/* Copyright 2002-2026 CS GROUP
    * Licensed to CS GROUP (CS) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * CS licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *   http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
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  package org.orekit.propagation.analytical.tle;
  
  import java.util.ArrayList;
  import java.util.Collections;
  import java.util.List;
  
  import org.hipparchus.geometry.euclidean.threed.Vector3D;
  import org.hipparchus.linear.RealMatrix;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.MathUtils;
  import org.hipparchus.util.Pair;
  import org.hipparchus.util.SinCos;
  import org.orekit.annotation.DefaultDataContext;
  import org.orekit.attitudes.Attitude;
  import org.orekit.attitudes.AttitudeProvider;
  import org.orekit.attitudes.FrameAlignedProvider;
  import org.orekit.data.DataContext;
  import org.orekit.errors.OrekitException;
  import org.orekit.errors.OrekitMessages;
  import org.orekit.frames.Frame;
  import org.orekit.orbits.CartesianOrbit;
  import org.orekit.orbits.Orbit;
  import org.orekit.propagation.AbstractMatricesHarvester;
  import org.orekit.propagation.MatricesHarvester;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.propagation.analytical.AbstractAnalyticalPropagator;
  import org.orekit.propagation.analytical.tle.generation.FixedPointTleGenerationAlgorithm;
  import org.orekit.propagation.analytical.tle.generation.TleGenerationAlgorithm;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.time.TimeScale;
  import org.orekit.utils.DoubleArrayDictionary;
  import org.orekit.utils.PVCoordinates;
  import org.orekit.utils.ParameterDriver;
  import org.orekit.utils.ParameterDriversProvider;
  import org.orekit.utils.ParameterObserver;
  import org.orekit.utils.TimeSpanMap;
  import org.orekit.utils.TimeSpanMap.Span;
  
  /** This class provides elements to propagate TLE's.
   * <p>
   * The models used are SGP4 and SDP4, initially proposed by NORAD as the unique convenient
   * propagator for TLE's. Inputs and outputs of this propagator are only suited for
   * NORAD two lines elements sets, since it uses estimations and mean values appropriate
   * for TLE's only.
   * </p>
   * <p>
   * Deep- or near- space propagator is selected internally according to NORAD recommendations
   * so that the user has not to worry about the used computation methods. One instance is created
   * for each TLE (this instance can only be get using {@link #selectExtrapolator(TLE)} method,
   * and can compute {@link PVCoordinates position and velocity coordinates} at any
   * time. Maximum accuracy is guaranteed in a 24h range period before and after the provided
   * TLE epoch (of course this accuracy is not really measurable nor predictable: according to
   * <a href="https://www.celestrak.com/">CelesTrak</a>, the precision is close to one kilometer
   * and error won't probably rise above 2 km).
   * </p>
   * <p>This implementation is largely inspired from the paper and source code <a
   * href="https://www.celestrak.com/publications/AIAA/2006-6753/">Revisiting Spacetrack
   * Report #3</a> and is fully compliant with its results and tests cases.</p>
   * @author Felix R. Hoots, Ronald L. Roehrich, December 1980 (original fortran)
   * @author David A. Vallado, Paul Crawford, Richard Hujsak, T.S. Kelso (C++ translation and improvements)
   * @author Fabien Maussion (java translation)
   * @see TLE
   */
  public abstract class TLEPropagator extends AbstractAnalyticalPropagator implements ParameterDriversProvider {
  
      // CHECKSTYLE: stop VisibilityModifier check
  
      /** Initial state. */
      protected TLE tle;
  
      /** UTC time scale. */
      protected final TimeScale utc;
  
      /** final RAAN. */
      protected double xnode;
  
      /** final semi major axis. */
      protected double a;
  
      /** final eccentricity. */
      protected double e;
  
      /** final inclination. */
     protected double i;
 
     /** final periapsis argument. */
     protected double omega;
 
     /** L from SPTRCK #3. */
     protected double xl;
 
     /** original recovered semi major axis. */
     protected double a0dp;
 
     /** original recovered mean motion. */
     protected double xn0dp;
 
     /** cosinus original inclination. */
     protected double cosi0;
 
     /** cos io squared. */
     protected double theta2;
 
     /** sinus original inclination. */
     protected double sini0;
 
     /** common parameter for mean anomaly (M) computation. */
     protected double xmdot;
 
