0.003129e-6,     6836.645252834,  0.003844094 },
      {    0.004080e-6,    -7058.598461315,  3.690360123 },
      {    0.003270e-6,       76.266071276,  1.517189902 },
      {    0.002954e-6,     6283.143160294,  4.447203799 },
      {    0.002872e-6,       28.449187468,  1.158692983 },
      {    0.002881e-6,      735.876513532,  0.349250250 },
      {    0.003279e-6,     5849.364112115,  4.893384368 },
      {    0.003625e-6,     6209.778724132,  1.473760578 },
   /* 141, 150 */
      {    0.003074e-6,      949.175608970,  5.185878737 },
      {    0.002775e-6,     9917.696874510,  1.030026325 },
      {    0.002646e-6,    10973.555686350,  3.918259169 },
      {    0.002575e-6,    25132.303399966,  6.109659023 },
      {    0.003500e-6,      263.083923373,  1.892100742 },
      {    0.002740e-6,    18319.536584880,  4.320519510 },
      {    0.002464e-6,      202.253395174,  4.698203059 },
      {    0.002409e-6,        2.542797281,  5.325009315 },
      {    0.003354e-6,   -90955.551694697,  1.942656623 },
      {    0.002296e-6,     6496.374945429,  5.061810696 },
   /* 151, 160 */
      {    0.003002e-6,     6172.869528772,  2.797822767 },
      {    0.003202e-6,    27511.467873537,  0.531673101 },
      {    0.002954e-6,    -6283.008539689,  4.533471191 },
      {    0.002353e-6,      639.897286314,  3.734548088 },
      {    0.002401e-6,    16200.772724501,  2.605547070 },
      {    0.003053e-6,   233141.314403759,  3.029030662 },
      {    0.003024e-6,    83286.914269554,  2.355556099 },
      {    0.002863e-6,    17298.182327326,  5.240963796 },
      {    0.002103e-6,    -7079.373856808,  5.756641637 },
      {    0.002303e-6,    83996.847317911,  2.013686814 },
   /* 161, 170 */
      {    0.002303e-6,    18073.704938650,  1.089100410 },
      {    0.002381e-6,       63.735898303,  0.759188178 },
      {    0.002493e-6,     6386.168624210,  0.645026535 },
      {    0.002366e-6,        3.932153263,  6.215885448 },
      {    0.002169e-6,    11015.106477335,  4.845297676 },
      {    0.002397e-6,     6243.458341645,  3.809290043 },
      {    0.002183e-6,     1162.474704408,  6.179611691 },
      {    0.002353e-6,     6246.427287062,  4.781719760 },
      {    0.002199e-6,     -245.831646229,  5.956152284 },
      {    0.001729e-6,     3894.181829542,  1.264976635 },
   /* 171, 180 */
      {    0.001896e-6,    -3128.388765096,  4.914231596 },
      {    0.002085e-6,       35.164090221,  1.405158503 },
      {    0.002024e-6,    14712.317116458,  2.752035928 },
      {    0.001737e-6,     6290.189396992,  5.280820144 },
      {    0.002229e-6,      491.557929457,  1.571007057 },
      {    0.001602e-6,    14314.168113050,  4.203664806 },
      {    0.002186e-6,      454.909366527,  1.402101526 },
      {    0.001897e-6,    22483.848574493,  4.167932508 },
      {    0.001825e-6,    -3738.761430108,  0.545828785 },
      {    0.001894e-6,     1052.268383188,  5.817167450 },
   /* 181, 190 */
      {    0.001421e-6,       20.355319399,  2.419886601 },
      {    0.001408e-6,    10984.192351700,  2.732084787 },
      {    0.001847e-6,    10873.986030480,  2.903477885 },
      {    0.001391e-6,    -8635.942003763,  0.593891500 },
      {    0.001388e-6,       -7.046236698,  1.166145902 },
      {    0.001810e-6,   -88860.057071188,  0.487355242 },
      {    0.001288e-6,    -1990.745017041,  3.913022880 },
      {    0.001297e-6,    23543.230504682,  3.063805171 },
      {    0.001335e-6,     -266.607041722,  3.995764039 },
      {    0.001376e-6,    10969.965257698,  5.152914309 },
   /* 191, 200 */
      {    0.001745e-6,   244287.600007027,  3.626395673 },
      {    0.001649e-6,    31441.677569757,  1.952049260 },
      {    0.001416e-6,     9225.539273283,  4.996408389 },
      {    0.001238e-6,     4804.209275927,  5.503379738 },
      {    0.001472e-6,     4590.910180489,  4.164913291 },
      {    0.001169e-6,     6040.347246017,  5.841719038 },
      {    0.001039e-6,     5540.085789459,  2.769753519 },
      {    0.001004e-6,     -170.672870619,  0.755008103 },
      {    0.001284e-6,    10575.406682942,  5.306538209 },
      {    0.001278e-6,       71.812653151,  4.713486491 },
   /* 201, 210 */
      {    0.001321e-6,    18209.330263660,  2.624866359 },
      {    0.001297e-6,    21228.392023546,  0.382603541 },
      {    0.000954e-6,     6282.095528923,  0.882213514 },
      {    0.001145e-6,     6058.731054289,  1.169483931 },
      {    0.000979e-6,     5547.199336460,  5.448375984 },
      {    0.000987e-6,    -6262.300454499,  2.656486959 },
      {    0.001070e-6,  -154717.609887482,  1.827624012 },
      {    0.000991e-6,     4701.116501708,  4.387001801 },
      {    0.001155e-6,      -14.227094002,  3.042700750 },
      {    0.001176e-6,      277.034993741,  3.335519004 },
   /* 211, 220 */
      {    0.000890e-6,    13916.019109642,  5.601498297 },
      {    0.000884e-6,    -1551.045222648,  1.088831705 },
      {    0.000876e-6,     5017.508371365,  3.969902609 },
      {    0.000806e-6,    15110.466119866,  5.142876744 },
      {    0.000773e-6,    -4136.910433516,  0.022067765 },
      {    0.001077e-6,      175.166059800,  1.844913056 },
      {    0.000954e-6,    -6284.056171060,  0.968480906 },
      {    0.000737e-6,     5326.786694021,  4.923831588 },
      {    0.000845e-6,     -433.711737877,  4.749245231 },
      {    0.000819e-6,     8662.240323563,  5.991247817 },
   /* 221, 230 */
      {    0.000852e-6,      199.072001436,  2.189604979 },
      {    0.000723e-6,    17256.631536341,  6.068719637 },
      {    0.000940e-6,     6037.244203762,  6.197428148 },
      {    0.000885e-6,    11712.955318231,  3.280414875 },
      {    0.000706e-6,    12559.038152982,  2.824848947 },
      {    0.000732e-6,     2379.164473572,  2.501813417 },
      {    0.000764e-6,    -6127.655450557,  2.236346329 },
      {    0.000908e-6,      131.541961686,  2.521257490 },
      {    0.000907e-6,    35371.887265976,  3.370195967 },
      {    0.000673e-6,     1066.495477190,  3.876512374 },
   /* 231, 240 */
      {    0.000814e-6,    17654.780539750,  4.627122566 },
      {    0.000630e-6,       36.027866677,  0.156368499 },
      {    0.000798e-6,      515.463871093,  5.151962502 },
      {    0.000798e-6,      148.078724426,  5.909225055 },
      {    0.000806e-6,      309.278322656,  6.054064447 },
      {    0.000607e-6,      -39.617508346,  2.839021623 },
      {    0.000601e-6,      412.371096874,  3.984225404 },
      {    0.000646e-6,    11403.676995575,  3.852959484 },
      {    0.000704e-6,    13521.751441591,  2.300991267 },
      {    0.000603e-6,   -65147.619767937,  4.140083146 },
   /* 241, 250 */
      {    0.000609e-6,    10177.257679534,  0.437122327 },
      {    0.000631e-6,     5767.611978898,  4.026532329 },
      {    0.000576e-6,    11087.285125918,  4.760293101 },
      {    0.000674e-6,    14945.316173554,  6.270510511 },
      {    0.000726e-6,     5429.879468239,  6.039606892 },
      {    0.000710e-6,    28766.924424484,  5.672617711 },
