IERSConventions.java

  1. /* Copyright 2002-2016 CS Systèmes d'Information
  2.  * Licensed to CS Systèmes d'Information (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
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  17. package org.orekit.utils;

  19. import java.io.BufferedReader;
  20. import java.io.IOException;
  21. import java.io.InputStream;
  22. import java.io.InputStreamReader;
  23. import java.io.Serializable;
  24. import java.util.List;

  26. import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
  27. import org.apache.commons.math3.analysis.interpolation.HermiteInterpolator;
  28. import org.apache.commons.math3.util.FastMath;
  29. import org.apache.commons.math3.util.MathUtils;
  30. import org.orekit.data.BodiesElements;
  31. import org.orekit.data.DelaunayArguments;
  32. import org.orekit.data.FieldBodiesElements;
  33. import org.orekit.data.FundamentalNutationArguments;
  34. import org.orekit.data.PoissonSeries;
  35. import org.orekit.data.PoissonSeriesParser;
  36. import org.orekit.data.PolynomialNutation;
  37. import org.orekit.data.PolynomialParser;
  38. import org.orekit.data.PolynomialParser.Unit;
  39. import org.orekit.data.SimpleTimeStampedTableParser;
  40. import org.orekit.errors.OrekitException;
  41. import org.orekit.errors.OrekitInternalError;
  42. import org.orekit.errors.OrekitMessages;
  43. import org.orekit.errors.TimeStampedCacheException;
  44. import org.orekit.frames.EOPHistory;
  45. import org.orekit.frames.PoleCorrection;
  46. import org.orekit.time.AbsoluteDate;
  47. import org.orekit.time.DateComponents;
  48. import org.orekit.time.TimeComponents;
  49. import org.orekit.time.TimeFunction;
  50. import org.orekit.time.TimeScale;
  51. import org.orekit.time.TimeScalesFactory;
  52. import org.orekit.time.TimeStamped;


  55. /** Supported IERS conventions.
  56.  * @since 6.0
  57.  * @author Luc Maisonobe
  58.  */
  59. public enum IERSConventions {

  61.     /** Constant for IERS 1996 conventions. */
  62.     IERS_1996 {

  64.         /** Nutation arguments resources. */
  65.         private static final String NUTATION_ARGUMENTS = IERS_BASE + "1996/nutation-arguments.txt";

  67.         /** X series resources. */
  68.         private static final String X_Y_SERIES         = IERS_BASE + "1996/tab5.4.txt";

  70.         /** Psi series resources. */
  71.         private static final String PSI_EPSILON_SERIES = IERS_BASE + "1996/tab5.1.txt";

  73.         /** Tidal correction for xp, yp series resources. */
  74.         private static final String TIDAL_CORRECTION_XP_YP_SERIES = IERS_BASE + "1996/tab8.4.txt";

  76.         /** Tidal correction for UT1 resources. */
  77.         private static final String TIDAL_CORRECTION_UT1_SERIES = IERS_BASE + "1996/tab8.3.txt";

  79.         /** Love numbers resources. */
  80.         private static final String LOVE_NUMBERS = IERS_BASE + "1996/tab6.1.txt";

  82.         /** Frequency dependence model for k₂₀. */
  83.         private static final String K20_FREQUENCY_DEPENDENCE = IERS_BASE + "1996/tab6.2b.txt";

  85.         /** Frequency dependence model for k₂₁. */
  86.         private static final String K21_FREQUENCY_DEPENDENCE = IERS_BASE + "1996/tab6.2a.txt";

  88.         /** Frequency dependence model for k₂₂. */
  89.         private static final String K22_FREQUENCY_DEPENDENCE = IERS_BASE + "1996/tab6.2c.txt";

  91.         /** {@inheritDoc} */
  92.         @Override
  93.         public FundamentalNutationArguments getNutationArguments(final TimeScale timeScale)
  94.             throws OrekitException {
  95.             return new FundamentalNutationArguments(this, timeScale,
  96.                                                     getStream(NUTATION_ARGUMENTS), NUTATION_ARGUMENTS);
  97.         }

  99.         /** {@inheritDoc} */
  100.         @Override
  101.         public TimeFunction<Double> getMeanObliquityFunction() throws OrekitException {

  103.             // value from chapter 5, page 22
  104.             final PolynomialNutation<DerivativeStructure> epsilonA =
  105.                     new PolynomialNutation<DerivativeStructure>(84381.448    * Constants.ARC_SECONDS_TO_RADIANS,
  106.                                                                   -46.8150   * Constants.ARC_SECONDS_TO_RADIANS,
  107.                                                                    -0.00059  * Constants.ARC_SECONDS_TO_RADIANS,
  108.                                                                     0.001813 * Constants.ARC_SECONDS_TO_RADIANS);

  110.             return new TimeFunction<Double>() {

  112.                 /** {@inheritDoc} */
  113.                 @Override
  114.                 public Double value(final AbsoluteDate date) {
  115.                     return epsilonA.value(evaluateTC(date));
  116.                 }

  118.             };

  120.         }

  122.         /** {@inheritDoc} */
  123.         @Override
  124.         public TimeFunction<double[]> getXYSpXY2Function()
  125.             throws OrekitException {

  127.             // set up nutation arguments
  128.             final FundamentalNutationArguments arguments = getNutationArguments(null);

  130.             // X = 2004.3109″t - 0.42665″t² - 0.198656″t³ + 0.0000140″t⁴
  131.             //     + 0.00006″t² cos Ω + sin ε0 { Σ [(Ai + Ai' t) sin(ARGUMENT) + Ai'' t cos(ARGUMENT)]}
  132.             //     + 0.00204″t² sin Ω + 0.00016″t² sin 2(F - D + Ω),
  133.             final PolynomialNutation<DerivativeStructure> xPolynomial =
  134.                     new PolynomialNutation<DerivativeStructure>(0,
  135.                                                                 2004.3109 * Constants.ARC_SECONDS_TO_RADIANS,
  136.                                                                 -0.42665  * Constants.ARC_SECONDS_TO_RADIANS,
  137.                                                                 -0.198656 * Constants.ARC_SECONDS_TO_RADIANS,
  138.                                                                 0.0000140 * Constants.ARC_SECONDS_TO_RADIANS);

  140.             final double fXCosOm    = 0.00006 * Constants.ARC_SECONDS_TO_RADIANS;
  141.             final double fXSinOm    = 0.00204 * Constants.ARC_SECONDS_TO_RADIANS;
  142.             final double fXSin2FDOm = 0.00016 * Constants.ARC_SECONDS_TO_RADIANS;
  143.             final double sinEps0   = FastMath.sin(getMeanObliquityFunction().value(getNutationReferenceEpoch()));

  145.             final double deciMilliAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-4;
  146.             final PoissonSeriesParser<DerivativeStructure> baseParser =
  147.                     new PoissonSeriesParser<DerivativeStructure>(12).withFirstDelaunay(1);

  149.             final PoissonSeriesParser<DerivativeStructure> xParser =
  150.                     baseParser.
  151.                     withSinCos(0, 7, deciMilliAS, -1, deciMilliAS).
  152.                     withSinCos(1, 8, deciMilliAS,  9, deciMilliAS);
  153.             final PoissonSeries<DerivativeStructure> xSum = xParser.parse(getStream(X_Y_SERIES), X_Y_SERIES);

  155.             // Y = -0.00013″ - 22.40992″t² + 0.001836″t³ + 0.0011130″t⁴
  156.             //     + Σ [(Bi + Bi' t) cos(ARGUMENT) + Bi'' t sin(ARGUMENT)]
  157.             //    - 0.00231″t² cos Ω − 0.00014″t² cos 2(F - D + Ω)
  158.             final PolynomialNutation<DerivativeStructure> yPolynomial =
  159.                     new PolynomialNutation<DerivativeStructure>(-0.00013  * Constants.ARC_SECONDS_TO_RADIANS,
  160.                                                                 0.0,
  161.                                                                 -22.40992 * Constants.ARC_SECONDS_TO_RADIANS,
  162.                                                                 0.001836  * Constants.ARC_SECONDS_TO_RADIANS,
  163.                                                                 0.0011130 * Constants.ARC_SECONDS_TO_RADIANS);

  165.             final double fYCosOm    = -0.00231 * Constants.ARC_SECONDS_TO_RADIANS;
  166.             final double fYCos2FDOm = -0.00014 * Constants.ARC_SECONDS_TO_RADIANS;

  168.             final PoissonSeriesParser<DerivativeStructure> yParser =
  169.                     baseParser.
  170.                     withSinCos(0, -1, deciMilliAS, 10, deciMilliAS).
  171.                     withSinCos(1, 12, deciMilliAS, 11, deciMilliAS);
  172.             final PoissonSeries<DerivativeStructure> ySum = yParser.parse(getStream(X_Y_SERIES), X_Y_SERIES);

  174.             @SuppressWarnings("unchecked")
  175.             final PoissonSeries.CompiledSeries<DerivativeStructure> xySum =
  176.                     PoissonSeries.compile(xSum, ySum);

  178.             // s = -XY/2 + 0.00385″t - 0.07259″t³ - 0.00264″ sin Ω - 0.00006″ sin 2Ω
  179.             //     + 0.00074″t² sin Ω + 0.00006″t² sin 2(F - D + Ω)
  180.             final double fST          =  0.00385 * Constants.ARC_SECONDS_TO_RADIANS;
  181.             final double fST3         = -0.07259 * Constants.ARC_SECONDS_TO_RADIANS;
  182.             final double fSSinOm      = -0.00264 * Constants.ARC_SECONDS_TO_RADIANS;
  183.             final double fSSin2Om     = -0.00006 * Constants.ARC_SECONDS_TO_RADIANS;
  184.             final double fST2SinOm    =  0.00074 * Constants.ARC_SECONDS_TO_RADIANS;
  185.             final double fST2Sin2FDOm =  0.00006 * Constants.ARC_SECONDS_TO_RADIANS;

  187.             return new TimeFunction<double[]>() {

  189.                 /** {@inheritDoc} */
  190.                 @Override
  191.                 public double[] value(final AbsoluteDate date) {

  193.                     final BodiesElements elements = arguments.evaluateAll(date);
  194.                     final double[] xy             = xySum.value(elements);

  196.                     final double omega     = elements.getOmega();
  197.                     final double f         = elements.getF();
  198.                     final double d         = elements.getD();
  199.                     final double t         = elements.getTC();

  201.                     final double cosOmega  = FastMath.cos(omega);
  202.                     final double sinOmega  = FastMath.sin(omega);
  203.                     final double sin2Omega = FastMath.sin(2 * omega);
  204.                     final double cos2FDOm  = FastMath.cos(2 * (f - d + omega));
  205.                     final double sin2FDOm  = FastMath.sin(2 * (f - d + omega));

  207.                     final double x = xPolynomial.value(t) + sinEps0 * xy[0] +
  208.                             t * t * (fXCosOm * cosOmega + fXSinOm * sinOmega + fXSin2FDOm * cos2FDOm);
  209.                     final double y = yPolynomial.value(t) + xy[1] +
  210.                             t * t * (fYCosOm * cosOmega + fYCos2FDOm * cos2FDOm);
  211.                     final double sPxy2 = fSSinOm * sinOmega + fSSin2Om * sin2Omega +
  212.                             t * (fST + t * (fST2SinOm * sinOmega + fST2Sin2FDOm * sin2FDOm + t * fST3));

  214.                     return new double[] {
  215.                         x, y, sPxy2
  216.                     };

  218.                 }

  220.             };

  222.         }

  224.         /** {@inheritDoc} */
  225.         @Override
  226.         public TimeFunction<double[]> getPrecessionFunction() throws OrekitException {

  228.             // set up the conventional polynomials
  229.             // the following values are from Lieske et al. paper:
  230.             // Expressions for the precession quantities based upon the IAU(1976) system of astronomical constants
  231.             // http://articles.adsabs.harvard.edu/full/1977A%26A....58....1L
  232.             // also available as equation 30 in IERS 2003 conventions
  233.             final PolynomialNutation<DerivativeStructure> psiA =
  234.                     new PolynomialNutation<DerivativeStructure>(   0.0,
  235.                                                                 5038.7784   * Constants.ARC_SECONDS_TO_RADIANS,
  236.                                                                   -1.07259  * Constants.ARC_SECONDS_TO_RADIANS,
  237.                                                                   -0.001147 * Constants.ARC_SECONDS_TO_RADIANS);
  238.             final PolynomialNutation<DerivativeStructure> omegaA =
  239.                     new PolynomialNutation<DerivativeStructure>(getMeanObliquityFunction().value(getNutationReferenceEpoch()),
  240.                                                                  0.0,
  241.                                                                  0.05127   * Constants.ARC_SECONDS_TO_RADIANS,
  242.                                                                 -0.007726  * Constants.ARC_SECONDS_TO_RADIANS);
  243.             final PolynomialNutation<DerivativeStructure> chiA =
  244.                     new PolynomialNutation<DerivativeStructure>( 0.0,
  245.                                                                 10.5526   * Constants.ARC_SECONDS_TO_RADIANS,
  246.                                                                 -2.38064  * Constants.ARC_SECONDS_TO_RADIANS,
  247.                                                                 -0.001125 * Constants.ARC_SECONDS_TO_RADIANS);

  249.             return new TimeFunction<double[]>() {
  250.                 /** {@inheritDoc} */
  251.                 @Override
  252.                 public double[] value(final AbsoluteDate date) {
  253.                     final double tc = evaluateTC(date);
  254.                     return new double[] {
  255.                         psiA.value(tc), omegaA.value(tc), chiA.value(tc)
  256.                     };
  257.                 }
  258.             };