     /** common parameter for periapsis argument (omega) computation. */
     protected double omgdot;
 
     /** common parameter for raan (OMEGA) computation. */
     protected double xnodot;
 
     /** original eccentricity squared. */
     protected double e0sq;
     /** 1 - e2. */
     protected double beta02;
 
     /** sqrt (1 - e2). */
     protected double beta0;
 
     /** periapsis, expressed in KM and ALTITUDE. */
     protected double perige;
 
     /** eta squared. */
     protected double etasq;
 
     /** original eccentricity * eta. */
     protected double eeta;
 
     /** s* new value for the contant s. */
     protected double s4;
 
     /** tsi from SPTRCK #3. */
     protected double tsi;
 
     /** eta from SPTRCK #3. */
     protected double eta;
 
     /** coef for SGP C3 computation. */
     protected double coef;
 
     /** coef for SGP C5 computation. */
     protected double coef1;
 
     /** C1 from SPTRCK #3. */
     protected double c1;
 
     /** C2 from SPTRCK #3. */
     protected double c2;
 
     /** C4 from SPTRCK #3. */
     protected double c4;
 
     /** common parameter for raan (OMEGA) computation. */
     protected double xnodcf;
 
     /** 3/2 * C1. */
     protected double t2cof;
 
     // CHECKSTYLE: resume VisibilityModifier check
 
     /** TLE frame. */
     private final Frame teme;
 
     /** All TLEs and masses. */
     private TimeSpanMap<Pair<TLE, Double>> tlesAndMasses;
 
     /** Driver for the ballistic parameter.
      * @since 14.0
      */
     private final ParameterDriver bStarDriver;
 
     /** TLE generation algorithm used when resetting TLE from state. */
     private TleGenerationAlgorithm generationAlgorithm;
 
      /** Protected constructor for derived classes.
      *
      * <p>This constructor uses the {@link DataContext#getDefault() default data context}.
      *
      * @param initialTLE the unique TLE to propagate
      * @param attitudeProvider provider for attitude computation
      * @param mass spacecraft mass (kg)
      * @see #TLEPropagator(TLE, AttitudeProvider, double, Frame)
      */
     @DefaultDataContext
     protected TLEPropagator(final TLE initialTLE, final AttitudeProvider attitudeProvider, final double mass) {
         this(initialTLE, attitudeProvider, mass,
              DataContext.getDefault().getFrames().getTEME());
     }
 
     /** Protected constructor for derived classes.
      * @param initialTLE the unique TLE to propagate
      * @param attitudeProvider provider for attitude computation
      * @param mass spacecraft mass (kg)
      * @param teme the TEME frame to use for propagation.
      * @since 10.1
      */
     protected TLEPropagator(final TLE initialTLE,
                             final AttitudeProvider attitudeProvider,
                             final double mass,
                             final Frame teme) {
         super(attitudeProvider);
         setStartDate(initialTLE.getDate());
         this.utc           = initialTLE.getUtc();
         initializeTle(initialTLE);
         this.teme          = teme;
         this.tlesAndMasses = new TimeSpanMap<>(new Pair<>(tle, mass));
         this.bStarDriver   = new ParameterDriver(TleGenerationAlgorithm.B_STAR,
                                                  initialTLE.getBStar(),
                                                  TleGenerationAlgorithm.B_STAR_SCALE,
                                                  Double.NEGATIVE_INFINITY,
                                                  Double.POSITIVE_INFINITY);
         bStarDriver.addObserver(new ParameterObserver() {
 
             @Override
             public void valueChanged(final double previousValue, final ParameterDriver driver,
                                      final AbsoluteDate date) {
                 resetBStar();
             }
 
             @Override
             public void valueSpanMapChanged(final TimeSpanMap<Double> previousValueSpanMap,
                                             final ParameterDriver driver) {
                 resetBStar();
             }
         });
         this.generationAlgorithm = getDefaultTleGenerationAlgorithm(initialTLE, utc, teme);
 
         // set the initial state
         final Orbit orbit = propagateOrbit(initialTLE.getDate());
         final Attitude attitude = attitudeProvider.getAttitude(orbit, orbit.getDate(), orbit.getFrame());
         super.resetInitialState(new SpacecraftState(orbit, attitude).withMass(mass));
     }
 