      {    0.000647e-6,    11856.218651625,  3.397132627 },
      {    0.000678e-6,    -5481.254918868,  6.249666675 },
      {    0.000618e-6,    22003.914634870,  2.466427018 },
      {    0.000738e-6,     6134.997125565,  2.242668890 },
   /* 251, 260 */
      {    0.000660e-6,      625.670192312,  5.864091907 },
      {    0.000694e-6,     3496.032826134,  2.668309141 },
      {    0.000531e-6,     6489.261398429,  1.681888780 },
      {    0.000611e-6,  -143571.324284214,  2.424978312 },
      {    0.000575e-6,    12043.574281889,  4.216492400 },
      {    0.000553e-6,    12416.588502848,  4.772158039 },
      {    0.000689e-6,     4686.889407707,  6.224271088 },
      {    0.000495e-6,     7342.457780181,  3.817285811 },
      {    0.000567e-6,     3634.621024518,  1.649264690 },
      {    0.000515e-6,    18635.928454536,  3.945345892 },
   /* 261, 270 */
      {    0.000486e-6,     -323.505416657,  4.061673868 },
      {    0.000662e-6,    25158.601719765,  1.794058369 },
      {    0.000509e-6,      846.082834751,  3.053874588 },
      {    0.000472e-6,   -12569.674818332,  5.112133338 },
      {    0.000461e-6,     6179.983075773,  0.513669325 },
      {    0.000641e-6,    83467.156352816,  3.210727723 },
      {    0.000520e-6,    10344.295065386,  2.445597761 },
      {    0.000493e-6,    18422.629359098,  1.676939306 },
      {    0.000478e-6,     1265.567478626,  5.487314569 },
      {    0.000472e-6,      -18.159247265,  1.999707589 },
   /* 271, 280 */
      {    0.000559e-6,    11190.377900137,  5.783236356 },
      {    0.000494e-6,     9623.688276691,  3.022645053 },
      {    0.000463e-6,     5739.157790895,  1.411223013 },
      {    0.000432e-6,    16858.482532933,  1.179256434 },
      {    0.000574e-6,    72140.628666286,  1.758191830 },
      {    0.000484e-6,    17267.268201691,  3.290589143 },
      {    0.000550e-6,     4907.302050146,  0.864024298 },
      {    0.000399e-6,       14.977853527,  2.094441910 },
      {    0.000491e-6,      224.344795702,  0.878372791 },
      {    0.000432e-6,    20426.571092422,  6.003829241 },
   /* 281, 290 */
      {    0.000481e-6,     5749.452731634,  4.309591964 },
      {    0.000480e-6,     5757.317038160,  1.142348571 },
      {    0.000485e-6,     6702.560493867,  0.210580917 },
      {    0.000426e-6,     6055.549660552,  4.274476529 },
      {    0.000480e-6,     5959.570433334,  5.031351030 },
      {    0.000466e-6,    12562.628581634,  4.959581597 },
      {    0.000520e-6,    39302.096962196,  4.788002889 },
      {    0.000458e-6,    12132.439962106,  1.880103788 },
      {    0.000470e-6,    12029.347187887,  1.405611197 },
      {    0.000416e-6,    -7477.522860216,  1.082356330 },
   /* 291, 300 */
      {    0.000449e-6,    11609.862544012,  4.179989585 },
      {    0.000465e-6,    17253.041107690,  0.353496295 },
      {    0.000362e-6,    -4535.059436924,  1.583849576 },
      {    0.000383e-6,    21954.157609398,  3.747376371 },
      {    0.000389e-6,       17.252277143,  1.395753179 },
      {    0.000331e-6,    18052.929543158,  0.566790582 },
      {    0.000430e-6,    13517.870106233,  0.685827538 },
      {    0.000368e-6,    -5756.908003246,  0.731374317 },
      {    0.000330e-6,    10557.594160824,  3.710043680 },
      {    0.000332e-6,    20199.094959633,  1.652901407 },
   /* 301, 310 */
      {    0.000384e-6,    11933.367960670,  5.827781531 },
      {    0.000387e-6,    10454.501386605,  2.541182564 },
      {    0.000325e-6,    15671.081759407,  2.178850542 },
      {    0.000318e-6,      138.517496871,  2.253253037 },
      {    0.000305e-6,     9388.005909415,  0.578340206 },
      {    0.000352e-6,     5749.861766548,  3.000297967 },
      {    0.000311e-6,     6915.859589305,  1.693574249 },
      {    0.000297e-6,    24072.921469776,  1.997249392 },
      {    0.000363e-6,     -640.877607382,  5.071820966 },
      {    0.000323e-6,    12592.450019783,  1.072262823 },
   /* 311, 320 */
      {    0.000341e-6,    12146.667056108,  4.700657997 },
      {    0.000290e-6,     9779.108676125,  1.812320441 },
      {    0.000342e-6,     6132.028180148,  4.322238614 },
      {    0.000329e-6,     6268.848755990,  3.033827743 },
      {    0.000374e-6,    17996.031168222,  3.388716544 },
      {    0.000285e-6,     -533.214083444,  4.687313233 },
      {    0.000338e-6,     6065.844601290,  0.877776108 },
      {    0.000276e-6,       24.298513841,  0.770299429 },
      {    0.000336e-6,    -2388.894020449,  5.353796034 },
      {    0.000290e-6,     3097.883822726,  4.075291557 },
   /* 321, 330 */
      {    0.000318e-6,      709.933048357,  5.941207518 },
      {    0.000271e-6,    13095.842665077,  3.208912203 },
      {    0.000331e-6,     6073.708907816,  4.007881169 },
      {    0.000292e-6,      742.990060533,  2.714333592 },
      {    0.000362e-6,    29088.811415985,  3.215977013 },
      {    0.000280e-6,    12359.966151546,  0.710872502 },
      {    0.000267e-6,    10440.274292604,  4.730108488 },
      {    0.000262e-6,      838.969287750,  1.327720272 },
      {    0.000250e-6,    16496.361396202,  0.898769761 },
      {    0.000325e-6,    20597.243963041,  0.180044365 },
   /* 331, 340 */
      {    0.000268e-6,     6148.010769956,  5.152666276 },
      {    0.000284e-6,     5636.065016677,  5.655385808 },
      {    0.000301e-6,     6080.822454817,  2.135396205 },
      {    0.000294e-6,     -377.373607916,  3.708784168 },
      {    0.000236e-6,     2118.763860378,  1.733578756 },
      {    0.000234e-6,     5867.523359379,  5.575209112 },
      {    0.000268e-6,  -226858.238553767,  0.069432392 },
      {    0.000265e-6,   167283.761587465,  4.369302826 },
      {    0.000280e-6,    28237.233459389,  5.304829118 },
      {    0.000292e-6,    12345.739057544,  4.096094132 },
   /* 341, 350 */
      {    0.000223e-6,    19800.945956225,  3.069327406 },
      {    0.000301e-6,    43232.306658416,  6.205311188 },
      {    0.000264e-6,    18875.525869774,  1.417263408 },
      {    0.000304e-6,    -1823.175188677,  3.409035232 },
      {    0.000301e-6,      109.945688789,  0.510922054 },
      {    0.000260e-6,      813.550283960,  2.389438934 },
      {    0.000299e-6,   316428.228673312,  5.384595078 },
      {    0.000211e-6,     5756.566278634,  3.789392838 },
      {    0.000209e-6,     5750.203491159,  1.661943545 },
      {    0.000240e-6,    12489.885628707,  5.684549045 },
   /* 351, 360 */
      {    0.000216e-6,     6303.851245484,  3.862942261 },
      {    0.000203e-6,     1581.959348283,  5.549853589 },
      {    0.000200e-6,     5642.198242609,  1.016115785 },
      {    0.000197e-6,      -70.849445304,  4.690702525 },
      {    0.000227e-6,     6287.008003254,  2.911891613 },
      {    0.000197e-6,      533.623118358,  1.048982898 },
      {    0.000205e-6,    -6279.485421340,  1.829362730 },
      {    0.000209e-6,   -10988.808157535,  2.636140084 },
      {    0.000208e-6,     -227.526189440,  4.127883842 },
      {    0.000191e-6,      415.552490612,  4.401165650 },
   /* 361, 370 */