  260.         }

  262.         /** {@inheritDoc} */
  263.         @Override
  264.         public TimeFunction<double[]> getNutationFunction()
  265.             throws OrekitException {

  267.             // set up nutation arguments
  268.             final FundamentalNutationArguments arguments = getNutationArguments(null);

  270.             // set up Poisson series
  271.             final double deciMilliAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-4;
  272.             final PoissonSeriesParser<DerivativeStructure> baseParser =
  273.                     new PoissonSeriesParser<DerivativeStructure>(10).withFirstDelaunay(1);

  275.             final PoissonSeriesParser<DerivativeStructure> psiParser =
  276.                     baseParser.
  277.                     withSinCos(0, 7, deciMilliAS, -1, deciMilliAS).
  278.                     withSinCos(1, 8, deciMilliAS, -1, deciMilliAS);
  279.             final PoissonSeries<DerivativeStructure> psiSeries = psiParser.parse(getStream(PSI_EPSILON_SERIES), PSI_EPSILON_SERIES);

  281.             final PoissonSeriesParser<DerivativeStructure> epsilonParser =
  282.                     baseParser.
  283.                     withSinCos(0, -1, deciMilliAS, 9, deciMilliAS).
  284.                     withSinCos(1, -1, deciMilliAS, 10, deciMilliAS);
  285.             final PoissonSeries<DerivativeStructure> epsilonSeries = epsilonParser.parse(getStream(PSI_EPSILON_SERIES), PSI_EPSILON_SERIES);

  287.             @SuppressWarnings("unchecked")
  288.             final PoissonSeries.CompiledSeries<DerivativeStructure> psiEpsilonSeries =
  289.                     PoissonSeries.compile(psiSeries, epsilonSeries);

  291.             return new TimeFunction<double[]>() {
  292.                 /** {@inheritDoc} */
  293.                 @Override
  294.                 public double[] value(final AbsoluteDate date) {
  295.                     final BodiesElements elements = arguments.evaluateAll(date);
  296.                     final double[] psiEpsilon = psiEpsilonSeries.value(elements);
  297.                     return new double[] {
  298.                         psiEpsilon[0], psiEpsilon[1], IAU1994ResolutionC7.value(elements)
  299.                     };
  300.                 }
  301.             };

  303.         }

  305.         /** {@inheritDoc} */
  306.         @Override
  307.         public TimeFunction<DerivativeStructure> getGMSTFunction(final TimeScale ut1)
  308.             throws OrekitException {

  310.             // Radians per second of time
  311.             final double radiansPerSecond = MathUtils.TWO_PI / Constants.JULIAN_DAY;

  313.             // constants from IERS 1996 page 21
  314.             // the underlying model is IAU 1982 GMST-UT1
  315.             final AbsoluteDate gmstReference =
  316.                 new AbsoluteDate(DateComponents.J2000_EPOCH, TimeComponents.H12, TimeScalesFactory.getTAI());
  317.             final double gmst0 = 24110.54841;
  318.             final double gmst1 = 8640184.812866;
  319.             final double gmst2 = 0.093104;
  320.             final double gmst3 = -6.2e-6;

  322.             return new TimeFunction<DerivativeStructure>() {

  324.                 /** {@inheritDoc} */
  325.                 @Override
  326.                 public DerivativeStructure value(final AbsoluteDate date) {

  328.                     // offset in Julian centuries from J2000 epoch (UT1 scale)
  329.                     final double dtai = date.durationFrom(gmstReference);
  330.                     final DerivativeStructure tut1 =
  331.                             new DerivativeStructure(1, 1, dtai + ut1.offsetFromTAI(date), 1.0);
  332.                     final DerivativeStructure tt = tut1.divide(Constants.JULIAN_CENTURY);

  334.                     // Seconds in the day, adjusted by 12 hours because the
  335.                     // UT1 is supplied as a Julian date beginning at noon.
  336.                     final DerivativeStructure sd = tut1.add(Constants.JULIAN_DAY / 2).remainder(Constants.JULIAN_DAY);

  338.                     // compute Greenwich mean sidereal time, in radians
  339.                     return tt.multiply(gmst3).add(gmst2).multiply(tt).add(gmst1).multiply(tt).add(gmst0).add(sd).multiply(radiansPerSecond);

  341.                 }

  343.             };

  345.         }

  347.         /** {@inheritDoc} */
  348.         @Override
  349.         public TimeFunction<DerivativeStructure> getGASTFunction(final TimeScale ut1,
  350.                                                                  final EOPHistory eopHistory)
  351.             throws OrekitException {

  353.             // obliquity
  354.             final TimeFunction<Double> epsilonA = getMeanObliquityFunction();

  356.             // GMST function
  357.             final TimeFunction<DerivativeStructure> gmst = getGMSTFunction(ut1);

  359.             // nutation function
  360.             final TimeFunction<double[]> nutation = getNutationFunction();

  362.             return new TimeFunction<DerivativeStructure>() {

  364.                 /** {@inheritDoc} */
  365.                 @Override
  366.                 public DerivativeStructure value(final AbsoluteDate date) {

  368.                     // compute equation of equinoxes
  369.                     final double[] angles = nutation.value(date);
  370.                     double deltaPsi = angles[0];
  371.                     if (eopHistory != null) {
  372.                         deltaPsi += eopHistory.getEquinoxNutationCorrection(date)[0];
  373.                     }
  374.                     final double eqe = deltaPsi  * FastMath.cos(epsilonA.value(date)) + angles[2];

  376.                     // add mean sidereal time and equation of equinoxes
  377.                     return gmst.value(date).add(eqe);

  379.                 }

  381.             };

  383.         }

  385.         /** {@inheritDoc} */
  386.         @Override
  387.         public TimeFunction<double[]> getEOPTidalCorrection()
  388.             throws OrekitException {

  390.             // set up nutation arguments
  391.             // BEWARE! Using TT as the time scale here and not UT1 is intentional!
  392.             // as this correction is used to compute UT1 itself, it is not surprising we cannot use UT1 yet,
  393.             // however, using the close UTC as would seem logical make the comparison with interp.f from IERS fail
  394.             // looking in the interp.f code, the same TT scale is used for both Delaunay and gamma argument
  395.             final FundamentalNutationArguments arguments = getNutationArguments(TimeScalesFactory.getTT());

  397.             // set up Poisson series
  398.             final double milliAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-3;
  399.             final PoissonSeriesParser<DerivativeStructure> xyParser = new PoissonSeriesParser<DerivativeStructure>(17).
  400.                     withOptionalColumn(1).
  401.                     withGamma(7).
  402.                     withFirstDelaunay(2);
  403.             final PoissonSeries<DerivativeStructure> xSeries =
  404.                     xyParser.
  405.                     withSinCos(0, 14, milliAS, 15, milliAS).
  406.                     parse(getStream(TIDAL_CORRECTION_XP_YP_SERIES), TIDAL_CORRECTION_XP_YP_SERIES);
  407.             final PoissonSeries<DerivativeStructure> ySeries =
  408.                     xyParser.
  409.                     withSinCos(0, 16, milliAS, 17, milliAS).
  410.                     parse(getStream(TIDAL_CORRECTION_XP_YP_SERIES),
  411.                                                          TIDAL_CORRECTION_XP_YP_SERIES);

  413.             final double deciMilliS = 1.0e-4;
  414.             final PoissonSeriesParser<DerivativeStructure> ut1Parser = new PoissonSeriesParser<DerivativeStructure>(17).
  415.                     withOptionalColumn(1).
  416.                     withGamma(7).
  417.                     withFirstDelaunay(2).
  418.                     withSinCos(0, 16, deciMilliS, 17, deciMilliS);
  419.             final PoissonSeries<DerivativeStructure> ut1Series =
  420.                     ut1Parser.parse(getStream(TIDAL_CORRECTION_UT1_SERIES), TIDAL_CORRECTION_UT1_SERIES);

  422.             @SuppressWarnings("unchecked")
  423.             final PoissonSeries.CompiledSeries<DerivativeStructure> correctionSeries =
  424.                 PoissonSeries.compile(xSeries, ySeries, ut1Series);

  426.             return new TimeFunction<double[]>() {
  427.                 /** {@inheritDoc} */
  428.                 @Override
  429.                 public double[] value(final AbsoluteDate date) {
  430.                     final FieldBodiesElements<DerivativeStructure> elements =
  431.                             arguments.evaluateDerivative(date);
  432.                     final DerivativeStructure[] correction = correctionSeries.value(elements);
  433.                     return new double[] {
  434.                         correction[0].getValue(),
  435.                         correction[1].getValue(),
  436.                         correction[2].getValue(),
  437.                         -correction[2].getPartialDerivative(1) * Constants.JULIAN_DAY
  438.                     };
  439.                 }
  440.             };

  442.         }

  444.         /** {@inheritDoc} */
  445.         public LoveNumbers getLoveNumbers() throws OrekitException {
  446.             return loadLoveNumbers(LOVE_NUMBERS);
  447.         }

  449.         /** {@inheritDoc} */
  450.         public TimeFunction<double[]> getTideFrequencyDependenceFunction(final TimeScale ut1)
  451.             throws OrekitException {

  453.             // set up nutation arguments
  454.             final FundamentalNutationArguments arguments = getNutationArguments(ut1);

  456.             // set up Poisson series
  457.             final PoissonSeriesParser<DerivativeStructure> k20Parser =
  458.                     new PoissonSeriesParser<DerivativeStructure>(18).
  459.                         withOptionalColumn(1).
  460.                         withDoodson(4, 2).
  461.                         withFirstDelaunay(10);
  462.             final PoissonSeriesParser<DerivativeStructure> k21Parser =
  463.                     new PoissonSeriesParser<DerivativeStructure>(18).
  464.                         withOptionalColumn(1).
  465.                         withDoodson(4, 3).
  466.                         withFirstDelaunay(10);
  467.             final PoissonSeriesParser<DerivativeStructure> k22Parser =
  468.                     new PoissonSeriesParser<DerivativeStructure>(16).
  469.                         withOptionalColumn(1).
  470.                         withDoodson(4, 2).
  471.                         withFirstDelaunay(10);

  473.             final double pico = 1.0e-12;
  474.             final PoissonSeries<DerivativeStructure> c20Series =
  475.                     k20Parser.
  476.                   withSinCos(0, 18, -pico, 16, pico).
  477.                     parse(getStream(K20_FREQUENCY_DEPENDENCE), K20_FREQUENCY_DEPENDENCE);
  478.             final PoissonSeries<DerivativeStructure> c21Series =
  479.                     k21Parser.
  480.                     withSinCos(0, 17, pico, 18, pico).
  481.                     parse(getStream(K21_FREQUENCY_DEPENDENCE), K21_FREQUENCY_DEPENDENCE);
  482.             final PoissonSeries<DerivativeStructure> s21Series =
  483.                     k21Parser.
  484.                     withSinCos(0, 18, -pico, 17, pico).
  485.                     parse(getStream(K21_FREQUENCY_DEPENDENCE), K21_FREQUENCY_DEPENDENCE);
  486.             final PoissonSeries<DerivativeStructure> c22Series =
  487.                     k22Parser.
  488.                     withSinCos(0, -1, pico, 16, pico).
  489.                     parse(getStream(K22_FREQUENCY_DEPENDENCE), K22_FREQUENCY_DEPENDENCE);
  490.             final PoissonSeries<DerivativeStructure> s22Series =
  491.                     k22Parser.
  492.                     withSinCos(0, 16, -pico, -1, pico).
  493.                     parse(getStream(K22_FREQUENCY_DEPENDENCE), K22_FREQUENCY_DEPENDENCE);

  495.             @SuppressWarnings("unchecked")
  496.             final PoissonSeries.CompiledSeries<DerivativeStructure> kSeries =
  497.                 PoissonSeries.compile(c20Series, c21Series, s21Series, c22Series, s22Series);

  499.             return new TimeFunction<double[]>() {
  500.                 /** {@inheritDoc} */
  501.                 @Override
  502.                 public double[] value(final AbsoluteDate date) {
  503.                     return kSeries.value(arguments.evaluateAll(date));
  504.                 }
  505.             };

  507.         }

  509.         /** {@inheritDoc} */
  510.         @Override
  511.         public double getPermanentTide() throws OrekitException {
  512.             return 4.4228e-8 * -0.31460 * getLoveNumbers().getReal(2, 0);
  513.         }

  515.         /** {@inheritDoc} */
  516.         @Override
  517.         public TimeFunction<double[]> getSolidPoleTide(final EOPHistory eopHistory) {

  519.             // constants from IERS 1996 page 47
  520.             final double globalFactor = -1.348e-9 / Constants.ARC_SECONDS_TO_RADIANS;
  521.             final double coupling     =  0.00112;

  523.             return new TimeFunction<double[]>() {
  524.                 /** {@inheritDoc} */
  525.                 @Override
  526.                 public double[] value(final AbsoluteDate date) {
  527.                     final PoleCorrection pole = eopHistory.getPoleCorrection(date);
  528.                     return new double[] {
  529.                         globalFactor * (pole.getXp() + coupling * pole.getYp()),
  530.                         globalFactor * (coupling * pole.getXp() - pole.getYp()),
  531.                     };
  532.                 }
  533.             };
  534.         }

  536.         /** {@inheritDoc} */
  537.         @Override
  538.         public TimeFunction<double[]> getOceanPoleTide(final EOPHistory eopHistory)
  539.             throws OrekitException {