     /** Selects the extrapolator to use with the selected TLE.
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @param tle the TLE to propagate.
      * @return the correct propagator.
      * @see #selectExtrapolator(TLE, Frame)
      */
     @DefaultDataContext
     public static TLEPropagator selectExtrapolator(final TLE tle) {
         return selectExtrapolator(tle, DataContext.getDefault().getFrames().getTEME());
     }
 
     /** Selects the extrapolator to use with the selected TLE.
      * @param tle the TLE to propagate.
      * @param teme TEME frame.
      * @return the correct propagator.
      * @since 10.1
      * @see #selectExtrapolator(TLE, Frame, AttitudeProvider)
      */
     public static TLEPropagator selectExtrapolator(final TLE tle, final Frame teme) {
         return selectExtrapolator(tle, teme, FrameAlignedProvider.of(teme));
     }
 
     /** Selects the extrapolator to use with the selected TLE.
      * @param tle the TLE to propagate.
      * @param teme TEME frame.
      * @param attitudeProvider provider for attitude computation
      * @return the correct propagator.
      * @since 12.2
      */
     public static TLEPropagator selectExtrapolator(final TLE tle, final Frame teme, final AttitudeProvider attitudeProvider) {
         return selectExtrapolator(tle, attitudeProvider, DEFAULT_MASS, teme);
     }
 
     /** Selects the extrapolator to use with the selected TLE.
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @param tle the TLE to propagate.
      * @param attitudeProvider provider for attitude computation
      * @param mass spacecraft mass (kg)
      * @return the correct propagator.
      * @see #selectExtrapolator(TLE, AttitudeProvider, double, Frame)
      */
     @DefaultDataContext
     public static TLEPropagator selectExtrapolator(final TLE tle, final AttitudeProvider attitudeProvider,
                                                    final double mass) {
         return selectExtrapolator(tle, attitudeProvider, mass,
                                   DataContext.getDefault().getFrames().getTEME());
     }
 
     /** Selects the extrapolator to use with the selected TLE.
      * @param tle the TLE to propagate.
      * @param attitudeProvider provider for attitude computation
      * @param mass spacecraft mass (kg)
      * @param teme the TEME frame to use for propagation.
      * @return the correct propagator.
      * @since 10.1
      */
     public static TLEPropagator selectExtrapolator(final TLE tle,
                                                    final AttitudeProvider attitudeProvider,
                                                    final double mass,
                                                    final Frame teme) {
 
         final double xkeOverN = TLEConstants.XKE / (tle.getMeanMotion() * 60.0);
         final double a1 = FastMath.cbrt(xkeOverN * xkeOverN);
         final double cosi0 = FastMath.cos(tle.getI());
         final double oMe2  = 1.0 - tle.getE() * tle.getE();
         final double temp = TLEConstants.CK2 * 1.5 * (3 * cosi0 * cosi0 - 1.0) / (oMe2 * FastMath.sqrt(oMe2));
         final double delta1 = temp / (a1 * a1);
         final double a0 = a1 * (1.0 - delta1 * (TLEConstants.ONE_THIRD + delta1 * (delta1 * 134.0 / 81.0 + 1.0)));
         final double delta0 = temp / (a0 * a0);
 
         // recover original mean motion :
         final double xn0dp = tle.getMeanMotion() * 60.0 / (delta0 + 1.0);
 
         // Period >= 225 minutes is deep space
         if (MathUtils.TWO_PI / (xn0dp * TLEConstants.MINUTES_PER_DAY) >= (1.0 / 6.4)) {
             return new DeepSDP4(tle, attitudeProvider, mass, teme);
         } else {
             return new SGP4(tle, attitudeProvider, mass, teme);
         }
     }
 
     /** Get the TLE generation algorithm used when resetting TLE from state.
      * @return TLE generation algorithm
      * @since 14.0
      */
     TleGenerationAlgorithm getTleGenerationAlgorithm() {
         return generationAlgorithm;
     }
 
     /** Set the TLE generation algorithm used when resetting TLE from state.
      * @param tleGenerationAlgorithm TLE generation algorithm
      * @since 14.0
      */
     public void setTleGenerationAlgorithm(final TleGenerationAlgorithm tleGenerationAlgorithm) {
         this.generationAlgorithm = tleGenerationAlgorithm;
     }
 
     /** Get the Earth gravity coefficient used for TLE propagation.
      * @return the Earth gravity coefficient.
      */
     public static double getMU() {
         return TLEConstants.MU;
     }
 