      {    0.000190e-6,    29296.615389579,  4.175658539 },
      {    0.000264e-6,    66567.485864652,  4.601102551 },
      {    0.000256e-6,    -3646.350377354,  0.506364778 },
      {    0.000188e-6,    13119.721102825,  2.032195842 },
      {    0.000185e-6,     -209.366942175,  4.694756586 },
      {    0.000198e-6,    25934.124331089,  3.832703118 },
      {    0.000195e-6,     4061.219215394,  3.308463427 },
      {    0.000234e-6,     5113.487598583,  1.716090661 },
      {    0.000188e-6,     1478.866574064,  5.686865780 },
      {    0.000222e-6,    11823.161639450,  1.942386641 },
   /* 371, 380 */
      {    0.000181e-6,    10770.893256262,  1.999482059 },
      {    0.000171e-6,     6546.159773364,  1.182807992 },
      {    0.000206e-6,       70.328180442,  5.934076062 },
      {    0.000169e-6,    20995.392966449,  2.169080622 },
      {    0.000191e-6,    10660.686935042,  5.405515999 },
      {    0.000228e-6,    33019.021112205,  4.656985514 },
      {    0.000184e-6,    -4933.208440333,  3.327476868 },
      {    0.000220e-6,     -135.625325010,  1.765430262 },
      {    0.000166e-6,    23141.558382925,  3.454132746 },
      {    0.000191e-6,     6144.558353121,  5.020393445 },
   /* 381, 390 */
      {    0.000180e-6,     6084.003848555,  0.602182191 },
      {    0.000163e-6,    17782.732072784,  4.960593133 },
      {    0.000225e-6,    16460.333529525,  2.596451817 },
      {    0.000222e-6,     5905.702242076,  3.731990323 },
      {    0.000204e-6,      227.476132789,  5.636192701 },
      {    0.000159e-6,    16737.577236597,  3.600691544 },
      {    0.000200e-6,     6805.653268085,  0.868220961 },
      {    0.000187e-6,    11919.140866668,  2.629456641 },
      {    0.000161e-6,      127.471796607,  2.862574720 },
      {    0.000205e-6,     6286.666278643,  1.742882331 },
   /* 391, 400 */
      {    0.000189e-6,      153.778810485,  4.812372643 },
      {    0.000168e-6,    16723.350142595,  0.027860588 },
      {    0.000149e-6,    11720.068865232,  0.659721876 },
      {    0.000189e-6,     5237.921013804,  5.245313000 },
      {    0.000143e-6,     6709.674040867,  4.317625647 },
      {    0.000146e-6,     4487.817406270,  4.815297007 },
      {    0.000144e-6,     -664.756045130,  5.381366880 },
      {    0.000175e-6,     5127.714692584,  4.728443327 },
      {    0.000162e-6,     6254.626662524,  1.435132069 },
      {    0.000187e-6,    47162.516354635,  1.354371923 },
   /* 401, 410 */
      {    0.000146e-6,    11080.171578918,  3.369695406 },
      {    0.000180e-6,     -348.924420448,  2.490902145 },
      {    0.000148e-6,      151.047669843,  3.799109588 },
      {    0.000157e-6,     6197.248551160,  1.284375887 },
      {    0.000167e-6,      146.594251718,  0.759969109 },
      {    0.000133e-6,    -5331.357443741,  5.409701889 },
      {    0.000154e-6,       95.979227218,  3.366890614 },
      {    0.000148e-6,    -6418.140930027,  3.384104996 },
      {    0.000128e-6,    -6525.804453965,  3.803419985 },
      {    0.000130e-6,    11293.470674356,  0.939039445 },
   /* 411, 420 */
      {    0.000152e-6,    -5729.506447149,  0.734117523 },
      {    0.000138e-6,      210.117701700,  2.564216078 },
      {    0.000123e-6,     6066.595360816,  4.517099537 },
      {    0.000140e-6,    18451.078546566,  0.642049130 },
      {    0.000126e-6,    11300.584221356,  3.485280663 },
      {    0.000119e-6,    10027.903195729,  3.217431161 },
      {    0.000151e-6,     4274.518310832,  4.404359108 },
      {    0.000117e-6,     6072.958148291,  0.366324650 },
      {    0.000165e-6,    -7668.637425143,  4.298212528 },
      {    0.000117e-6,    -6245.048177356,  5.379518958 },
   /* 421, 430 */
      {    0.000130e-6,    -5888.449964932,  4.527681115 },
      {    0.000121e-6,     -543.918059096,  6.109429504 },
      {    0.000162e-6,     9683.594581116,  5.720092446 },
      {    0.000141e-6,     6219.339951688,  0.679068671 },
      {    0.000118e-6,    22743.409379516,  4.881123092 },
      {    0.000129e-6,     1692.165669502,  0.351407289 },
      {    0.000126e-6,     5657.405657679,  5.146592349 },
      {    0.000114e-6,      728.762966531,  0.520791814 },
      {    0.000120e-6,       52.596639600,  0.948516300 },
      {    0.000115e-6,       65.220371012,  3.504914846 },
   /* 431, 440 */
      {    0.000126e-6,     5881.403728234,  5.577502482 },
      {    0.000158e-6,   163096.180360983,  2.957128968 },
      {    0.000134e-6,    12341.806904281,  2.598576764 },
      {    0.000151e-6,    16627.370915377,  3.985702050 },
      {    0.000109e-6,     1368.660252845,  0.014730471 },
      {    0.000131e-6,     6211.263196841,  0.085077024 },
      {    0.000146e-6,     5792.741760812,  0.708426604 },
      {    0.000146e-6,      -77.750543984,  3.121576600 },
      {    0.000107e-6,     5341.013788022,  0.288231904 },
      {    0.000138e-6,     6281.591377283,  2.797450317 },
   /* 441, 450 */
      {    0.000113e-6,    -6277.552925684,  2.788904128 },
      {    0.000115e-6,     -525.758811831,  5.895222200 },
      {    0.000138e-6,     6016.468808270,  6.096188999 },
      {    0.000139e-6,    23539.707386333,  2.028195445 },
      {    0.000146e-6,    -4176.041342449,  4.660008502 },
      {    0.000107e-6,    16062.184526117,  4.066520001 },
      {    0.000142e-6,    83783.548222473,  2.936315115 },
      {    0.000128e-6,     9380.959672717,  3.223844306 },
      {    0.000135e-6,     6205.325306007,  1.638054048 },
      {    0.000101e-6,     2699.734819318,  5.481603249 },
   /* 451, 460 */
      {    0.000104e-6,     -568.821874027,  2.205734493 },
      {    0.000103e-6,     6321.103522627,  2.440421099 },
      {    0.000119e-6,     6321.208885629,  2.547496264 },
      {    0.000138e-6,     1975.492545856,  2.314608466 },
      {    0.000121e-6,      137.033024162,  4.539108237 },
      {    0.000123e-6,    19402.796952817,  4.538074405 },
      {    0.000119e-6,    22805.735565994,  2.869040566 },
      {    0.000133e-6,    64471.991241142,  6.056405489 },
      {    0.000129e-6,      -85.827298831,  2.540635083 },
      {    0.000131e-6,    13613.804277336,  4.005732868 },
   /* 461, 470 */
      {    0.000104e-6,     9814.604100291,  1.959967212 },
      {    0.000112e-6,    16097.679950283,  3.589026260 },
      {    0.000123e-6,     2107.034507542,  1.728627253 },
      {    0.000121e-6,    36949.230808424,  6.072332087 },
      {    0.000108e-6,   -12539.853380183,  3.716133846 },
      {    0.000113e-6,    -7875.671863624,  2.725771122 },
      {    0.000109e-6,     4171.425536614,  4.033338079 },
      {    0.000101e-6,     6247.911759770,  3.441347021 },
      {    0.000113e-6,     7330.728427345,  0.656372122 },
      {    0.000113e-6,    51092.726050855,  2.791483066 },
   /* 471, 480 */
      {    0.000106e-6,     5621.842923210,  1.815323326 },
      {    0.000101e-6,      111.430161497,  5.711033677 },
      {    0.000103e-6,      909.818733055,  2.812745443 },
      {    0.000101e-6,     1790.642637886,  1.965746028 },