  541.             return new TimeFunction<double[]>() {
  542.                 /** {@inheritDoc} */
  543.                 @Override
  544.                 public double[] value(final AbsoluteDate date) {
  545.                     // there are no model for ocean pole tide prior to conventions 2010
  546.                     return new double[] {
  547.                         0.0, 0.0
  548.                     };
  549.                 }
  550.             };
  551.         }

  553.     },

  555.     /** Constant for IERS 2003 conventions. */
  556.     IERS_2003 {

  558.         /** Nutation arguments resources. */
  559.         private static final String NUTATION_ARGUMENTS = IERS_BASE + "2003/nutation-arguments.txt";

  561.         /** X series resources. */
  562.         private static final String X_SERIES           = IERS_BASE + "2003/tab5.2a.txt";

  564.         /** Y series resources. */
  565.         private static final String Y_SERIES           = IERS_BASE + "2003/tab5.2b.txt";

  567.         /** S series resources. */
  568.         private static final String S_SERIES           = IERS_BASE + "2003/tab5.2c.txt";

  570.         /** Luni-solar series resources. */
  571.         private static final String LUNI_SOLAR_SERIES  = IERS_BASE + "2003/tab5.3a-first-table.txt";

  573.         /** Planetary series resources. */
  574.         private static final String PLANETARY_SERIES   = IERS_BASE + "2003/tab5.3b.txt";

  576.         /** Greenwhich sidereal time series resources. */
  577.         private static final String GST_SERIES         = IERS_BASE + "2003/tab5.4.txt";

  579.         /** Tidal correction for xp, yp series resources. */
  580.         private static final String TIDAL_CORRECTION_XP_YP_SERIES = IERS_BASE + "2003/tab8.2ab.txt";

  582.         /** Tidal correction for UT1 resources. */
  583.         private static final String TIDAL_CORRECTION_UT1_SERIES = IERS_BASE + "2003/tab8.3ab.txt";

  585.         /** Love numbers resources. */
  586.         private static final String LOVE_NUMBERS = IERS_BASE + "2003/tab6.1.txt";

  588.         /** Frequency dependence model for k₂₀. */
  589.         private static final String K20_FREQUENCY_DEPENDENCE = IERS_BASE + "2003/tab6.3b.txt";

  591.         /** Frequency dependence model for k₂₁. */
  592.         private static final String K21_FREQUENCY_DEPENDENCE = IERS_BASE + "2003/tab6.3a.txt";

  594.         /** Frequency dependence model for k₂₂. */
  595.         private static final String K22_FREQUENCY_DEPENDENCE = IERS_BASE + "2003/tab6.3c.txt";

  597.         /** Annual pole table. */
  598.         private static final String ANNUAL_POLE = IERS_BASE + "2003/annual.pole";

  600.         /** {@inheritDoc} */
  601.         public FundamentalNutationArguments getNutationArguments(final TimeScale timeScale)
  602.             throws OrekitException {
  603.             return new FundamentalNutationArguments(this, timeScale,
  604.                                                     getStream(NUTATION_ARGUMENTS), NUTATION_ARGUMENTS);
  605.         }

  607.         /** {@inheritDoc} */
  608.         @Override
  609.         public TimeFunction<Double> getMeanObliquityFunction() throws OrekitException {

  611.             // epsilon 0 value from chapter 5, page 41, other terms from equation 32 page 45
  612.             final PolynomialNutation<DerivativeStructure> epsilonA =
  613.                     new PolynomialNutation<DerivativeStructure>(84381.448    * Constants.ARC_SECONDS_TO_RADIANS,
  614.                                                                   -46.84024  * Constants.ARC_SECONDS_TO_RADIANS,
  615.                                                                    -0.00059  * Constants.ARC_SECONDS_TO_RADIANS,
  616.                                                                     0.001813 * Constants.ARC_SECONDS_TO_RADIANS);

  618.             return new TimeFunction<Double>() {

  620.                 /** {@inheritDoc} */
  621.                 @Override
  622.                 public Double value(final AbsoluteDate date) {
  623.                     return epsilonA.value(evaluateTC(date));
  624.                 }

  626.             };

  628.         }

  630.         /** {@inheritDoc} */
  631.         @Override
  632.         public TimeFunction<double[]> getXYSpXY2Function()
  633.             throws OrekitException {

  635.             // set up nutation arguments
  636.             final FundamentalNutationArguments arguments = getNutationArguments(null);

  638.             // set up Poisson series
  639.             final double microAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-6;
  640.             final PoissonSeriesParser<DerivativeStructure> parser =
  641.                     new PoissonSeriesParser<DerivativeStructure>(17).
  642.                         withPolynomialPart('t', PolynomialParser.Unit.MICRO_ARC_SECONDS).
  643.                         withFirstDelaunay(4).
  644.                         withFirstPlanetary(9).
  645.                         withSinCos(0, 2, microAS, 3, microAS);

  647.             final PoissonSeries<DerivativeStructure> xSeries = parser.parse(getStream(X_SERIES), X_SERIES);
  648.             final PoissonSeries<DerivativeStructure> ySeries = parser.parse(getStream(Y_SERIES), Y_SERIES);
  649.             final PoissonSeries<DerivativeStructure> sSeries = parser.parse(getStream(S_SERIES), S_SERIES);
  650.             @SuppressWarnings("unchecked")
  651.             final PoissonSeries.CompiledSeries<DerivativeStructure> xys = PoissonSeries.compile(xSeries, ySeries, sSeries);

  653.             // create a function evaluating the series
  654.             return new TimeFunction<double[]>() {

  656.                 /** {@inheritDoc} */
  657.                 @Override
  658.                 public double[] value(final AbsoluteDate date) {
  659.                     return xys.value(arguments.evaluateAll(date));
  660.                 }

  662.             };

  664.         }


  667.         /** {@inheritDoc} */
  668.         @Override
  669.         public TimeFunction<double[]> getPrecessionFunction() throws OrekitException {

  671.             // set up the conventional polynomials
  672.             // the following values are from equation 32 in IERS 2003 conventions
  673.             final PolynomialNutation<DerivativeStructure> psiA =
  674.                     new PolynomialNutation<DerivativeStructure>(    0.0,
  675.                                                                  5038.47875   * Constants.ARC_SECONDS_TO_RADIANS,
  676.                                                                    -1.07259   * Constants.ARC_SECONDS_TO_RADIANS,
  677.                                                                    -0.001147  * Constants.ARC_SECONDS_TO_RADIANS);
  678.             final PolynomialNutation<DerivativeStructure> omegaA =
  679.                     new PolynomialNutation<DerivativeStructure>(getMeanObliquityFunction().value(getNutationReferenceEpoch()),
  680.                                                                 -0.02524   * Constants.ARC_SECONDS_TO_RADIANS,
  681.                                                                  0.05127   * Constants.ARC_SECONDS_TO_RADIANS,
  682.                                                                 -0.007726  * Constants.ARC_SECONDS_TO_RADIANS);
  683.             final PolynomialNutation<DerivativeStructure> chiA =
  684.                     new PolynomialNutation<DerivativeStructure>( 0.0,
  685.                                                                 10.5526   * Constants.ARC_SECONDS_TO_RADIANS,
  686.                                                                 -2.38064  * Constants.ARC_SECONDS_TO_RADIANS,
  687.                                                                 -0.001125 * Constants.ARC_SECONDS_TO_RADIANS);

  689.             return new TimeFunction<double[]>() {
  690.                 /** {@inheritDoc} */
  691.                 @Override
  692.                 public double[] value(final AbsoluteDate date) {
  693.                     final double tc = evaluateTC(date);
  694.                     return new double[] {
  695.                         psiA.value(tc), omegaA.value(tc), chiA.value(tc)
  696.                     };
  697.                 }
  698.             };

  700.         }

  702.         /** {@inheritDoc} */
  703.         @Override
  704.         public TimeFunction<double[]> getNutationFunction()
  705.             throws OrekitException {

  707.             // set up nutation arguments
  708.             final FundamentalNutationArguments arguments = getNutationArguments(null);

  710.             // set up Poisson series
  711.             final double milliAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-3;
  712.             final PoissonSeriesParser<DerivativeStructure> luniSolarParser =
  713.                     new PoissonSeriesParser<DerivativeStructure>(14).withFirstDelaunay(1);
  714.             final PoissonSeriesParser<DerivativeStructure> luniSolarPsiParser =
  715.                     luniSolarParser.
  716.                     withSinCos(0, 7, milliAS, 11, milliAS).
  717.                     withSinCos(1, 8, milliAS, 12, milliAS);
  718.             final PoissonSeries<DerivativeStructure> psiLuniSolarSeries =
  719.                     luniSolarPsiParser.parse(getStream(LUNI_SOLAR_SERIES), LUNI_SOLAR_SERIES);
  720.             final PoissonSeriesParser<DerivativeStructure> luniSolarEpsilonParser =
  721.                     luniSolarParser.
  722.                     withSinCos(0, 13, milliAS, 9, milliAS).
  723.                     withSinCos(1, 14, milliAS, 10, milliAS);
  724.             final PoissonSeries<DerivativeStructure> epsilonLuniSolarSeries =
  725.                     luniSolarEpsilonParser.parse(getStream(LUNI_SOLAR_SERIES), LUNI_SOLAR_SERIES);

  727.             final PoissonSeriesParser<DerivativeStructure> planetaryParser =
  728.                     new PoissonSeriesParser<DerivativeStructure>(21).
  729.                         withFirstDelaunay(2).
  730.                         withFirstPlanetary(7);
  731.             final PoissonSeriesParser<DerivativeStructure> planetaryPsiParser =
  732.                     planetaryParser.withSinCos(0, 17, milliAS, 18, milliAS);
  733.             final PoissonSeries<DerivativeStructure> psiPlanetarySeries =
  734.                     planetaryPsiParser.parse(getStream(PLANETARY_SERIES), PLANETARY_SERIES);
  735.             final PoissonSeriesParser<DerivativeStructure> planetaryEpsilonParser =
  736.                     planetaryParser.withSinCos(0, 19, milliAS, 20, milliAS);
  737.             final PoissonSeries<DerivativeStructure> epsilonPlanetarySeries =
  738.                     planetaryEpsilonParser.parse(getStream(PLANETARY_SERIES), PLANETARY_SERIES);

  740.             @SuppressWarnings("unchecked")
  741.             final PoissonSeries.CompiledSeries<DerivativeStructure> luniSolarSeries =
  742.                     PoissonSeries.compile(psiLuniSolarSeries, epsilonLuniSolarSeries);
  743.             @SuppressWarnings("unchecked")
  744.             final PoissonSeries.CompiledSeries<DerivativeStructure> planetarySeries =
  745.                     PoissonSeries.compile(psiPlanetarySeries, epsilonPlanetarySeries);

  747.             return new TimeFunction<double[]>() {
  748.                 /** {@inheritDoc} */
  749.                 @Override
  750.                 public double[] value(final AbsoluteDate date) {
  751.                     final BodiesElements elements = arguments.evaluateAll(date);
  752.                     final double[] luniSolar = luniSolarSeries.value(elements);
  753.                     final double[] planetary = planetarySeries.value(elements);
  754.                     return new double[] {
  755.                         luniSolar[0] + planetary[0], luniSolar[1] + planetary[1],
  756.                         IAU1994ResolutionC7.value(elements)
  757.                     };
  758.                 }
  759.             };

  761.         }

  763.         /** {@inheritDoc} */
  764.         @Override
  765.         public TimeFunction<DerivativeStructure> getGMSTFunction(final TimeScale ut1)
  766.             throws OrekitException {

  768.             // Earth Rotation Angle
  769.             final StellarAngleCapitaine era = new StellarAngleCapitaine(ut1);

  771.             // Polynomial part of the apparent sidereal time series
  772.             // which is the opposite of Equation of Origins (EO)
  773.             final double microAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-6;
  774.             final PoissonSeriesParser<DerivativeStructure> parser =
  775.                     new PoissonSeriesParser<DerivativeStructure>(17).
  776.                         withFirstDelaunay(4).
  777.                         withFirstPlanetary(9).
  778.                         withSinCos(0, 2, microAS, 3, microAS).
  779.                         withPolynomialPart('t', Unit.ARC_SECONDS);
  780.             final PolynomialNutation<DerivativeStructure> minusEO =
  781.                     parser.parse(getStream(GST_SERIES), GST_SERIES).getPolynomial();

  783.             // create a function evaluating the series
  784.             return new TimeFunction<DerivativeStructure>() {

  786.                 /** {@inheritDoc} */
  787.                 @Override
  788.                 public DerivativeStructure value(final AbsoluteDate date) {
  789.                     return era.value(date).add(minusEO.value(dsEvaluateTC(date)));
  790.                 }

  792.             };

  794.         }

  796.         /** {@inheritDoc} */
  797.         @Override
  798.         public TimeFunction<DerivativeStructure> getGASTFunction(final TimeScale ut1,
  799.                                                                  final EOPHistory eopHistory)
  800.             throws OrekitException {

  802.             // set up nutation arguments
  803.             final FundamentalNutationArguments arguments = getNutationArguments(null);

  805.             // mean obliquity function
  806.             final TimeFunction<Double> epsilon = getMeanObliquityFunction();

  808.             // set up Poisson series
  809.             final double milliAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-3;
  810.             final PoissonSeriesParser<DerivativeStructure> luniSolarPsiParser =
  811.                     new PoissonSeriesParser<DerivativeStructure>(14).
  812.                         withFirstDelaunay(1).
  813.                         withSinCos(0, 7, milliAS, 11, milliAS).
  814.                         withSinCos(1, 8, milliAS, 12, milliAS);
  815.             final PoissonSeries<DerivativeStructure> psiLuniSolarSeries =
  816.                     luniSolarPsiParser.parse(getStream(LUNI_SOLAR_SERIES), LUNI_SOLAR_SERIES);