     /** Get the extrapolated position and velocity from an initial TLE.
      * @param date the final date
      * @return the final PVCoordinates
      */
     public PVCoordinates getPVCoordinates(final AbsoluteDate date) {
 
         sxpPropagate(date.durationFrom(tle.getDate()) / 60.0, tle.getBStar());
 
         // Compute PV with previous calculated parameters
         return computePVCoordinates();
     }
 
     /** Computation of the first commons parameters.
      * @param bStar value of the ballistic coefficient to use for propagation
      */
     private void initializeCommons(final double bStar) {
 
         // Sine and cosine of inclination
         final SinCos scI0 = FastMath.sinCos(tle.getI());
 
         final double xkeOverN = TLEConstants.XKE / (tle.getMeanMotion() * 60.0);
         final double a1 = FastMath.cbrt(xkeOverN * xkeOverN);
         cosi0 = scI0.cos();
         theta2 = cosi0 * cosi0;
         final double x3thm1 = 3.0 * theta2 - 1.0;
         e0sq = tle.getE() * tle.getE();
         beta02 = 1.0 - e0sq;
         beta0 = FastMath.sqrt(beta02);
         final double tval = TLEConstants.CK2 * 1.5 * x3thm1 / (beta0 * beta02);
         final double delta1 = tval / (a1 * a1);
         final double a0 = a1 * (1.0 - delta1 * (TLEConstants.ONE_THIRD + delta1 * (1.0 + 134.0 / 81.0 * delta1)));
         final double delta0 = tval / (a0 * a0);
 
         // recover original mean motion and semi-major axis :
         xn0dp = tle.getMeanMotion() * 60.0 / (delta0 + 1.0);
         a0dp = a0 / (1.0 - delta0);
 
         // Values of s and qms2t :
         s4 = TLEConstants.S;  // unmodified value for s
         double q0ms24 = TLEConstants.QOMS2T; // unmodified value for q0ms2T
 
         perige = (a0dp * (1 - tle.getE()) - TLEConstants.NORMALIZED_EQUATORIAL_RADIUS) * TLEConstants.EARTH_RADIUS; // perige
 
         //  For periapsis below 156 km, the values of s and qoms2t are changed :
         if (perige < 156.0) {
             if (perige <= 98.0) {
                 s4 = 20.0;
             } else {
                 s4 = perige - 78.0;
             }
             final double temp_val = (120.0 - s4) * TLEConstants.NORMALIZED_EQUATORIAL_RADIUS / TLEConstants.EARTH_RADIUS;
             final double temp_val_squared = temp_val * temp_val;
             q0ms24 = temp_val_squared * temp_val_squared;
             s4 = s4 / TLEConstants.EARTH_RADIUS + TLEConstants.NORMALIZED_EQUATORIAL_RADIUS; // new value for q0ms2T and s
         }
 
         final double pinv = 1.0 / (a0dp * beta02);
         final double pinvsq = pinv * pinv;
         tsi = 1.0 / (a0dp - s4);
         eta = a0dp * tle.getE() * tsi;
         etasq = eta * eta;
         eeta = tle.getE() * eta;
 
         final double psisq = FastMath.abs(1.0 - etasq); // abs because pow 3.5 needs positive value
         final double tsi_squared = tsi * tsi;
         coef = q0ms24 * tsi_squared * tsi_squared;
         coef1 = coef / FastMath.pow(psisq, 3.5);
 
         // C2 and C1 coefficients computation :
         c2 = coef1 * xn0dp * (a0dp * (1.0 + 1.5 * etasq + eeta * (4.0 + etasq)) +
              0.75 * TLEConstants.CK2 * tsi / psisq * x3thm1 * (8.0 + 3.0 * etasq * (8.0 + etasq)));
         c1 = bStar * c2;
         sini0 = scI0.sin();
 
         final double x1mth2 = 1.0 - theta2;
 
         // C4 coefficient computation :
         c4 = 2.0 * xn0dp * coef1 * a0dp * beta02 * (eta * (2.0 + 0.5 * etasq) +
                 tle.getE() * (0.5 + 2.0 * etasq) -
                 2 * TLEConstants.CK2 * tsi / (a0dp * psisq) *
                         (-3.0 * x3thm1 * (1.0 - 2.0 * eeta + etasq * (1.5 - 0.5 * eeta)) +
                                 0.75 * x1mth2 * (2.0 * etasq - eeta * (1.0 + etasq)) * FastMath.cos(2.0 * tle.getPeriapsisArgument())));
 
         final double theta4 = theta2 * theta2;
         final double temp1 = 3 * TLEConstants.CK2 * pinvsq * xn0dp;
         final double temp2 = temp1 * TLEConstants.CK2 * pinvsq;
         final double temp3 = 1.25 * TLEConstants.CK4 * pinvsq * pinvsq * xn0dp;
 