   /* T */
      {  102.156724e-6,     6283.075849991,  4.249032005 },
      {    1.706807e-6,    12566.151699983,  4.205904248 },
      {    0.269668e-6,      213.299095438,  3.400290479 },
      {    0.265919e-6,      529.690965095,  5.836047367 },
      {    0.210568e-6,       -3.523118349,  6.262738348 },
      {    0.077996e-6,     5223.693919802,  4.670344204 },
   /* 481, 490 */
      {    0.054764e-6,     1577.343542448,  4.534800170 },
      {    0.059146e-6,       26.298319800,  1.083044735 },
      {    0.034420e-6,     -398.149003408,  5.980077351 },
      {    0.032088e-6,    18849.227549974,  4.162913471 },
      {    0.033595e-6,     5507.553238667,  5.980162321 },
      {    0.029198e-6,     5856.477659115,  0.623811863 },
      {    0.027764e-6,      155.420399434,  3.745318113 },
      {    0.025190e-6,     5746.271337896,  2.980330535 },
      {    0.022997e-6,     -796.298006816,  1.174411803 },
      {    0.024976e-6,     5760.498431898,  2.467913690 },
   /* 491, 500 */
      {    0.021774e-6,      206.185548437,  3.854787540 },
      {    0.017925e-6,     -775.522611324,  1.092065955 },
      {    0.013794e-6,      426.598190876,  2.699831988 },
      {    0.013276e-6,     6062.663207553,  5.845801920 },
      {    0.011774e-6,    12036.460734888,  2.292832062 },
      {    0.012869e-6,     6076.890301554,  5.333425680 },
      {    0.012152e-6,     1059.381930189,  6.222874454 },
      {    0.011081e-6,       -7.113547001,  5.154724984 },
      {    0.010143e-6,     4694.002954708,  4.044013795 },
      {    0.009357e-6,     5486.777843175,  3.416081409 },
   /* 501, 510 */
      {    0.010084e-6,      522.577418094,  0.749320262 },
      {    0.008587e-6,    10977.078804699,  2.777152598 },
      {    0.008628e-6,     6275.962302991,  4.562060226 },
      {    0.008158e-6,     -220.412642439,  5.806891533 },
      {    0.007746e-6,     2544.314419883,  1.603197066 },
      {    0.007670e-6,     2146.165416475,  3.000200440 },
      {    0.007098e-6,       74.781598567,  0.443725817 },
      {    0.006180e-6,     -536.804512095,  1.302642751 },
      {    0.005818e-6,     5088.628839767,  4.827723531 },
      {    0.004945e-6,    -6286.598968340,  0.268305170 },
   /* 511, 520 */
      {    0.004774e-6,     1349.867409659,  5.808636673 },
      {    0.004687e-6,     -242.728603974,  5.154890570 },
      {    0.006089e-6,     1748.016413067,  4.403765209 },
      {    0.005975e-6,    -1194.447010225,  2.583472591 },
      {    0.004229e-6,      951.718406251,  0.931172179 },
      {    0.005264e-6,      553.569402842,  2.336107252 },
      {    0.003049e-6,     5643.178563677,  1.362634430 },
      {    0.002974e-6,     6812.766815086,  1.583012668 },
      {    0.003403e-6,    -2352.866153772,  2.552189886 },
      {    0.003030e-6,      419.484643875,  5.286473844 },
   /* 521, 530 */
      {    0.003210e-6,       -7.046236698,  1.863796539 },
      {    0.003058e-6,     9437.762934887,  4.226420633 },
      {    0.002589e-6,    12352.852604545,  1.991935820 },
      {    0.002927e-6,     5216.580372801,  2.319951253 },
      {    0.002425e-6,     5230.807466803,  3.084752833 },
      {    0.002656e-6,     3154.687084896,  2.487447866 },
      {    0.002445e-6,    10447.387839604,  2.347139160 },
      {    0.002990e-6,     4690.479836359,  6.235872050 },
      {    0.002890e-6,     5863.591206116,  0.095197563 },
      {    0.002498e-6,     6438.496249426,  2.994779800 },
   /* 531, 540 */
      {    0.001889e-6,     8031.092263058,  3.569003717 },
      {    0.002567e-6,      801.820931124,  3.425611498 },
      {    0.001803e-6,   -71430.695617928,  2.192295512 },
      {    0.001782e-6,        3.932153263,  5.180433689 },
      {    0.001694e-6,    -4705.732307544,  4.641779174 },
      {    0.001704e-6,    -1592.596013633,  3.997097652 },
      {    0.001735e-6,     5849.364112115,  0.417558428 },
      {    0.001643e-6,     8429.241266467,  2.180619584 },
      {    0.001680e-6,       38.133035638,  4.164529426 },
      {    0.002045e-6,     7084.896781115,  0.526323854 },
   /* 541, 550 */
      {    0.001458e-6,     4292.330832950,  1.356098141 },
      {    0.001437e-6,       20.355319399,  3.895439360 },
      {    0.001738e-6,     6279.552731642,  0.087484036 },
      {    0.001367e-6,    14143.495242431,  3.987576591 },
      {    0.001344e-6,     7234.794256242,  0.090454338 },
      {    0.001438e-6,    11499.656222793,  0.974387904 },
      {    0.001257e-6,     6836.645252834,  1.509069366 },
      {    0.001358e-6,    11513.883316794,  0.495572260 },
      {    0.001628e-6,     7632.943259650,  4.968445721 },
      {    0.001169e-6,      103.092774219,  2.838496795 },
   /* 551, 560 */
      {    0.001162e-6,     4164.311989613,  3.408387778 },
      {    0.001092e-6,     6069.776754553,  3.617942651 },
      {    0.001008e-6,    17789.845619785,  0.286350174 },
      {    0.001008e-6,      639.897286314,  1.610762073 },
      {    0.000918e-6,    10213.285546211,  5.532798067 },
      {    0.001011e-6,    -6256.777530192,  0.661826484 },
      {    0.000753e-6,    16730.463689596,  3.905030235 },
      {    0.000737e-6,    11926.254413669,  4.641956361 },
      {    0.000694e-6,     3340.612426700,  2.111120332 },
      {    0.000701e-6,     3894.181829542,  2.760823491 },
   /* 561, 570 */
      {    0.000689e-6,     -135.065080035,  4.768800780 },
      {    0.000700e-6,    13367.972631107,  5.760439898 },
      {    0.000664e-6,     6040.347246017,  1.051215840 },
      {    0.000654e-6,     5650.292110678,  4.911332503 },
      {    0.000788e-6,     6681.224853400,  4.699648011 },
      {    0.000628e-6,     5333.900241022,  5.024608847 },
      {    0.000755e-6,     -110.206321219,  4.370971253 },
      {    0.000628e-6,     6290.189396992,  3.660478857 },
      {    0.000635e-6,    25132.303399966,  4.121051532 },
      {    0.000534e-6,     5966.683980335,  1.173284524 },
   /* 571, 580 */
      {    0.000543e-6,     -433.711737877,  0.345585464 },
      {    0.000517e-6,    -1990.745017041,  5.414571768 },
      {    0.000504e-6,     5767.611978898,  2.328281115 },
      {    0.000485e-6,     5753.384884897,  1.685874771 },
      {    0.000463e-6,     7860.419392439,  5.297703006 },
      {    0.000604e-6,      515.463871093,  0.591998446 },