  818.             final PoissonSeriesParser<DerivativeStructure> planetaryPsiParser =
  819.                     new PoissonSeriesParser<DerivativeStructure>(21).
  820.                         withFirstDelaunay(2).
  821.                         withFirstPlanetary(7).
  822.                         withSinCos(0, 17, milliAS, 18, milliAS);
  823.             final PoissonSeries<DerivativeStructure> psiPlanetarySeries =
  824.                     planetaryPsiParser.parse(getStream(PLANETARY_SERIES), PLANETARY_SERIES);

  826.             final double microAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-6;
  827.             final PoissonSeriesParser<DerivativeStructure> gstParser =
  828.                     new PoissonSeriesParser<DerivativeStructure>(17).
  829.                         withFirstDelaunay(4).
  830.                         withFirstPlanetary(9).
  831.                         withSinCos(0, 2, microAS, 3, microAS).
  832.                         withPolynomialPart('t', Unit.ARC_SECONDS);
  833.             final PoissonSeries<DerivativeStructure> gstSeries = gstParser.parse(getStream(GST_SERIES), GST_SERIES);
  834.             @SuppressWarnings("unchecked")
  835.             final PoissonSeries.CompiledSeries<DerivativeStructure> psiGstSeries =
  836.                     PoissonSeries.compile(psiLuniSolarSeries, psiPlanetarySeries, gstSeries);

  838.             // ERA function
  839.             final TimeFunction<DerivativeStructure> era = getEarthOrientationAngleFunction(ut1);

  841.             return new TimeFunction<DerivativeStructure>() {

  843.                 /** {@inheritDoc} */
  844.                 @Override
  845.                 public DerivativeStructure value(final AbsoluteDate date) {

  847.                     // evaluate equation of origins
  848.                     final BodiesElements elements = arguments.evaluateAll(date);
  849.                     final double[] angles = psiGstSeries.value(elements);
  850.                     final double ddPsi    = (eopHistory == null) ? 0 : eopHistory.getEquinoxNutationCorrection(date)[0];
  851.                     final double deltaPsi = angles[0] + angles[1] + ddPsi;
  852.                     final double epsilonA = epsilon.value(date);

  854.                     // subtract equation of origin from EA
  855.                     // (hence add the series above which have the sign included)
  856.                     return era.value(date).add(deltaPsi * FastMath.cos(epsilonA) + angles[2]);

  858.                 }

  860.             };

  862.         }

  864.         /** {@inheritDoc} */
  865.         @Override
  866.         public TimeFunction<double[]> getEOPTidalCorrection()
  867.             throws OrekitException {

  869.             // set up nutation arguments
  870.             // BEWARE! Using TT as the time scale here and not UT1 is intentional!
  871.             // as this correction is used to compute UT1 itself, it is not surprising we cannot use UT1 yet,
  872.             // however, using the close UTC as would seem logical make the comparison with interp.f from IERS fail
  873.             // looking in the interp.f code, the same TT scale is used for both Delaunay and gamma argument
  874.             final FundamentalNutationArguments arguments = getNutationArguments(TimeScalesFactory.getTT());

  876.             // set up Poisson series
  877.             final double microAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-6;
  878.             final PoissonSeriesParser<DerivativeStructure> xyParser = new PoissonSeriesParser<DerivativeStructure>(13).
  879.                     withOptionalColumn(1).
  880.                     withGamma(2).
  881.                     withFirstDelaunay(3);
  882.             final PoissonSeries<DerivativeStructure> xSeries =
  883.                     xyParser.
  884.                     withSinCos(0, 10, microAS, 11, microAS).
  885.                     parse(getStream(TIDAL_CORRECTION_XP_YP_SERIES), TIDAL_CORRECTION_XP_YP_SERIES);
  886.             final PoissonSeries<DerivativeStructure> ySeries =
  887.                     xyParser.
  888.                     withSinCos(0, 12, microAS, 13, microAS).
  889.                     parse(getStream(TIDAL_CORRECTION_XP_YP_SERIES), TIDAL_CORRECTION_XP_YP_SERIES);

  891.             final double microS = 1.0e-6;
  892.             final PoissonSeriesParser<DerivativeStructure> ut1Parser = new PoissonSeriesParser<DerivativeStructure>(11).
  893.                     withOptionalColumn(1).
  894.                     withGamma(2).
  895.                     withFirstDelaunay(3).
  896.                     withSinCos(0, 10, microS, 11, microS);
  897.             final PoissonSeries<DerivativeStructure> ut1Series =
  898.                     ut1Parser.parse(getStream(TIDAL_CORRECTION_UT1_SERIES), TIDAL_CORRECTION_UT1_SERIES);

  900.             @SuppressWarnings("unchecked")
  901.             final PoissonSeries.CompiledSeries<DerivativeStructure> correctionSeries =
  902.                 PoissonSeries.compile(xSeries, ySeries, ut1Series);

  904.             return new TimeFunction<double[]>() {
  905.                 /** {@inheritDoc} */
  906.                 @Override
  907.                 public double[] value(final AbsoluteDate date) {
  908.                     final FieldBodiesElements<DerivativeStructure> elements =
  909.                             arguments.evaluateDerivative(date);
  910.                     final DerivativeStructure[] correction = correctionSeries.value(elements);
  911.                     return new double[] {
  912.                         correction[0].getValue(),
  913.                         correction[1].getValue(),
  914.                         correction[2].getValue(),
  915.                         -correction[2].getPartialDerivative(1) * Constants.JULIAN_DAY
  916.                     };
  917.                 }
  918.             };

  920.         }

  922.         /** {@inheritDoc} */
  923.         public LoveNumbers getLoveNumbers() throws OrekitException {
  924.             return loadLoveNumbers(LOVE_NUMBERS);
  925.         }

  927.         /** {@inheritDoc} */
  928.         public TimeFunction<double[]> getTideFrequencyDependenceFunction(final TimeScale ut1)
  929.             throws OrekitException {

  931.             // set up nutation arguments
  932.             final FundamentalNutationArguments arguments = getNutationArguments(ut1);

  934.             // set up Poisson series
  935.             final PoissonSeriesParser<DerivativeStructure> k20Parser =
  936.                     new PoissonSeriesParser<DerivativeStructure>(18).
  937.                         withOptionalColumn(1).
  938.                         withDoodson(4, 2).
  939.                         withFirstDelaunay(10);
  940.             final PoissonSeriesParser<DerivativeStructure> k21Parser =
  941.                     new PoissonSeriesParser<DerivativeStructure>(18).
  942.                         withOptionalColumn(1).
  943.                         withDoodson(4, 3).
  944.                         withFirstDelaunay(10);
  945.             final PoissonSeriesParser<DerivativeStructure> k22Parser =
  946.                     new PoissonSeriesParser<DerivativeStructure>(16).
  947.                         withOptionalColumn(1).
  948.                         withDoodson(4, 2).
  949.                         withFirstDelaunay(10);

  951.             final double pico = 1.0e-12;
  952.             final PoissonSeries<DerivativeStructure> c20Series =
  953.                     k20Parser.
  954.                   withSinCos(0, 18, -pico, 16, pico).
  955.                     parse(getStream(K20_FREQUENCY_DEPENDENCE), K20_FREQUENCY_DEPENDENCE);
  956.             final PoissonSeries<DerivativeStructure> c21Series =
  957.                     k21Parser.
  958.                     withSinCos(0, 17, pico, 18, pico).
  959.                     parse(getStream(K21_FREQUENCY_DEPENDENCE), K21_FREQUENCY_DEPENDENCE);
  960.             final PoissonSeries<DerivativeStructure> s21Series =
  961.                     k21Parser.
  962.                     withSinCos(0, 18, -pico, 17, pico).
  963.                     parse(getStream(K21_FREQUENCY_DEPENDENCE), K21_FREQUENCY_DEPENDENCE);
  964.             final PoissonSeries<DerivativeStructure> c22Series =
  965.                     k22Parser.
  966.                     withSinCos(0, -1, pico, 16, pico).
  967.                     parse(getStream(K22_FREQUENCY_DEPENDENCE), K22_FREQUENCY_DEPENDENCE);
  968.             final PoissonSeries<DerivativeStructure> s22Series =
  969.                     k22Parser.
  970.                     withSinCos(0, 16, -pico, -1, pico).
  971.                     parse(getStream(K22_FREQUENCY_DEPENDENCE), K22_FREQUENCY_DEPENDENCE);

  973.             @SuppressWarnings("unchecked")
  974.             final PoissonSeries.CompiledSeries<DerivativeStructure> kSeries =
  975.                 PoissonSeries.compile(c20Series, c21Series, s21Series, c22Series, s22Series);

  977.             return new TimeFunction<double[]>() {
  978.                 /** {@inheritDoc} */
  979.                 @Override
  980.                 public double[] value(final AbsoluteDate date) {
  981.                     return kSeries.value(arguments.evaluateAll(date));
  982.                 }
  983.             };

  985.         }

  987.         /** {@inheritDoc} */
  988.         @Override
  989.         public double getPermanentTide() throws OrekitException {
  990.             return 4.4228e-8 * -0.31460 * getLoveNumbers().getReal(2, 0);
  991.         }

  993.         /** {@inheritDoc} */
  994.         @Override
  995.         public TimeFunction<double[]> getSolidPoleTide(final EOPHistory eopHistory)
  996.             throws OrekitException {

  998.             // annual pole from ftp://tai.bipm.org/iers/conv2003/chapter7/annual.pole
  999.             final TimeScale utc = TimeScalesFactory.getUTC();
  1000.             final SimpleTimeStampedTableParser.RowConverter<MeanPole> converter =
  1001.                 new SimpleTimeStampedTableParser.RowConverter<MeanPole>() {
  1002.                     /** {@inheritDoc} */
  1003.                     @Override
  1004.                     public MeanPole convert(final double[] rawFields) throws OrekitException {
  1005.                         return new MeanPole(new AbsoluteDate((int) rawFields[0], 1, 1, utc),
  1006.                                             rawFields[1] * Constants.ARC_SECONDS_TO_RADIANS,
  1007.                                             rawFields[2] * Constants.ARC_SECONDS_TO_RADIANS);
  1008.                     }
  1009.                 };
  1010.             final SimpleTimeStampedTableParser<MeanPole> parser =
  1011.                     new SimpleTimeStampedTableParser<MeanPole>(3, converter);
  1012.             final List<MeanPole> annualPoleList = parser.parse(getStream(ANNUAL_POLE), ANNUAL_POLE);
  1013.             final AbsoluteDate firstAnnualPoleDate = annualPoleList.get(0).getDate();
  1014.             final AbsoluteDate lastAnnualPoleDate  = annualPoleList.get(annualPoleList.size() - 1).getDate();
  1015.             final ImmutableTimeStampedCache<MeanPole> annualCache =
  1016.                     new ImmutableTimeStampedCache<MeanPole>(2, annualPoleList);

  1018.             // polynomial extension from IERS 2003, section 7.1.4, equations 23a and 23b
  1019.             final double xp0    = 0.054   * Constants.ARC_SECONDS_TO_RADIANS;
  1020.             final double xp0Dot = 0.00083 * Constants.ARC_SECONDS_TO_RADIANS / Constants.JULIAN_YEAR;
  1021.             final double yp0    = 0.357   * Constants.ARC_SECONDS_TO_RADIANS;
  1022.             final double yp0Dot = 0.00395 * Constants.ARC_SECONDS_TO_RADIANS / Constants.JULIAN_YEAR;

  1024.             // constants from IERS 2003, section 6.2
  1025.             final double globalFactor = -1.333e-9 / Constants.ARC_SECONDS_TO_RADIANS;
  1026.             final double ratio        =  0.00115;

  1028.             return new TimeFunction<double[]>() {
  1029.                 /** {@inheritDoc} */
  1030.                 @Override
  1031.                 public double[] value(final AbsoluteDate date) {

  1033.                     // we can't compute anything before the range covered by the annual pole file
  1034.                     if (date.compareTo(firstAnnualPoleDate) <= 0) {
  1035.                         return new double[] {
  1036.                             0.0, 0.0
  1037.                         };
  1038.                     }

  1040.                     // evaluate mean pole
  1041.                     double meanPoleX = 0;
  1042.                     double meanPoleY = 0;
  1043.                     if (date.compareTo(lastAnnualPoleDate) <= 0) {
  1044.                         // we are within the range covered by the annual pole file,
  1045.                         // we interpolate within it
  1046.                         try {
  1047.                             final List<MeanPole> neighbors = annualCache.getNeighbors(date);
  1048.                             final HermiteInterpolator interpolator = new HermiteInterpolator();
  1049.                             for (final MeanPole neighbor : neighbors) {
  1050.                                 interpolator.addSamplePoint(neighbor.getDate().durationFrom(date),
  1051.                                                             new double[] {
  1052.                                                                 neighbor.getX(), neighbor.getY()
  1053.                                                             });
  1054.                             }
  1055.                             final double[] interpolated = interpolator.value(0);
  1056.                             meanPoleX = interpolated[0];
  1057.                             meanPoleY = interpolated[1];
  1058.                         } catch (TimeStampedCacheException tsce) {
  1059.                             // this should never happen
  1060.                             throw new OrekitInternalError(tsce);
  1061.                         }
  1062.                     } else {