         // atmospheric and gravitation coefs :(Mdf and OMEGAdf)
         xmdot = xn0dp +
                 0.5 * temp1 * beta0 * x3thm1 +
                 0.0625 * temp2 * beta0 * (13.0 - 78.0 * theta2 + 137.0 * theta4);
 
         final double x1m5th = 1.0 - 5.0 * theta2;
 
         omgdot = -0.5 * temp1 * x1m5th +
                 0.0625 * temp2 * (7.0 - 114.0 * theta2 + 395.0 * theta4) +
                 temp3 * (3.0 - 36.0 * theta2 + 49.0 * theta4);
 
         final double xhdot1 = -temp1 * cosi0;
 
         xnodot = xhdot1 + (0.5 * temp2 * (4.0 - 19.0 * theta2) + 2.0 * temp3 * (3.0 - 7.0 * theta2)) * cosi0;
         xnodcf = 3.5 * beta02 * xhdot1 * c1;
         t2cof = 1.5 * c1;
 
     }
 
     /** Retrieves the position and velocity.
      * @return the computed PVCoordinates.
      */
     private PVCoordinates computePVCoordinates() {
 
         // Sine and cosine of final periapsis argument
         final SinCos scOmega = FastMath.sinCos(omega);
 
         // Long period periodics
         final double axn = e * scOmega.cos();
         double temp = 1.0 / (a * (1.0 - e * e));
         final double xlcof = 0.125 * TLEConstants.A3OVK2 * sini0 * (3.0 + 5.0 * cosi0) / (1.0 + cosi0);
         final double aycof = 0.25 * TLEConstants.A3OVK2 * sini0;
         final double xll = temp * xlcof * axn;
         final double aynl = temp * aycof;
         final double xlt = xl + xll;
         final double ayn = e * scOmega.sin() + aynl;
         final double elsq = axn * axn + ayn * ayn;
         final double capu = MathUtils.normalizeAngle(xlt - xnode, FastMath.PI);
         double epw = capu;
         double ecosE = 0;
         double esinE = 0;
         double sinEPW = 0;
         double cosEPW = 0;
 
         // Dundee changes:  items dependent on cosio get recomputed:
         final double cosi0Sq = cosi0 * cosi0;
         final double x3thm1 = 3.0 * cosi0Sq - 1.0;
         final double x1mth2 = 1.0 - cosi0Sq;
         final double x7thm1 = 7.0 * cosi0Sq - 1.0;
 
         if (e > (1 - 1e-6)) {
             throw new OrekitException(OrekitMessages.TOO_LARGE_ECCENTRICITY_FOR_PROPAGATION_MODEL, e);
         }
 
         // Solve Kepler's' Equation.
         final double newtonRaphsonEpsilon = 1e-12;
         for (int j = 0; j < 10; j++) {
 
             boolean doSecondOrderNewtonRaphson = true;
 
             final SinCos scEPW = FastMath.sinCos(epw);
             sinEPW = scEPW.sin();
             cosEPW = scEPW.cos();
             ecosE = axn * cosEPW + ayn * sinEPW;
             esinE = axn * sinEPW - ayn * cosEPW;
             final double f = capu - epw + esinE;
             if (FastMath.abs(f) < newtonRaphsonEpsilon) {
                 break;
             }
             final double fdot = 1.0 - ecosE;
             double delta_epw = f / fdot;
             if (j == 0) {
                 final double maxNewtonRaphson = 1.25 * FastMath.abs(e);
                 doSecondOrderNewtonRaphson = false;
                 if (delta_epw > maxNewtonRaphson) {
                     delta_epw = maxNewtonRaphson;
                 } else if (delta_epw < -maxNewtonRaphson) {
                     delta_epw = -maxNewtonRaphson;
                 } else {
                     doSecondOrderNewtonRaphson = true;
                 }
             }
             if (doSecondOrderNewtonRaphson) {
                 delta_epw = f / (fdot + 0.5 * esinE * delta_epw);
             }
             epw += delta_epw;
         }
 