      {    0.000443e-6,    12168.002696575,  4.830881244 },
      {    0.000570e-6,      199.072001436,  3.899190272 },
      {    0.000465e-6,    10969.965257698,  0.476681802 },
      {    0.000424e-6,    -7079.373856808,  1.112242763 },
   /* 581, 590 */
      {    0.000427e-6,      735.876513532,  1.994214480 },
      {    0.000478e-6,    -6127.655450557,  3.778025483 },
      {    0.000414e-6,    10973.555686350,  5.441088327 },
      {    0.000512e-6,     1589.072895284,  0.107123853 },
      {    0.000378e-6,    10984.192351700,  0.915087231 },
      {    0.000402e-6,    11371.704689758,  4.107281715 },
      {    0.000453e-6,     9917.696874510,  1.917490952 },
      {    0.000395e-6,      149.563197135,  2.763124165 },
      {    0.000371e-6,     5739.157790895,  3.112111866 },
      {    0.000350e-6,    11790.629088659,  0.440639857 },
   /* 591, 600 */
      {    0.000356e-6,     6133.512652857,  5.444568842 },
      {    0.000344e-6,      412.371096874,  5.676832684 },
      {    0.000383e-6,      955.599741609,  5.559734846 },
      {    0.000333e-6,     6496.374945429,  0.261537984 },
      {    0.000340e-6,     6055.549660552,  5.975534987 },
      {    0.000334e-6,     1066.495477190,  2.335063907 },
      {    0.000399e-6,    11506.769769794,  5.321230910 },
      {    0.000314e-6,    18319.536584880,  2.313312404 },
      {    0.000424e-6,     1052.268383188,  1.211961766 },
      {    0.000307e-6,       63.735898303,  3.169551388 },
   /* 601, 610 */
      {    0.000329e-6,       29.821438149,  6.106912080 },
      {    0.000357e-6,     6309.374169791,  4.223760346 },
      {    0.000312e-6,    -3738.761430108,  2.180556645 },
      {    0.000301e-6,      309.278322656,  1.499984572 },
      {    0.000268e-6,    12043.574281889,  2.447520648 },
      {    0.000257e-6,    12491.370101415,  3.662331761 },
      {    0.000290e-6,      625.670192312,  1.272834584 },
      {    0.000256e-6,     5429.879468239,  1.913426912 },
      {    0.000339e-6,     3496.032826134,  4.165930011 },
      {    0.000283e-6,     3930.209696220,  4.325565754 },
   /* 611, 620 */
      {    0.000241e-6,    12528.018664345,  3.832324536 },
      {    0.000304e-6,     4686.889407707,  1.612348468 },
      {    0.000259e-6,    16200.772724501,  3.470173146 },
      {    0.000238e-6,    12139.553509107,  1.147977842 },
      {    0.000236e-6,     6172.869528772,  3.776271728 },
      {    0.000296e-6,    -7058.598461315,  0.460368852 },
      {    0.000306e-6,    10575.406682942,  0.554749016 },
      {    0.000251e-6,    17298.182327326,  0.834332510 },
      {    0.000290e-6,     4732.030627343,  4.759564091 },
      {    0.000261e-6,     5884.926846583,  0.298259862 },
   /* 621, 630 */
      {    0.000249e-6,     5547.199336460,  3.749366406 },
      {    0.000213e-6,    11712.955318231,  5.415666119 },
      {    0.000223e-6,     4701.116501708,  2.703203558 },
      {    0.000268e-6,     -640.877607382,  0.283670793 },
      {    0.000209e-6,     5636.065016677,  1.238477199 },
      {    0.000193e-6,    10177.257679534,  1.943251340 },
      {    0.000182e-6,     6283.143160294,  2.456157599 },
      {    0.000184e-6,     -227.526189440,  5.888038582 },
      {    0.000182e-6,    -6283.008539689,  0.241332086 },
      {    0.000228e-6,    -6284.056171060,  2.657323816 },
   /* 631, 640 */
      {    0.000166e-6,     7238.675591600,  5.930629110 },
      {    0.000167e-6,     3097.883822726,  5.570955333 },
      {    0.000159e-6,     -323.505416657,  5.786670700 },
      {    0.000154e-6,    -4136.910433516,  1.517805532 },
      {    0.000176e-6,    12029.347187887,  3.139266834 },
      {    0.000167e-6,    12132.439962106,  3.556352289 },
      {    0.000153e-6,      202.253395174,  1.463313961 },
      {    0.000157e-6,    17267.268201691,  1.586837396 },
      {    0.000142e-6,    83996.847317911,  0.022670115 },
      {    0.000152e-6,    17260.154654690,  0.708528947 },
   /* 641, 650 */
      {    0.000144e-6,     6084.003848555,  5.187075177 },
      {    0.000135e-6,     5756.566278634,  1.993229262 },
      {    0.000134e-6,     5750.203491159,  3.457197134 },
      {    0.000144e-6,     5326.786694021,  6.066193291 },
      {    0.000160e-6,    11015.106477335,  1.710431974 },
      {    0.000133e-6,     3634.621024518,  2.836451652 },
      {    0.000134e-6,    18073.704938650,  5.453106665 },
      {    0.000134e-6,     1162.474704408,  5.326898811 },
      {    0.000128e-6,     5642.198242609,  2.511652591 },
      {    0.000160e-6,      632.783739313,  5.628785365 },
   /* 651, 660 */
      {    0.000132e-6,    13916.019109642,  0.819294053 },
      {    0.000122e-6,    14314.168113050,  5.677408071 },
      {    0.000125e-6,    12359.966151546,  5.251984735 },
      {    0.000121e-6,     5749.452731634,  2.210924603 },
      {    0.000136e-6,     -245.831646229,  1.646502367 },
      {    0.000120e-6,     5757.317038160,  3.240883049 },
      {    0.000134e-6,    12146.667056108,  3.059480037 },
      {    0.000137e-6,     6206.809778716,  1.867105418 },
      {    0.000141e-6,    17253.041107690,  2.069217456 },
      {    0.000129e-6,    -7477.522860216,  2.781469314 },
   /* 661, 670 */
      {    0.000116e-6,     5540.085789459,  4.281176991 },
      {    0.000116e-6,     9779.108676125,  3.320925381 },
      {    0.000129e-6,     5237.921013804,  3.497704076 },
      {    0.000113e-6,     5959.570433334,  0.983210840 },
      {    0.000122e-6,     6282.095528923,  2.674938860 },
      {    0.000140e-6,      -11.045700264,  4.957936982 },
      {    0.000108e-6,    23543.230504682,  1.390113589 },
      {    0.000106e-6,   -12569.674818332,  0.429631317 },
      {    0.000110e-6,     -266.607041722,  5.501340197 },
      {    0.000115e-6,    12559.038152982,  4.691456618 },
   /* 671, 680 */
      {    0.000134e-6,    -2388.894020449,  0.577313584 },
      {    0.000109e-6,    10440.274292604,  6.218148717 },
      {    0.000102e-6,     -543.918059096,  1.477842615 },
      {    0.000108e-6,    21228.392023546,  2.237753948 },
      {    0.000101e-6,    -4535.059436924,  3.100492232 },
      {    0.000103e-6,       76.266071276,  5.594294322 },
      {    0.000104e-6,      949.175608970,  5.674287810 },
      {    0.000101e-6,    13517.870106233,  2.196632348 },
      {    0.000100e-6,    11933.367960670,  4.056084160 },