  1064.                         // we are after the range covered by the annual pole file,
  1065.                         // we use the polynomial extension
  1066.                         final double t = date.durationFrom(AbsoluteDate.J2000_EPOCH);
  1067.                         meanPoleX = xp0 + t * xp0Dot;
  1068.                         meanPoleY = yp0 + t * yp0Dot;

  1070.                     }

  1072.                     // evaluate wobble variables
  1073.                     final PoleCorrection correction = eopHistory.getPoleCorrection(date);
  1074.                     final double m1 = correction.getXp() - meanPoleX;
  1075.                     final double m2 = meanPoleY - correction.getYp();

  1077.                     return new double[] {
  1078.                         // the following correspond to the equations published in IERS 2003 conventions,
  1079.                         // section 6.2 page 65. In the publication, the equations read:
  1080.                         // ∆C₂₁ = −1.333 × 10⁻⁹ (m₁ − 0.0115m₂)
  1081.                         // ∆S₂₁ = −1.333 × 10⁻⁹ (m₂ + 0.0115m₁)
  1082.                         // However, it seems there are sign errors in these equations, which have
  1083.                         // been fixed in IERS 2010 conventions, section 6.4 page 94. In these newer
  1084.                         // publication, the equations read:
  1085.                         // ∆C₂₁ = −1.333 × 10⁻⁹ (m₁ + 0.0115m₂)
  1086.                         // ∆S₂₁ = −1.333 × 10⁻⁹ (m₂ − 0.0115m₁)
  1087.                         // the newer equations seem more consistent with the premises as the
  1088.                         // deformation due to the centrifugal potential has the form:
  1089.                         // −Ω²r²/2 sin 2θ Re [k₂(m₁ − im₂) exp(iλ)] where k₂ is the complex
  1090.                         // number 0.3077 + 0.0036i, so the real part in the previous equation is:
  1091.                         // A[Re(k₂) m₁ + Im(k₂) m₂)] cos λ + A[Re(k₂) m₂ - Im(k₂) m₁] sin λ
  1092.                         // identifying this with ∆C₂₁ cos λ + ∆S₂₁ sin λ we get:
  1093.                         // ∆C₂₁ = A Re(k₂) [m₁ + Im(k₂)/Re(k₂) m₂)]
  1094.                         // ∆S₂₁ = A Re(k₂) [m₂ - Im(k₂)/Re(k₂) m₁)]
  1095.                         // and Im(k₂)/Re(k₂) is very close to +0.00115
  1096.                         // As the equation as written in the IERS 2003 conventions are used in
  1097.                         // legacy systems, we have reproduced this alleged error here (and fixed it in
  1098.                         // the IERS 2010 conventions below) for validation purposes. We don't recommend
  1099.                         // using the IERS 2003 conventions for solid pole tide computation other than
  1100.                         // for validation or reproducibility of legacy applications behavior.
  1101.                         // As solid pole tide is small and as the sign change is on the smallest coefficient,
  1102.                         // the effect is quite small. A test case on a propagated orbit showed a position change
  1103.                         // slightly below 0.4m after a 30 days propagation on a Low Earth Orbit
  1104.                         globalFactor * (m1 - ratio * m2),
  1105.                         globalFactor * (m2 + ratio * m1),
  1106.                     };

  1108.                 }
  1109.             };

  1111.         }

  1113.         /** {@inheritDoc} */
  1114.         @Override
  1115.         public TimeFunction<double[]> getOceanPoleTide(final EOPHistory eopHistory)
  1116.             throws OrekitException {

  1118.             return new TimeFunction<double[]>() {
  1119.                 /** {@inheritDoc} */
  1120.                 @Override
  1121.                 public double[] value(final AbsoluteDate date) {
  1122.                     // there are no model for ocean pole tide prior to conventions 2010
  1123.                     return new double[] {
  1124.                         0.0, 0.0
  1125.                     };
  1126.                 }
  1127.             };
  1128.         }

  1130.     },

  1132.     /** Constant for IERS 2010 conventions. */
  1133.     IERS_2010 {

  1135.         /** Nutation arguments resources. */
  1136.         private static final String NUTATION_ARGUMENTS = IERS_BASE + "2010/nutation-arguments.txt";

  1138.         /** X series resources. */
  1139.         private static final String X_SERIES           = IERS_BASE + "2010/tab5.2a.txt";

  1141.         /** Y series resources. */
  1142.         private static final String Y_SERIES           = IERS_BASE + "2010/tab5.2b.txt";

  1144.         /** S series resources. */
  1145.         private static final String S_SERIES           = IERS_BASE + "2010/tab5.2d.txt";

  1147.         /** Psi series resources. */
  1148.         private static final String PSI_SERIES         = IERS_BASE + "2010/tab5.3a.txt";

  1150.         /** Epsilon series resources. */
  1151.         private static final String EPSILON_SERIES     = IERS_BASE + "2010/tab5.3b.txt";

  1153.         /** Greenwhich sidereal time series resources. */
  1154.         private static final String GST_SERIES         = IERS_BASE + "2010/tab5.2e.txt";

  1156.         /** Tidal correction for xp, yp series resources. */
  1157.         private static final String TIDAL_CORRECTION_XP_YP_SERIES = IERS_BASE + "2010/tab8.2ab.txt";

  1159.         /** Tidal correction for UT1 resources. */
  1160.         private static final String TIDAL_CORRECTION_UT1_SERIES = IERS_BASE + "2010/tab8.3ab.txt";

  1162.         /** Love numbers resources. */
  1163.         private static final String LOVE_NUMBERS = IERS_BASE + "2010/tab6.3.txt";

  1165.         /** Frequency dependence model for k₂₀. */
  1166.         private static final String K20_FREQUENCY_DEPENDENCE = IERS_BASE + "2010/tab6.5b.txt";

  1168.         /** Frequency dependence model for k₂₁. */
  1169.         private static final String K21_FREQUENCY_DEPENDENCE = IERS_BASE + "2010/tab6.5a.txt";

  1171.         /** Frequency dependence model for k₂₂. */
  1172.         private static final String K22_FREQUENCY_DEPENDENCE = IERS_BASE + "2010/tab6.5c.txt";

  1174.         /** {@inheritDoc} */
  1175.         public FundamentalNutationArguments getNutationArguments(final TimeScale timeScale)
  1176.             throws OrekitException {
  1177.             return new FundamentalNutationArguments(this, timeScale,
  1178.                                                     getStream(NUTATION_ARGUMENTS), NUTATION_ARGUMENTS);
  1179.         }

  1181.         /** {@inheritDoc} */
  1182.         @Override
  1183.         public TimeFunction<Double> getMeanObliquityFunction() throws OrekitException {

  1185.             // epsilon 0 value from chapter 5, page 56, other terms from equation 5.40 page 65
  1186.             final PolynomialNutation<DerivativeStructure> epsilonA =
  1187.                     new PolynomialNutation<DerivativeStructure>(84381.406        * Constants.ARC_SECONDS_TO_RADIANS,
  1188.                                                                   -46.836769     * Constants.ARC_SECONDS_TO_RADIANS,
  1189.                                                                    -0.0001831    * Constants.ARC_SECONDS_TO_RADIANS,
  1190.                                                                     0.00200340   * Constants.ARC_SECONDS_TO_RADIANS,
  1191.                                                                    -0.000000576  * Constants.ARC_SECONDS_TO_RADIANS,
  1192.                                                                    -0.0000000434 * Constants.ARC_SECONDS_TO_RADIANS);

  1194.             return new TimeFunction<Double>() {

  1196.                 /** {@inheritDoc} */
  1197.                 @Override
  1198.                 public Double value(final AbsoluteDate date) {
  1199.                     return epsilonA.value(evaluateTC(date));
  1200.                 }

  1202.             };

  1204.         }

  1206.         /** {@inheritDoc} */
  1207.         @Override
  1208.         public TimeFunction<double[]> getXYSpXY2Function() throws OrekitException {

  1210.             // set up nutation arguments
  1211.             final FundamentalNutationArguments arguments = getNutationArguments(null);

  1213.             // set up Poisson series
  1214.             final double microAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-6;
  1215.             final PoissonSeriesParser<DerivativeStructure> parser =
  1216.                     new PoissonSeriesParser<DerivativeStructure>(17).
  1217.                         withPolynomialPart('t', PolynomialParser.Unit.MICRO_ARC_SECONDS).
  1218.                         withFirstDelaunay(4).
  1219.                         withFirstPlanetary(9).
  1220.                         withSinCos(0, 2, microAS, 3, microAS);
  1221.             final PoissonSeries<DerivativeStructure> xSeries = parser.parse(getStream(X_SERIES), X_SERIES);
  1222.             final PoissonSeries<DerivativeStructure> ySeries = parser.parse(getStream(Y_SERIES), Y_SERIES);
  1223.             final PoissonSeries<DerivativeStructure> sSeries = parser.parse(getStream(S_SERIES), S_SERIES);
  1224.             @SuppressWarnings("unchecked")
  1225.             final PoissonSeries.CompiledSeries<DerivativeStructure> xys = PoissonSeries.compile(xSeries, ySeries, sSeries);

  1227.             // create a function evaluating the series
  1228.             return new TimeFunction<double[]>() {

  1230.                 /** {@inheritDoc} */
  1231.                 @Override
  1232.                 public double[] value(final AbsoluteDate date) {
  1233.                     return xys.value(arguments.evaluateAll(date));
  1234.                 }

  1236.             };

  1238.         }

  1240.         /** {@inheritDoc} */
  1241.         public LoveNumbers getLoveNumbers() throws OrekitException {
  1242.             return loadLoveNumbers(LOVE_NUMBERS);
  1243.         }

  1245.         /** {@inheritDoc} */
  1246.         public TimeFunction<double[]> getTideFrequencyDependenceFunction(final TimeScale ut1)
  1247.             throws OrekitException {

  1249.             // set up nutation arguments
  1250.             final FundamentalNutationArguments arguments = getNutationArguments(ut1);

  1252.             // set up Poisson series
  1253.             final PoissonSeriesParser<DerivativeStructure> k20Parser =
  1254.                     new PoissonSeriesParser<DerivativeStructure>(18).
  1255.                         withOptionalColumn(1).
  1256.                         withDoodson(4, 2).
  1257.                         withFirstDelaunay(10);
  1258.             final PoissonSeriesParser<DerivativeStructure> k21Parser =
  1259.                     new PoissonSeriesParser<DerivativeStructure>(18).
  1260.                         withOptionalColumn(1).
  1261.                         withDoodson(4, 3).
  1262.                         withFirstDelaunay(10);
  1263.             final PoissonSeriesParser<DerivativeStructure> k22Parser =
  1264.                     new PoissonSeriesParser<DerivativeStructure>(16).
  1265.                         withOptionalColumn(1).
  1266.                         withDoodson(4, 2).
  1267.                         withFirstDelaunay(10);

  1269.             final double pico = 1.0e-12;
  1270.             final PoissonSeries<DerivativeStructure> c20Series =
  1271.                     k20Parser.
  1272.                     withSinCos(0, 18, -pico, 16, pico).
  1273.                     parse(getStream(K20_FREQUENCY_DEPENDENCE), K20_FREQUENCY_DEPENDENCE);
  1274.             final PoissonSeries<DerivativeStructure> c21Series =
  1275.                     k21Parser.
  1276.                     withSinCos(0, 17, pico, 18, pico).
  1277.                     parse(getStream(K21_FREQUENCY_DEPENDENCE), K21_FREQUENCY_DEPENDENCE);
  1278.             final PoissonSeries<DerivativeStructure> s21Series =
  1279.                     k21Parser.
  1280.                     withSinCos(0, 18, -pico, 17, pico).
  1281.                     parse(getStream(K21_FREQUENCY_DEPENDENCE), K21_FREQUENCY_DEPENDENCE);
  1282.             final PoissonSeries<DerivativeStructure> c22Series =
  1283.                     k22Parser.
  1284.                     withSinCos(0, -1, pico, 16, pico).
  1285.                     parse(getStream(K22_FREQUENCY_DEPENDENCE), K22_FREQUENCY_DEPENDENCE);
  1286.             final PoissonSeries<DerivativeStructure> s22Series =
  1287.                     k22Parser.
  1288.                     withSinCos(0, 16, -pico, -1, pico).
  1289.                     parse(getStream(K22_FREQUENCY_DEPENDENCE), K22_FREQUENCY_DEPENDENCE);

  1291.             @SuppressWarnings("unchecked")
  1292.             final PoissonSeries.CompiledSeries<DerivativeStructure> kSeries =
  1293.                 PoissonSeries.compile(c20Series, c21Series, s21Series, c22Series, s22Series);

  1295.             return new TimeFunction<double[]>() {
  1296.                 /** {@inheritDoc} */
  1297.                 @Override
  1298.                 public double[] value(final AbsoluteDate date) {
  1299.                     return kSeries.value(arguments.evaluateAll(date));
  1300.                 }
  1301.             };

  1303.         }

  1305.         /** {@inheritDoc} */
  1306.         @Override
  1307.         public double getPermanentTide() throws OrekitException {
  1308.             return 4.4228e-8 * -0.31460 * getLoveNumbers().getReal(2, 0);
  1309.         }

  1311.         /** Compute pole wobble variables m₁ and m₂.
  1312.          * @param date current date
  1313.          * @param eopHistory EOP history
  1314.          * @return array containing m₁ and m₂
  1315.          */
  1316.         private double[] computePoleWobble(final AbsoluteDate date, final EOPHistory eopHistory) {