         // Short period preliminary quantities
         temp = 1.0 - elsq;
         final double pl = a * temp;
         final double r = a * (1.0 - ecosE);
         double temp2 = a / r;
         final double betal = FastMath.sqrt(temp);
         temp = esinE / (1.0 + betal);
         final double cosu = temp2 * (cosEPW - axn + ayn * temp);
         final double sinu = temp2 * (sinEPW - ayn - axn * temp);
         final double u = FastMath.atan2(sinu, cosu);
         final double sin2u = 2.0 * sinu * cosu;
         final double cos2u = 2.0 * cosu * cosu - 1.0;
         final double temp1 = TLEConstants.CK2 / pl;
         temp2 = temp1 / pl;
 
         // Update for short periodics
         final double rk = r * (1.0 - 1.5 * temp2 * betal * x3thm1) + 0.5 * temp1 * x1mth2 * cos2u;
         final double uk = u - 0.25 * temp2 * x7thm1 * sin2u;
         final double xnodek = xnode + 1.5 * temp2 * cosi0 * sin2u;
         final double xinck = i + 1.5 * temp2 * cosi0 * sini0 * cos2u;
 
         // Orientation vectors
         final SinCos scuk   = FastMath.sinCos(uk);
         final SinCos scik   = FastMath.sinCos(xinck);
         final SinCos scnok  = FastMath.sinCos(xnodek);
         final double sinuk  = scuk.sin();
         final double cosuk  = scuk.cos();
         final double sinik  = scik.sin();
         final double cosik  = scik.cos();
         final double sinnok = scnok.sin();
         final double cosnok = scnok.cos();
         final double xmx = -sinnok * cosik;
         final double xmy = cosnok * cosik;
         final double ux  = xmx * sinuk + cosnok * cosuk;
         final double uy  = xmy * sinuk + sinnok * cosuk;
         final double uz  = sinik * sinuk;
 
         // Position and velocity
         final double cr = 1000 * rk * TLEConstants.EARTH_RADIUS;
         final Vector3D pos = new Vector3D(cr * ux, cr * uy, cr * uz);
 
         final double rdot   = TLEConstants.XKE * FastMath.sqrt(a) * esinE / r;
         final double rfdot  = TLEConstants.XKE * FastMath.sqrt(pl) / r;
         final double xn     = TLEConstants.XKE / (a * FastMath.sqrt(a));
         final double rdotk  = rdot - xn * temp1 * x1mth2 * sin2u;
         final double rfdotk = rfdot + xn * temp1 * (x1mth2 * cos2u + 1.5 * x3thm1);
         final double vx     = xmx * cosuk - cosnok * sinuk;
         final double vy     = xmy * cosuk - sinnok * sinuk;
         final double vz     = sinik * cosuk;
 
         final double cv = 1000.0 * TLEConstants.EARTH_RADIUS / 60.0;
         final Vector3D vel = new Vector3D(cv * (rdotk * ux + rfdotk * vx),
                                           cv * (rdotk * uy + rfdotk * vy),
                                           cv * (rdotk * uz + rfdotk * vz));
 
         return new PVCoordinates(pos, vel);
 
     }
 
     /** {@inheritDoc} */
     @Override
     public List<ParameterDriver> getParametersDrivers() {
         return Collections.singletonList(bStarDriver);
     }
 
     /** Initialization proper to each propagator (SGP or SDP).
      * @param bStar value of the ballistic coefficient to use for propagation
      */
     protected abstract void sxpInitialize(double bStar);
 
     /** Propagation proper to each propagator (SGP or SDP).
      * @param t the offset from initial epoch (min)
      * @param bStar value of the ballistic coefficient to use for propagation
      */
     protected abstract void sxpPropagate(double t, double bStar);
 
     /** {@inheritDoc}
      * <p>
      * For TLE propagator, calling this method is only recommended
      * for covariance propagation when the new <code>state</code>
      * differs from the previous one by only adding the additional
      * state containing the derivatives.
      * </p>
      */
     public void resetInitialState(final SpacecraftState state) {
         super.resetInitialState(state);
         resetTle(state);
         tlesAndMasses = new TimeSpanMap<>(new Pair<>(tle, state.getMass()));
     }
 