   /* T^2 */
      {    4.322990e-6,     6283.075849991,  2.642893748 },
   /* 681, 690 */
      {    0.406495e-6,        0.000000000,  4.712388980 },
      {    0.122605e-6,    12566.151699983,  2.438140634 },
      {    0.019476e-6,      213.299095438,  1.642186981 },
      {    0.016916e-6,      529.690965095,  4.510959344 },
      {    0.013374e-6,       -3.523118349,  1.502210314 },
      {    0.008042e-6,       26.298319800,  0.478549024 },
      {    0.007824e-6,      155.420399434,  5.254710405 },
      {    0.004894e-6,     5746.271337896,  4.683210850 },
      {    0.004875e-6,     5760.498431898,  0.759507698 },
      {    0.004416e-6,     5223.693919802,  6.028853166 },
   /* 691, 700 */
      {    0.004088e-6,       -7.113547001,  0.060926389 },
      {    0.004433e-6,    77713.771467920,  3.627734103 },
      {    0.003277e-6,    18849.227549974,  2.327912542 },
      {    0.002703e-6,     6062.663207553,  1.271941729 },
      {    0.003435e-6,     -775.522611324,  0.747446224 },
      {    0.002618e-6,     6076.890301554,  3.633715689 },
      {    0.003146e-6,      206.185548437,  5.647874613 },
      {    0.002544e-6,     1577.343542448,  6.232904270 },
      {    0.002218e-6,     -220.412642439,  1.309509946 },
      {    0.002197e-6,     5856.477659115,  2.407212349 },
   /* 701, 710 */
      {    0.002897e-6,     5753.384884897,  5.863842246 },
      {    0.001766e-6,      426.598190876,  0.754113147 },
      {    0.001738e-6,     -796.298006816,  2.714942671 },
      {    0.001695e-6,      522.577418094,  2.629369842 },
      {    0.001584e-6,     5507.553238667,  1.341138229 },
      {    0.001503e-6,     -242.728603974,  0.377699736 },
      {    0.001552e-6,     -536.804512095,  2.904684667 },
      {    0.001370e-6,     -398.149003408,  1.265599125 },
      {    0.001889e-6,    -5573.142801634,  4.413514859 },
      {    0.001722e-6,     6069.776754553,  2.445966339 },
   /* 711, 720 */
      {    0.001124e-6,     1059.381930189,  5.041799657 },
      {    0.001258e-6,      553.569402842,  3.849557278 },
      {    0.000831e-6,      951.718406251,  2.471094709 },
      {    0.000767e-6,     4694.002954708,  5.363125422 },
      {    0.000756e-6,     1349.867409659,  1.046195744 },
      {    0.000775e-6,      -11.045700264,  0.245548001 },
      {    0.000597e-6,     2146.165416475,  4.543268798 },
      {    0.000568e-6,     5216.580372801,  4.178853144 },
      {    0.000711e-6,     1748.016413067,  5.934271972 },
      {    0.000499e-6,    12036.460734888,  0.624434410 },
   /* 721, 730 */
      {    0.000671e-6,    -1194.447010225,  4.136047594 },
      {    0.000488e-6,     5849.364112115,  2.209679987 },
      {    0.000621e-6,     6438.496249426,  4.518860804 },
      {    0.000495e-6,    -6286.598968340,  1.868201275 },
      {    0.000456e-6,     5230.807466803,  1.271231591 },
      {    0.000451e-6,     5088.628839767,  0.084060889 },
      {    0.000435e-6,     5643.178563677,  3.324456609 },
      {    0.000387e-6,    10977.078804699,  4.052488477 },
      {    0.000547e-6,   161000.685737473,  2.841633844 },
      {    0.000522e-6,     3154.687084896,  2.171979966 },
   /* 731, 740 */
      {    0.000375e-6,     5486.777843175,  4.983027306 },
      {    0.000421e-6,     5863.591206116,  4.546432249 },
      {    0.000439e-6,     7084.896781115,  0.522967921 },
      {    0.000309e-6,     2544.314419883,  3.172606705 },
      {    0.000347e-6,     4690.479836359,  1.479586566 },
      {    0.000317e-6,      801.820931124,  3.553088096 },
      {    0.000262e-6,      419.484643875,  0.606635550 },
      {    0.000248e-6,     6836.645252834,  3.014082064 },
      {    0.000245e-6,    -1592.596013633,  5.519526220 },
      {    0.000225e-6,     4292.330832950,  2.877956536 },
   /* 741, 750 */
      {    0.000214e-6,     7234.794256242,  1.605227587 },
      {    0.000205e-6,     5767.611978898,  0.625804796 },
      {    0.000180e-6,    10447.387839604,  3.499954526 },
      {    0.000229e-6,      199.072001436,  5.632304604 },
      {    0.000214e-6,      639.897286314,  5.960227667 },
      {    0.000175e-6,     -433.711737877,  2.162417992 },
      {    0.000209e-6,      515.463871093,  2.322150893 },
      {    0.000173e-6,     6040.347246017,  2.556183691 },
      {    0.000184e-6,     6309.374169791,  4.732296790 },
      {    0.000227e-6,   149854.400134205,  5.385812217 },
   /* 751, 760 */
      {    0.000154e-6,     8031.092263058,  5.120720920 },
      {    0.000151e-6,     5739.157790895,  4.815000443 },
      {    0.000197e-6,     7632.943259650,  0.222827271 },
      {    0.000197e-6,       74.781598567,  3.910456770 },
      {    0.000138e-6,     6055.549660552,  1.397484253 },
      {    0.000149e-6,    -6127.655450557,  5.333727496 },
      {    0.000137e-6,     3894.181829542,  4.281749907 },
      {    0.000135e-6,     9437.762934887,  5.979971885 },
      {    0.000139e-6,    -2352.866153772,  4.715630782 },
      {    0.000142e-6,     6812.766815086,  0.513330157 },
   /* 761, 770 */
      {    0.000120e-6,    -4705.732307544,  0.194160689 },
      {    0.000131e-6,   -71430.695617928,  0.000379226 },
      {    0.000124e-6,     6279.552731642,  2.122264908 },
      {    0.000108e-6,    -6256.777530192,  0.883445696 },