  1318.             // polynomial model from IERS 2010, table 7.7
  1319.             final double f0 = Constants.ARC_SECONDS_TO_RADIANS / 1000.0;
  1320.             final double f1 = f0 / Constants.JULIAN_YEAR;
  1321.             final double f2 = f1 / Constants.JULIAN_YEAR;
  1322.             final double f3 = f2 / Constants.JULIAN_YEAR;
  1323.             final AbsoluteDate changeDate = new AbsoluteDate(2010, 1, 1, TimeScalesFactory.getTT());

  1325.             // evaluate mean pole
  1326.             final double[] xPolynomial;
  1327.             final double[] yPolynomial;
  1328.             if (date.compareTo(changeDate) <= 0) {
  1329.                 xPolynomial = new double[] {
  1330.                     55.974 * f0, 1.8243 * f1, 0.18413 * f2, 0.007024 * f3
  1331.                 };
  1332.                 yPolynomial = new double[] {
  1333.                     346.346 * f0, 1.7896 * f1, -0.10729 * f2, -0.000908 * f3
  1334.                 };
  1335.             } else {
  1336.                 xPolynomial = new double[] {
  1337.                     23.513 * f0, 7.6141 * f1
  1338.                 };
  1339.                 yPolynomial = new double[] {
  1340.                     358.891 * f0,  -0.6287 * f1
  1341.                 };
  1342.             }
  1343.             double meanPoleX = 0;
  1344.             double meanPoleY = 0;
  1345.             final double t = date.durationFrom(AbsoluteDate.J2000_EPOCH);
  1346.             for (int i = xPolynomial.length - 1; i >= 0; --i) {
  1347.                 meanPoleX = meanPoleX * t + xPolynomial[i];
  1348.             }
  1349.             for (int i = yPolynomial.length - 1; i >= 0; --i) {
  1350.                 meanPoleY = meanPoleY * t + yPolynomial[i];
  1351.             }

  1353.             // evaluate wobble variables
  1354.             final PoleCorrection correction = eopHistory.getPoleCorrection(date);
  1355.             final double m1 = correction.getXp() - meanPoleX;
  1356.             final double m2 = meanPoleY - correction.getYp();

  1358.             return new double[] {
  1359.                 m1, m2
  1360.             };

  1362.         }

  1364.         /** {@inheritDoc} */
  1365.         @Override
  1366.         public TimeFunction<double[]> getSolidPoleTide(final EOPHistory eopHistory)
  1367.             throws OrekitException {

  1369.             // constants from IERS 2010, section 6.4
  1370.             final double globalFactor = -1.333e-9 / Constants.ARC_SECONDS_TO_RADIANS;
  1371.             final double ratio        =  0.00115;

  1373.             return new TimeFunction<double[]>() {
  1374.                 /** {@inheritDoc} */
  1375.                 @Override
  1376.                 public double[] value(final AbsoluteDate date) {

  1378.                     // evaluate wobble variables
  1379.                     final double[] wobbleM = computePoleWobble(date, eopHistory);

  1381.                     return new double[] {
  1382.                         // the following correspond to the equations published in IERS 2010 conventions,
  1383.                         // section 6.4 page 94. The equations read:
  1384.                         // ∆C₂₁ = −1.333 × 10⁻⁹ (m₁ + 0.0115m₂)
  1385.                         // ∆S₂₁ = −1.333 × 10⁻⁹ (m₂ − 0.0115m₁)
  1386.                         // These equations seem to fix what was probably a sign error in IERS 2003
  1387.                         // conventions section 6.2 page 65. In this older publication, the equations read:
  1388.                         // ∆C₂₁ = −1.333 × 10⁻⁹ (m₁ − 0.0115m₂)
  1389.                         // ∆S₂₁ = −1.333 × 10⁻⁹ (m₂ + 0.0115m₁)
  1390.                         globalFactor * (wobbleM[0] + ratio * wobbleM[1]),
  1391.                         globalFactor * (wobbleM[1] - ratio * wobbleM[0])
  1392.                     };

  1394.                 }
  1395.             };

  1397.         }

  1399.         /** {@inheritDoc} */
  1400.         @Override
  1401.         public TimeFunction<double[]> getOceanPoleTide(final EOPHistory eopHistory)
  1402.             throws OrekitException {

  1404.             return new TimeFunction<double[]>() {
  1405.                 /** {@inheritDoc} */
  1406.                 @Override
  1407.                 public double[] value(final AbsoluteDate date) {

  1409.                     // evaluate wobble variables
  1410.                     final double[] wobbleM = computePoleWobble(date, eopHistory);

  1412.                     return new double[] {
  1413.                         // the following correspond to the equations published in IERS 2010 conventions,
  1414.                         // section 6.4 page 94 equation 6.24:
  1415.                         // ∆C₂₁ = −2.1778 × 10⁻¹⁰ (m₁ − 0.01724m₂)
  1416.                         // ∆S₂₁ = −1.7232 × 10⁻¹⁰ (m₂ − 0.03365m₁)
  1417.                         -2.1778e-10 * (wobbleM[0] - 0.01724 * wobbleM[1]) / Constants.ARC_SECONDS_TO_RADIANS,
  1418.                         -1.7232e-10 * (wobbleM[1] - 0.03365 * wobbleM[0]) / Constants.ARC_SECONDS_TO_RADIANS
  1419.                     };

  1421.                 }
  1422.             };

  1424.         }

  1426.         /** {@inheritDoc} */
  1427.         @Override
  1428.         public TimeFunction<double[]> getPrecessionFunction() throws OrekitException {

  1430.             // set up the conventional polynomials
  1431.             // the following values are from equation 5.40 in IERS 2010 conventions
  1432.             final PolynomialNutation<DerivativeStructure> psiA =
  1433.                     new PolynomialNutation<DerivativeStructure>(   0.0,
  1434.                                                                 5038.481507     * Constants.ARC_SECONDS_TO_RADIANS,
  1435.                                                                   -1.0790069    * Constants.ARC_SECONDS_TO_RADIANS,
  1436.                                                                   -0.00114045   * Constants.ARC_SECONDS_TO_RADIANS,
  1437.                                                                    0.000132851  * Constants.ARC_SECONDS_TO_RADIANS,
  1438.                                                                   -0.0000000951 * Constants.ARC_SECONDS_TO_RADIANS);
  1439.             final PolynomialNutation<DerivativeStructure> omegaA =
  1440.                     new PolynomialNutation<DerivativeStructure>(getMeanObliquityFunction().value(getNutationReferenceEpoch()),
  1441.                                                                 -0.025754     * Constants.ARC_SECONDS_TO_RADIANS,
  1442.                                                                  0.0512623    * Constants.ARC_SECONDS_TO_RADIANS,
  1443.                                                                 -0.00772503   * Constants.ARC_SECONDS_TO_RADIANS,
  1444.                                                                 -0.000000467  * Constants.ARC_SECONDS_TO_RADIANS,
  1445.                                                                  0.0000003337 * Constants.ARC_SECONDS_TO_RADIANS);
  1446.             final PolynomialNutation<DerivativeStructure> chiA =
  1447.                     new PolynomialNutation<DerivativeStructure>( 0.0,
  1448.                                                                 10.556403     * Constants.ARC_SECONDS_TO_RADIANS,
  1449.                                                                 -2.3814292    * Constants.ARC_SECONDS_TO_RADIANS,
  1450.                                                                 -0.00121197   * Constants.ARC_SECONDS_TO_RADIANS,
  1451.                                                                  0.000170663  * Constants.ARC_SECONDS_TO_RADIANS,
  1452.                                                                 -0.0000000560 * Constants.ARC_SECONDS_TO_RADIANS);

  1454.             return new TimeFunction<double[]>() {
  1455.                 /** {@inheritDoc} */
  1456.                 @Override
  1457.                 public double[] value(final AbsoluteDate date) {
  1458.                     final double tc = evaluateTC(date);
  1459.                     return new double[] {
  1460.                         psiA.value(tc), omegaA.value(tc), chiA.value(tc)
  1461.                     };
  1462.                 }
  1463.             };

  1465.         }

  1467.          /** {@inheritDoc} */
  1468.         @Override
  1469.         public TimeFunction<double[]> getNutationFunction()
  1470.             throws OrekitException {

  1472.             // set up nutation arguments
  1473.             final FundamentalNutationArguments arguments = getNutationArguments(null);

  1475.             // set up Poisson series
  1476.             final double microAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-6;
  1477.             final PoissonSeriesParser<DerivativeStructure> parser =
  1478.                     new PoissonSeriesParser<DerivativeStructure>(17).
  1479.                         withFirstDelaunay(4).
  1480.                         withFirstPlanetary(9).
  1481.                         withSinCos(0, 2, microAS, 3, microAS);
  1482.             final PoissonSeries<DerivativeStructure> psiSeries     = parser.parse(getStream(PSI_SERIES), PSI_SERIES);
  1483.             final PoissonSeries<DerivativeStructure> epsilonSeries = parser.parse(getStream(EPSILON_SERIES), EPSILON_SERIES);
  1484.             @SuppressWarnings("unchecked")
  1485.             final PoissonSeries.CompiledSeries<DerivativeStructure> psiEpsilonSeries =
  1486.                     PoissonSeries.compile(psiSeries, epsilonSeries);

  1488.             return new TimeFunction<double[]>() {
  1489.                 /** {@inheritDoc} */
  1490.                 @Override
  1491.                 public double[] value(final AbsoluteDate date) {
  1492.                     final BodiesElements elements = arguments.evaluateAll(date);
  1493.                     final double[] psiEpsilon = psiEpsilonSeries.value(elements);
  1494.                     return new double[] {
  1495.                         psiEpsilon[0], psiEpsilon[1], IAU1994ResolutionC7.value(elements)
  1496.                     };
  1497.                 }
  1498.             };

  1500.         }

  1502.         /** {@inheritDoc} */
  1503.         @Override
  1504.         public TimeFunction<DerivativeStructure> getGMSTFunction(final TimeScale ut1) throws OrekitException {

  1506.             // Earth Rotation Angle
  1507.             final StellarAngleCapitaine era = new StellarAngleCapitaine(ut1);

  1509.             // Polynomial part of the apparent sidereal time series
  1510.             // which is the opposite of Equation of Origins (EO)
  1511.             final double microAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-6;
  1512.             final PoissonSeriesParser<DerivativeStructure> parser =
  1513.                     new PoissonSeriesParser<DerivativeStructure>(17).
  1514.                         withFirstDelaunay(4).
  1515.                         withFirstPlanetary(9).
  1516.                         withSinCos(0, 2, microAS, 3, microAS).
  1517.                         withPolynomialPart('t', Unit.ARC_SECONDS);
  1518.             final PolynomialNutation<DerivativeStructure> minusEO =
  1519.                     parser.parse(getStream(GST_SERIES), GST_SERIES).getPolynomial();

  1521.             // create a function evaluating the series
  1522.             return new TimeFunction<DerivativeStructure>() {

  1524.                 /** {@inheritDoc} */
  1525.                 @Override
  1526.                 public DerivativeStructure value(final AbsoluteDate date) {
  1527.                     return era.value(date).add(minusEO.value(dsEvaluateTC(date)));
  1528.                 }

  1530.             };

  1532.         }

  1534.         /** {@inheritDoc} */
  1535.         @Override
  1536.         public TimeFunction<DerivativeStructure> getGASTFunction(final TimeScale ut1,
  1537.                                                                  final EOPHistory eopHistory)
  1538.             throws OrekitException {

  1540.             // set up nutation arguments
  1541.             final FundamentalNutationArguments arguments = getNutationArguments(null);

  1543.             // mean obliquity function
  1544.             final TimeFunction<Double> epsilon = getMeanObliquityFunction();

  1546.             // set up Poisson series
  1547.             final double microAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-6;
  1548.             final PoissonSeriesParser<DerivativeStructure> baseParser =
  1549.                     new PoissonSeriesParser<DerivativeStructure>(17).
  1550.                         withFirstDelaunay(4).
  1551.                         withFirstPlanetary(9).
  1552.                         withSinCos(0, 2, microAS, 3, microAS);
  1553.             final PoissonSeriesParser<DerivativeStructure> gstParser  = baseParser.withPolynomialPart('t', Unit.ARC_SECONDS);
  1554.             final PoissonSeries<DerivativeStructure> psiSeries        = baseParser.parse(getStream(PSI_SERIES), PSI_SERIES);
  1555.             final PoissonSeries<DerivativeStructure> gstSeries        = gstParser.parse(getStream(GST_SERIES), GST_SERIES);
  1556.             @SuppressWarnings("unchecked")
  1557.             final PoissonSeries.CompiledSeries<DerivativeStructure> psiGstSeries =
  1558.                     PoissonSeries.compile(psiSeries, gstSeries);

  1560.             // ERA function
  1561.             final TimeFunction<DerivativeStructure> era = getEarthOrientationAngleFunction(ut1);

  1563.             return new TimeFunction<DerivativeStructure>() {

  1565.                 /** {@inheritDoc} */
  1566.                 @Override
  1567.                 public DerivativeStructure value(final AbsoluteDate date) {

  1569.                     // evaluate equation of origins
  1570.                     final BodiesElements elements = arguments.evaluateAll(date);
  1571.                     final double[] angles = psiGstSeries.value(elements);
  1572.                     final double ddPsi    = (eopHistory == null) ? 0 : eopHistory.getEquinoxNutationCorrection(date)[0];
  1573.                     final double deltaPsi = angles[0] + ddPsi;
  1574.                     final double epsilonA = epsilon.value(date);