     /** {@inheritDoc} */
     protected void resetIntermediateState(final SpacecraftState state, final boolean forward) {
         resetTle(state);
         final Pair<TLE, Double> tleAndMass = new Pair<>(tle, state.getMass());
         if (forward) {
             tlesAndMasses.addValidAfter(tleAndMass, state.getDate(), false);
         } else {
             tlesAndMasses.addValidBefore(tleAndMass, state.getDate(), false);
         }
         stateChanged(state);
     }
 
     /** Reset internal TLE from a SpacecraftState.
      * @param state spacecraft state on which to base new TLE
      */
     private void resetTle(final SpacecraftState state) {
 
         final TLE newTle = generationAlgorithm.createFromDrivers();
         initializeTle(newTle);
     }
 
     /** Reset the B-star value from the parameter driver.
      * @since 14.0
      */
     private void resetBStar() {
         tle = new TLE(tle.getSatelliteNumber(), tle.getClassification(),
                       tle.getLaunchYear(), tle.getLaunchNumber(), tle.getLaunchPiece(),
                       tle.getEphemerisType(), tle.getElementNumber(), tle.getDate(),
                       tle.getMeanMotion(), tle.getMeanMotionFirstDerivative(),
                       tle.getMeanMotionSecondDerivative(),
                       tle.getE(), tle.getI(), tle.getPeriapsisArgument(), tle.getRaan(),
                       tle.getMeanAnomaly(), tle.getRevolutionNumberAtEpoch(),
                       bStarDriver.getValue());
         initializeTle(tle);
     }
 
     /** Initialize internal TLE.
      * @param newTle tle to replace current one
      */
     private void initializeTle(final TLE newTle) {
         tle = newTle;
         initializeCommons(newTle.getBStar());
         sxpInitialize(newTle.getBStar());
     }
 
     /** {@inheritDoc} */
     protected double getMass(final AbsoluteDate date) {
         return tlesAndMasses.get(date).getValue();
     }
 
     /** {@inheritDoc} */
     public Orbit propagateOrbit(final AbsoluteDate date) {
         final TLE closestTle = tlesAndMasses.get(date).getKey();
         if (!tle.equals(closestTle)) {
             initializeTle(closestTle);
         }
         return new CartesianOrbit(getPVCoordinates(date), teme, date, TLEConstants.MU);
     }
 
     /** Get the underlying TLE.
      * If there has been calls to #resetInitialState or #resetIntermediateState,
      * it will not be the same as given to the constructor.
      * @return underlying TLE
      */
     public TLE getTLE() {
         return tle;
     }
 
     /** {@inheritDoc} */
     public Frame getFrame() {
         return teme;
     }
 
     /** {@inheritDoc} */
     @Override
     protected AbstractMatricesHarvester createHarvester(final String stmName, final RealMatrix initialStm,
                                                         final DoubleArrayDictionary initialJacobianColumns) {
         // Create the harvester
         final TLEHarvester harvester = new TLEHarvester(this, stmName, initialStm, initialJacobianColumns);
         // Update the list of additional state provider
         addAdditionalDataProvider(harvester);
         // Return the configured harvester
         return harvester;
     }
 
     /**
      * Get the names of the parameters in the matrix returned by {@link MatricesHarvester#getParametersJacobian}.
      * @return names of the parameters (i.e. columns) of the Jacobian matrix
      */
     protected List<String> getJacobiansColumnsNames() {
         if (bStarDriver.isSelected()) {
             final List<String> columnsNames = new ArrayList<>();
             for (Span<String> span = bStarDriver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 columnsNames.add(span.getData());
             }
             return columnsNames;
         } else {
             return Collections.emptyList();
         }
     }
 
     /**
      * Get the default TLE generation algorithm.
      * @param templateTLE template TLE
      * @param utc UTC time scale
      * @param teme TEME frame
      * @return a TLE generation algorithm
      */
     public static TleGenerationAlgorithm getDefaultTleGenerationAlgorithm(final TLE templateTLE,
                                                                           final TimeScale utc, final Frame teme) {
         return new FixedPointTleGenerationAlgorithm(templateTLE,
                                                     FixedPointTleGenerationAlgorithm.EPSILON_DEFAULT,
                                                     FixedPointTleGenerationAlgorithm.MAX_ITERATIONS_DEFAULT,
                                                     FixedPointTleGenerationAlgorithm.SCALE_DEFAULT, utc, teme);
     }
 
 }