   /* T^3 */
      {    0.143388e-6,     6283.075849991,  1.131453581 },
      {    0.006671e-6,    12566.151699983,  0.775148887 },
      {    0.001480e-6,      155.420399434,  0.480016880 },
      {    0.000934e-6,      213.299095438,  6.144453084 },
      {    0.000795e-6,      529.690965095,  2.941595619 },
      {    0.000673e-6,     5746.271337896,  0.120415406 },
   /* 771, 780 */
      {    0.000672e-6,     5760.498431898,  5.317009738 },
      {    0.000389e-6,     -220.412642439,  3.090323467 },
      {    0.000373e-6,     6062.663207553,  3.003551964 },
      {    0.000360e-6,     6076.890301554,  1.918913041 },
      {    0.000316e-6,      -21.340641002,  5.545798121 },
      {    0.000315e-6,     -242.728603974,  1.884932563 },
      {    0.000278e-6,      206.185548437,  1.266254859 },
      {    0.000238e-6,     -536.804512095,  4.532664830 },
      {    0.000185e-6,      522.577418094,  4.578313856 },
      {    0.000245e-6,    18849.227549974,  0.587467082 },
   /* 781, 787 */
      {    0.000180e-6,      426.598190876,  5.151178553 },
      {    0.000200e-6,      553.569402842,  5.355983739 },
      {    0.000141e-6,     5223.693919802,  1.336556009 },
      {    0.000104e-6,     5856.477659115,  4.239842759 },