  1576.                     // subtract equation of origin from EA
  1577.                     // (hence add the series above which have the sign included)
  1578.                     return era.value(date).add(deltaPsi * FastMath.cos(epsilonA) + angles[1]);

  1580.                 }

  1582.             };

  1584.         }

  1586.         /** {@inheritDoc} */
  1587.         @Override
  1588.         public TimeFunction<double[]> getEOPTidalCorrection()
  1589.             throws OrekitException {

  1591.             // set up nutation arguments
  1592.             // BEWARE! Using TT as the time scale here and not UT1 is intentional!
  1593.             // as this correction is used to compute UT1 itself, it is not surprising we cannot use UT1 yet,
  1594.             // however, using the close UTC as would seem logical make the comparison with interp.f from IERS fail
  1595.             // looking in the interp.f code, the same TT scale is used for both Delaunay and gamma argument
  1596.             final FundamentalNutationArguments arguments = getNutationArguments(TimeScalesFactory.getTT());

  1598.             // set up Poisson series
  1599.             final double microAS = Constants.ARC_SECONDS_TO_RADIANS * 1.0e-6;
  1600.             final PoissonSeriesParser<DerivativeStructure> xyParser = new PoissonSeriesParser<DerivativeStructure>(13).
  1601.                     withOptionalColumn(1).
  1602.                     withGamma(2).
  1603.                     withFirstDelaunay(3);
  1604.             final PoissonSeries<DerivativeStructure> xSeries =
  1605.                     xyParser.
  1606.                     withSinCos(0, 10, microAS, 11, microAS).
  1607.                     parse(getStream(TIDAL_CORRECTION_XP_YP_SERIES), TIDAL_CORRECTION_XP_YP_SERIES);
  1608.             final PoissonSeries<DerivativeStructure> ySeries =
  1609.                     xyParser.
  1610.                     withSinCos(0, 12, microAS, 13, microAS).
  1611.                     parse(getStream(TIDAL_CORRECTION_XP_YP_SERIES), TIDAL_CORRECTION_XP_YP_SERIES);

  1613.             final double microS = 1.0e-6;
  1614.             final PoissonSeriesParser<DerivativeStructure> ut1Parser = new PoissonSeriesParser<DerivativeStructure>(11).
  1615.                     withOptionalColumn(1).
  1616.                     withGamma(2).
  1617.                     withFirstDelaunay(3).
  1618.                     withSinCos(0, 10, microS, 11, microS);
  1619.             final PoissonSeries<DerivativeStructure> ut1Series =
  1620.                     ut1Parser.parse(getStream(TIDAL_CORRECTION_UT1_SERIES), TIDAL_CORRECTION_UT1_SERIES);

  1622.             @SuppressWarnings("unchecked")
  1623.             final PoissonSeries.CompiledSeries<DerivativeStructure> correctionSeries =
  1624.                     PoissonSeries.compile(xSeries, ySeries, ut1Series);

  1626.             return new TimeFunction<double[]>() {
  1627.                 /** {@inheritDoc} */
  1628.                 @Override
  1629.                 public double[] value(final AbsoluteDate date) {
  1630.                     final FieldBodiesElements<DerivativeStructure> elements =
  1631.                             arguments.evaluateDerivative(date);
  1632.                     final DerivativeStructure[] correction = correctionSeries.value(elements);
  1633.                     return new double[] {
  1634.                         correction[0].getValue(),
  1635.                         correction[1].getValue(),
  1636.                         correction[2].getValue(),
  1637.                         -correction[2].getPartialDerivative(1) * Constants.JULIAN_DAY
  1638.                     };
  1639.                 }
  1640.             };

  1642.         }

  1644.     };

  1646.     /** IERS conventions resources base directory. */
  1647.     private static final String IERS_BASE = "/assets/org/orekit/IERS-conventions/";

  1649.     /** Get the reference epoch for fundamental nutation arguments.
  1650.      * @return reference epoch for fundamental nutation arguments
  1651.      * @since 6.1
  1652.      */
  1653.     public AbsoluteDate getNutationReferenceEpoch() {
  1654.         // IERS 1996, IERS 2003 and IERS 2010 use the same J2000.0 reference date
  1655.         return AbsoluteDate.J2000_EPOCH;
  1656.     }

  1658.     /** Evaluate the date offset between the current date and the {@link #getNutationReferenceEpoch() reference date}.
  1659.      * @param date current date
  1660.      * @return date offset in Julian centuries
  1661.      * @since 6.1
  1662.      */
  1663.     public double evaluateTC(final AbsoluteDate date) {
  1664.         return date.durationFrom(getNutationReferenceEpoch()) / Constants.JULIAN_CENTURY;
  1665.     }

  1667.     /** Evaluate the date offset between the current date and the {@link #getNutationReferenceEpoch() reference date}.
  1668.      * @param date current date
  1669.      * @return date offset in Julian centuries
  1670.      * @since 6.1
  1671.      */
  1672.     public DerivativeStructure dsEvaluateTC(final AbsoluteDate date) {
  1673.         return new DerivativeStructure(1, 1, evaluateTC(date), 1.0 / Constants.JULIAN_CENTURY);
  1674.     }

  1676.     /** Get the fundamental nutation arguments.
  1677.      * @param timeScale time scale for computing Greenwich Mean Sidereal Time
  1678.      * (typically {@link TimeScalesFactory#getUT1(IERSConventions, boolean) UT1})
  1679.      * @return fundamental nutation arguments
  1680.      * @exception OrekitException if fundamental nutation arguments cannot be loaded
  1681.      * @since 6.1
  1682.      */
  1683.     public abstract FundamentalNutationArguments getNutationArguments(final TimeScale timeScale)
  1684.         throws OrekitException;

  1686.     /** Get the function computing mean obliquity of the ecliptic.
  1687.      * @return function computing mean obliquity of the ecliptic
  1688.      * @exception OrekitException if table cannot be loaded
  1689.      * @since 6.1
  1690.      */
  1691.     public abstract TimeFunction<Double> getMeanObliquityFunction() throws OrekitException;

  1693.     /** Get the function computing the Celestial Intermediate Pole and Celestial Intermediate Origin components.
  1694.      * <p>
  1695.      * The returned function computes the two X, Y components of CIP and the S+XY/2 component of the non-rotating CIO.
  1696.      * </p>
  1697.      * @return function computing the Celestial Intermediate Pole and Celestial Intermediate Origin components
  1698.      * @exception OrekitException if table cannot be loaded
  1699.      * @since 6.1
  1700.      */
  1701.     public abstract TimeFunction<double[]> getXYSpXY2Function()
  1702.         throws OrekitException;

  1704.     /** Get the function computing the raw Earth Orientation Angle.
  1705.      * <p>
  1706.      * The raw angle does not contain any correction. If for example dTU1 correction
  1707.      * due to tidal effect is desired, it must be added afterward by the caller.
  1708.      * The returned value contain the angle as the value and the angular rate as
  1709.      * the first derivative.
  1710.      * </p>
  1711.      * @param ut1 UT1 time scale
  1712.      * @return function computing the rawEarth Orientation Angle, in the non-rotating origin paradigm,
  1713.      * the return value containing both the angle and its first time derivative
  1714.      * @since 6.1
  1715.      */
  1716.     public TimeFunction<DerivativeStructure> getEarthOrientationAngleFunction(final TimeScale ut1) {
  1717.         return new StellarAngleCapitaine(ut1);
  1718.     }


  1721.     /** Get the function computing the precession angles.
  1722.      * <p>
  1723.      * The function returned computes the three precession angles
  1724.      * ψ<sub>A</sub> (around Z axis), ω<sub>A</sub> (around X axis)
  1725.      * and χ<sub>A</sub> (around Z axis). The constant angle ε₀
  1726.      * for the fourth rotation (around X axis) can be retrieved by evaluating the
  1727.      * function returned by {@link #getMeanObliquityFunction()} at {@link
  1728.      * #getNutationReferenceEpoch() nutation reference epoch}.
  1729.      * </p>
  1730.      * @return function computing the precession angle
  1731.      * @exception OrekitException if table cannot be loaded
  1732.      * @since 6.1
  1733.      */
  1734.     public abstract TimeFunction<double[]> getPrecessionFunction() throws OrekitException;

  1736.     /** Get the function computing the nutation angles.
  1737.      * <p>
  1738.      * The function returned computes the two classical angles ΔΨ and Δε,
  1739.      * and the correction to the equation of equinoxes introduced since 1997-02-27 by IAU 1994
  1740.      * resolution C7 (the correction is forced to 0 before this date)
  1741.      * </p>
  1742.      * @return function computing the nutation in longitude ΔΨ and Δε
  1743.      * and the correction of equation of equinoxes
  1744.      * @exception OrekitException if table cannot be loaded
  1745.      * @since 6.1
  1746.      */
  1747.     public abstract TimeFunction<double[]> getNutationFunction()
  1748.         throws OrekitException;

  1750.     /** Get the function computing Greenwich mean sidereal time, in radians.
  1751.      * @param ut1 UT1 time scale
  1752.      * @return function computing Greenwich mean sidereal time,
  1753.      * the return value containing both the angle and its first time derivative
  1754.      * @exception OrekitException if table cannot be loaded
  1755.      * @since 6.1
  1756.      */
  1757.     public abstract TimeFunction<DerivativeStructure> getGMSTFunction(TimeScale ut1)
  1758.         throws OrekitException;

  1760.     /** Get the function computing Greenwich apparent sidereal time, in radians.
  1761.      * @param ut1 UT1 time scale
  1762.      * @param eopHistory EOP history
  1763.      * @return function computing Greenwich apparent sidereal time,
  1764.      * the return value containing both the angle and its first time derivative
  1765.      * @exception OrekitException if table cannot be loaded
  1766.      * @since 6.1
  1767.      */
  1768.     public abstract TimeFunction<DerivativeStructure> getGASTFunction(TimeScale ut1,
  1769.                                                                       EOPHistory eopHistory)
  1770.         throws OrekitException;

  1772.     /** Get the function computing tidal corrections for Earth Orientation Parameters.
  1773.      * @return function computing tidal corrections for Earth Orientation Parameters,
  1774.      * for xp, yp, ut1 and lod respectively
  1775.      * @exception OrekitException if table cannot be loaded
  1776.      * @since 6.1
  1777.      */
  1778.     public abstract TimeFunction<double[]> getEOPTidalCorrection()
  1779.         throws OrekitException;

  1781.     /** Get the Love numbers.
  1782.      * @return Love numbers
  1783.      * @exception OrekitException if table cannot be loaded
  1784.      * @since 6.1
  1785.      */
  1786.     public abstract LoveNumbers getLoveNumbers()
  1787.         throws OrekitException;

  1789.     /** Get the function computing frequency dependent terms (ΔC₂₀, ΔC₂₁, ΔS₂₁, ΔC₂₂, ΔS₂₂).
  1790.      * @param ut1 UT1 time scale
  1791.      * @return frequency dependence model for tides computation (ΔC₂₀, ΔC₂₁, ΔS₂₁, ΔC₂₂, ΔS₂₂).
  1792.      * @exception OrekitException if table cannot be loaded
  1793.      * @since 6.1
  1794.      */
  1795.     public abstract TimeFunction<double[]> getTideFrequencyDependenceFunction(TimeScale ut1)
  1796.         throws OrekitException;

  1798.     /** Get the permanent tide to be <em>removed</em> from ΔC₂₀ when zero-tide potentials are used.
  1799.      * @return permanent tide to remove
  1800.      * @exception OrekitException if table cannot be loaded
  1801.      */
  1802.     public abstract double getPermanentTide() throws OrekitException;

  1804.     /** Get the function computing solid pole tide (ΔC₂₁, ΔS₂₁).
  1805.      * @param eopHistory EOP history
  1806.      * @return model for solid pole tide (ΔC₂₀, ΔC₂₁, ΔS₂₁, ΔC₂₂, ΔS₂₂).
  1807.      * @exception OrekitException if table cannot be loaded
  1808.      * @since 6.1
  1809.      */
  1810.     public abstract TimeFunction<double[]> getSolidPoleTide(EOPHistory eopHistory)
  1811.         throws OrekitException;

  1813.     /** Get the function computing ocean pole tide (ΔC₂₁, ΔS₂₁).
  1814.      * @param eopHistory EOP history
  1815.      * @return model for ocean pole tide (ΔC₂₀, ΔC₂₁, ΔS₂₁, ΔC₂₂, ΔS₂₂).
  1816.      * @exception OrekitException if table cannot be loaded
  1817.      * @since 6.1
  1818.      */
  1819.     public abstract TimeFunction<double[]> getOceanPoleTide(EOPHistory eopHistory)
  1820.         throws OrekitException;

  1822.     /** Interface for functions converting nutation corrections between
  1823.      * δΔψ/δΔε to δX/δY.
  1824.      * <ul>
  1825.      * <li>δΔψ/δΔε nutation corrections are used with the equinox-based paradigm.</li>
  1826.      * <li>δX/δY nutation corrections are used with the Non-Rotating Origin paradigm.</li>
  1827.      * </ul>
  1828.      * @since 6.1
  1829.      */
  1830.     public interface NutationCorrectionConverter {

  1832.         /** Convert nutation corrections.
  1833.          * @param date current date
  1834.          * @param ddPsi δΔψ part of the nutation correction
  1835.          * @param ddEpsilon δΔε part of the nutation correction
  1836.          * @return array containing δX and δY
  1837.          * @exception OrekitException if correction cannot be converted
  1838.          */
  1839.         double[] toNonRotating(AbsoluteDate date, double ddPsi, double ddEpsilon)
  1840.             throws OrekitException;