   /* T^4 */
      {    0.003826e-6,     6283.075849991,  5.705257275 },
      {    0.000303e-6,    12566.151699983,  5.407132842 },
      {    0.000209e-6,      155.420399434,  1.989815753 }
   };


/* Time since J2000.0 in Julian millennia. */
   t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJM;

/* ================= */
/* Topocentric terms */
/* ================= */

/* Convert UT to local solar time in radians. */
   tsol = fmod(ut, 1.0) * ERFA_D2PI + elong;

/* FUNDAMENTAL ARGUMENTS:  Simon et al. 1994. */

/* Combine time argument (millennia) with deg/arcsec factor. */
   w = t / 3600.0;

/* Sun Mean Longitude. */
   elsun = fmod(280.46645683 + 1296027711.03429 * w, 360.0) * ERFA_DD2R;

/* Sun Mean Anomaly. */
   emsun = fmod(357.52910918 + 1295965810.481 * w, 360.0) * ERFA_DD2R;

/* Mean Elongation of Moon from Sun. */
   d = fmod(297.85019547 + 16029616012.090 * w, 360.0) * ERFA_DD2R;

/* Mean Longitude of Jupiter. */
   elj = fmod(34.35151874 + 109306899.89453 * w, 360.0) * ERFA_DD2R;

/* Mean Longitude of Saturn. */
   els = fmod(50.07744430 + 44046398.47038 * w, 360.0) * ERFA_DD2R;

/* TOPOCENTRIC TERMS:  Moyer 1981 and Murray 1983. */
   wt =   +  0.00029e-10 * u * sin(tsol + elsun - els)
          +  0.00100e-10 * u * sin(tsol - 2.0 * emsun)
          +  0.00133e-10 * u * sin(tsol - d)
          +  0.00133e-10 * u * sin(tsol + elsun - elj)
          -  0.00229e-10 * u * sin(tsol + 2.0 * elsun + emsun)
          -  0.02200e-10 * v * cos(elsun + emsun)
          +  0.05312e-10 * u * sin(tsol - emsun)
          -  0.13677e-10 * u * sin(tsol + 2.0 * elsun)
          -  1.31840e-10 * v * cos(elsun)
          +  3.17679e-10 * u * sin(tsol);

/* ===================== */
/* Fairhead et al. model */
/* ===================== */

/* T**0 */
   w0 = 0;
   for (j = 473; j >= 0; j--) {
      w0 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
   }

/* T**1 */
   w1 = 0;
   for (j = 678; j >= 474; j--) {
      w1 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
   }

/* T**2 */
   w2 = 0;
   for (j = 763; j >= 679; j--) {
      w2 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
   }

/* T**3 */
   w3 = 0;
   for (j = 783; j >= 764; j--) {
      w3 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
   }

/* T**4 */
   w4 = 0;
   for (j = 786; j >= 784; j--) {
      w4 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
   }

/* Multiply by powers of T and combine. */
   wf = t * (t * (t * (t * w4 + w3) + w2) + w1) + w0;

/* Adjustments to use JPL planetary masses instead of IAU. */
   wj =   0.00065e-6 * sin(6069.776754 * t + 4.021194) +
          0.00033e-6 * sin( 213.299095 * t + 5.543132) +
        (-0.00196e-6 * sin(6208.294251 * t + 5.696701)) +
        (-0.00173e-6 * sin(  74.781599 * t + 2.435900)) +
          0.03638e-6 * t * t;

/* ============ */
/* Final result */
/* ============ */

/* TDB-TT in seconds. */
   w = wt + wf + wj;

   return w;

}
/*----------------------------------------------------------------------
**  
**  
**  Copyright (C) 2013-2016, 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.
**  
*/