  1842.         /** Convert nutation corrections.
  1843.          * @param date current date
  1844.          * @param dX δX part of the nutation correction
  1845.          * @param dY δY part of the nutation correction
  1846.          * @return array containing δΔψ and δΔε
  1847.          * @exception OrekitException if correction cannot be converted
  1848.          */
  1849.         double[] toEquinox(AbsoluteDate date, double dX, double dY)
  1850.             throws OrekitException;

  1852.     }

  1854.     /** Create a function converting nutation corrections between
  1855.      * δX/δY and δΔψ/δΔε.
  1856.      * <ul>
  1857.      * <li>δX/δY nutation corrections are used with the Non-Rotating Origin paradigm.</li>
  1858.      * <li>δΔψ/δΔε nutation corrections are used with the equinox-based paradigm.</li>
  1859.      * </ul>
  1860.      * @return a new converter
  1861.      * @exception OrekitException if some convention table cannot be loaded
  1862.      * @since 6.1
  1863.      */
  1864.     public NutationCorrectionConverter getNutationCorrectionConverter()
  1865.         throws OrekitException {

  1867.         // get models parameters
  1868.         final TimeFunction<double[]> precessionFunction = getPrecessionFunction();
  1869.         final TimeFunction<Double> epsilonAFunction = getMeanObliquityFunction();
  1870.         final AbsoluteDate date0 = getNutationReferenceEpoch();
  1871.         final double cosE0 = FastMath.cos(epsilonAFunction.value(date0));

  1873.         return new NutationCorrectionConverter() {

  1875.             /** {@inheritDoc} */
  1876.             @Override
  1877.             public double[] toNonRotating(final AbsoluteDate date,
  1878.                                           final double ddPsi, final double ddEpsilon)
  1879.                 throws OrekitException {
  1880.                 // compute precession angles psiA, omegaA and chiA
  1881.                 final double[] angles = precessionFunction.value(date);

  1883.                 // conversion coefficients
  1884.                 final double sinEA = FastMath.sin(epsilonAFunction.value(date));
  1885.                 final double c     = angles[0] * cosE0 - angles[2];

  1887.                 // convert nutation corrections (equation 23/IERS-2003 or 5.25/IERS-2010)
  1888.                 return new double[] {
  1889.                     sinEA * ddPsi + c * ddEpsilon,
  1890.                     ddEpsilon - c * sinEA * ddPsi
  1891.                 };

  1893.             }

  1895.             /** {@inheritDoc} */
  1896.             @Override
  1897.             public double[] toEquinox(final AbsoluteDate date,
  1898.                                       final double dX, final double dY)
  1899.                 throws OrekitException {
  1900.                 // compute precession angles psiA, omegaA and chiA
  1901.                 final double[] angles   = precessionFunction.value(date);

  1903.                 // conversion coefficients
  1904.                 final double sinEA = FastMath.sin(epsilonAFunction.value(date));
  1905.                 final double c     = angles[0] * cosE0 - angles[2];
  1906.                 final double opC2  = 1 + c * c;

  1908.                 // convert nutation corrections (inverse of equation 23/IERS-2003 or 5.25/IERS-2010)
  1909.                 return new double[] {
  1910.                     (dX - c * dY) / (sinEA * opC2),
  1911.                     (dY + c * dX) / opC2
  1912.                 };
  1913.             }

  1915.         };

  1917.     }

  1919.     /** Load the Love numbers.
  1920.      * @param nameLove name of the Love number resource
  1921.      * @return Love numbers
  1922.      * @exception OrekitException if the Love numbers embedded in the
  1923.      * library cannot be read
  1924.      */
  1925.     protected LoveNumbers loadLoveNumbers(final String nameLove) throws OrekitException {
  1926.         InputStream stream = null;
  1927.         BufferedReader reader = null;
  1928.         try {

  1930.             // allocate the three triangular arrays for real, imaginary and time-dependent numbers
  1931.             final double[][] real      = new double[4][];
  1932.             final double[][] imaginary = new double[4][];
  1933.             final double[][] plus      = new double[4][];
  1934.             for (int i = 0; i < real.length; ++i) {
  1935.                 real[i]      = new double[i + 1];
  1936.                 imaginary[i] = new double[i + 1];
  1937.                 plus[i]      = new double[i + 1];
  1938.             }

  1940.             stream = IERSConventions.class.getResourceAsStream(nameLove);
  1941.             if (stream == null) {
  1942.                 // this should never happen with files embedded within Orekit
  1943.                 throw new OrekitException(OrekitMessages.UNABLE_TO_FIND_FILE, nameLove);
  1944.             }

  1946.             // setup the reader
  1947.             reader = new BufferedReader(new InputStreamReader(stream, "UTF-8"));

  1949.             String line = reader.readLine();
  1950.             int lineNumber = 1;

  1952.             // look for the Love numbers
  1953.             while (line != null) {

  1955.                 line = line.trim();
  1956.                 if (!(line.isEmpty() || line.startsWith("#"))) {
  1957.                     final String[] fields = line.split("\\p{Space}+");
  1958.                     if (fields.length != 5) {
  1959.                         // this should never happen with files embedded within Orekit
  1960.                         throw new OrekitException(OrekitMessages.UNABLE_TO_PARSE_LINE_IN_FILE,
  1961.                                                   lineNumber, nameLove, line);
  1962.                     }
  1963.                     final int n = Integer.parseInt(fields[0]);
  1964.                     final int m = Integer.parseInt(fields[1]);
  1965.                     if ((n < 2) || (n > 3) || (m < 0) || (m > n)) {
  1966.                         // this should never happen with files embedded within Orekit
  1967.                         throw new OrekitException(OrekitMessages.UNABLE_TO_PARSE_LINE_IN_FILE,
  1968.                                                   lineNumber, nameLove, line);

  1970.                     }
  1971.                     real[n][m]      = Double.parseDouble(fields[2]);
  1972.                     imaginary[n][m] = Double.parseDouble(fields[3]);
  1973.                     plus[n][m]      = Double.parseDouble(fields[4]);
  1974.                 }

  1976.                 // next line
  1977.                 lineNumber++;
  1978.                 line = reader.readLine();

  1980.             }

  1982.             return new LoveNumbers(real, imaginary, plus);

  1984.         } catch (IOException ioe) {
  1985.             // this should never happen with files embedded within Orekit
  1986.             throw new OrekitException(OrekitMessages.NOT_A_SUPPORTED_IERS_DATA_FILE, nameLove);
  1987.         } finally {
  1988.             try {
  1989.                 if (stream != null) {
  1990.                     stream.close();
  1991.                 }
  1992.                 if (reader != null) {
  1993.                     reader.close();
  1994.                 }
  1995.             } catch (IOException ioe) {
  1996.                 // ignored here
  1997.             }
  1998.         }
  1999.     }

  2001.     /** Get a data stream.
  2002.      * @param name file name of the resource stream
  2003.      * @return stream
  2004.      */
  2005.     private static InputStream getStream(final String name) {
  2006.         return IERSConventions.class.getResourceAsStream(name);
  2007.     }

  2009.     /** Correction to equation of equinoxes.
  2010.      * <p>IAU 1994 resolution C7 added two terms to the equation of equinoxes
  2011.      * taking effect since 1997-02-27 for continuity
  2012.      * </p>
  2013.      */
  2014.     private static class IAU1994ResolutionC7 {

  2016.         /** First Moon correction term for the Equation of the Equinoxes. */
  2017.         private static final double EQE1 =     0.00264  * Constants.ARC_SECONDS_TO_RADIANS;

  2019.         /** Second Moon correction term for the Equation of the Equinoxes. */
  2020.         private static final double EQE2 =     0.000063 * Constants.ARC_SECONDS_TO_RADIANS;

  2022.         /** Start date for applying Moon corrections to the equation of the equinoxes.
  2023.          * This date corresponds to 1997-02-27T00:00:00 UTC, hence the 30s offset from TAI.
  2024.          */
  2025.         private static final AbsoluteDate MODEL_START =
  2026.             new AbsoluteDate(1997, 2, 27, 0, 0, 30, TimeScalesFactory.getTAI());

  2028.         /** Evaluate the correction.
  2029.          * @param arguments Delaunay for nutation
  2030.          * @return correction value (0 before 1997-02-27)
  2031.          */
  2032.         public static double value(final DelaunayArguments arguments) {
  2033.             if (arguments.getDate().compareTo(MODEL_START) >= 0) {

  2035.                 // IAU 1994 resolution C7 added two terms to the equation of equinoxes
  2036.                 // taking effect since 1997-02-27 for continuity

  2038.                 // Mean longitude of the ascending node of the Moon
  2039.                 final double om = arguments.getOmega();

  2041.                 // add the two correction terms
  2042.                 return EQE1 * FastMath.sin(om) + EQE2 * FastMath.sin(om + om);

  2044.             } else {
  2045.                 return 0.0;
  2046.             }
  2047.         }

  2049.     };

  2051.     /** Stellar angle model.
  2052.      * <p>
  2053.      * The stellar angle computed here has been defined in the paper "A non-rotating origin on the
  2054.      * instantaneous equator: Definition, properties and use", N. Capitaine, Guinot B., and Souchay J.,
  2055.      * Celestial Mechanics, Volume 39, Issue 3, pp 283-307. It has been proposed as a conventional
  2056.      * conventional relationship between UT1 and Earth rotation in the paper "Definition of the Celestial
  2057.      * Ephemeris origin and of UT1 in the International Celestial Reference Frame", Capitaine, N.,
  2058.      * Guinot, B., and McCarthy, D. D., 2000, “,” Astronomy and Astrophysics, 355(1), pp. 398–405.
  2059.      * </p>
  2060.      * <p>
  2061.      * It is presented simply as stellar angle in IERS conventions 1996 but as since been adopted as
  2062.      * the conventional relationship defining UT1 from ICRF and is called Earth Rotation Angle in
  2063.      * IERS conventions 2003 and 2010.
  2064.      * </p>
  2065.      */
  2066.     private static class StellarAngleCapitaine implements TimeFunction<DerivativeStructure> {

  2068.         /** Reference date of Capitaine's Earth Rotation Angle model. */
  2069.         private static final AbsoluteDate REFERENCE_DATE = new AbsoluteDate(DateComponents.J2000_EPOCH,
  2070.                                                                             TimeComponents.H12,
  2071.                                                                             TimeScalesFactory.getTAI());

  2073.         /** Constant term of Capitaine's Earth Rotation Angle model. */
  2074.         private static final double ERA_0   = MathUtils.TWO_PI * 0.7790572732640;

  2076.         /** Rate term of Capitaine's Earth Rotation Angle model.
  2077.          * (radians per day, main part) */
  2078.         private static final double ERA_1A  = MathUtils.TWO_PI / Constants.JULIAN_DAY;

  2080.         /** Rate term of Capitaine's Earth Rotation Angle model.
  2081.          * (radians per day, fractional part) */
  2082.         private static final double ERA_1B  = ERA_1A * 0.00273781191135448;

  2084.         /** Total rate term of Capitaine's Earth Rotation Angle model. */
  2085.         private static final double ERA_1AB = ERA_1A + ERA_1B;

  2087.         /** UT1 time scale. */
  2088.         private final TimeScale ut1;

  2090.         /** Simple constructor.
  2091.          * @param ut1 UT1 time scale
  2092.          */
  2093.         StellarAngleCapitaine(final TimeScale ut1) {
  2094.             this.ut1 = ut1;
  2095.         }

  2097.         /** {@inheritDoc} */
  2098.         @Override
  2099.         public DerivativeStructure value(final AbsoluteDate date) {

  2101.             // split the date offset as a full number of days plus a smaller part
  2102.             final int secondsInDay = 86400;
  2103.             final double dt  = date.durationFrom(REFERENCE_DATE);
  2104.             final long days  = ((long) dt) / secondsInDay;
  2105.             final double dtA = secondsInDay * days;
  2106.             final double dtB = (dt - dtA) + ut1.offsetFromTAI(date);

  2108.             return new DerivativeStructure(1, 1,
  2109.                                            ERA_0 + ERA_1A * dtB + ERA_1B * (dtA + dtB),
  2110.                                            ERA_1AB);

  2112.         }

  2114.     }

  2116.     /** Mean pole. */
  2117.     private static class MeanPole implements TimeStamped, Serializable {

  2119.         /** Serializable UID. */
  2120.         private static final long serialVersionUID = 20131028l;

  2122.         /** Date. */
  2123.         private final AbsoluteDate date;

  2125.         /** X coordinate. */
  2126.         private double x;

  2128.         /** Y coordinate. */
  2129.         private double y;

  2131.         /** Simple constructor.
  2132.          * @param date date
  2133.          * @param x x coordinate
  2134.          * @param y y coordinate
  2135.          */
  2136.         MeanPole(final AbsoluteDate date, final double x, final double y) {
  2137.             this.date = date;
  2138.             this.x    = x;
  2139.             this.y    = y;
  2140.         }

  2142.         /** {@inheritDoc} */
  2143.         @Override
  2144.         public AbsoluteDate getDate() {
  2145.             return date;
  2146.         }

  2148.         /** Get x coordinate.
  2149.          * @return x coordinate
  2150.          */
  2151.         public double getX() {
  2152.             return x;
  2153.         }

  2155.         /** Get y coordinate.
  2156.          * @return y coordinate
  2157.          */
  2158.         public double getY() {
  2159.             return y;
  2160.         }

  2162.     }
  2163. }
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