/* Copyright 2002-2022 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
   * limitations under the License.
   */
  package org.orekit.propagation.analytical.tle;
  
  import java.io.Serializable;
  import java.text.DecimalFormat;
  import java.text.DecimalFormatSymbols;
  import java.util.Collections;
  import java.util.List;
  import java.util.Locale;
  import java.util.Objects;
  import java.util.regex.Pattern;
  
  import org.hipparchus.geometry.euclidean.threed.Rotation;
  import org.hipparchus.util.ArithmeticUtils;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.MathUtils;
  import org.orekit.annotation.DefaultDataContext;
  import org.orekit.attitudes.InertialProvider;
  import org.orekit.data.DataContext;
  import org.orekit.errors.OrekitException;
  import org.orekit.errors.OrekitMessages;
  import org.orekit.frames.Frame;
  import org.orekit.orbits.EquinoctialOrbit;
  import org.orekit.orbits.KeplerianOrbit;
  import org.orekit.orbits.Orbit;
  import org.orekit.orbits.OrbitType;
  import org.orekit.orbits.PositionAngle;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.time.DateComponents;
  import org.orekit.time.DateTimeComponents;
  import org.orekit.time.TimeComponents;
  import org.orekit.time.TimeScale;
  import org.orekit.time.TimeStamped;
  import org.orekit.utils.ParameterDriver;
  
  /** This class is a container for a single set of TLE data.
   *
   * <p>TLE sets can be built either by providing directly the two lines, in
   * which case parsing is performed internally or by providing the already
   * parsed elements.</p>
   * <p>TLE are not transparently convertible to {@link org.orekit.orbits.Orbit Orbit}
   * instances. They are significant only with respect to their dedicated {@link
   * TLEPropagator propagator}, which also computes position and velocity coordinates.
   * Any attempt to directly use orbital parameters like {@link #getE() eccentricity},
   * {@link #getI() inclination}, etc. without any reference to the {@link TLEPropagator
   * TLE propagator} is prone to errors.</p>
   * <p>More information on the TLE format can be found on the
   * <a href="https://www.celestrak.com/">CelesTrak website.</a></p>
   * @author Fabien Maussion
   * @author Luc Maisonobe
   */
  public class TLE implements TimeStamped, Serializable {
  
      /** Identifier for SGP type of ephemeris. */
      public static final int SGP = 1;
  
      /** Identifier for SGP4 type of ephemeris. */
      public static final int SGP4 = 2;
  
      /** Identifier for SDP4 type of ephemeris. */
      public static final int SDP4 = 3;
  
      /** Identifier for SGP8 type of ephemeris. */
      public static final int SGP8 = 4;
  
      /** Identifier for SDP8 type of ephemeris. */
      public static final int SDP8 = 5;
  
      /** Identifier for default type of ephemeris (SGP4/SDP4). */
      public static final int DEFAULT = 0;
  
      /** Parameter name for B* coefficient. */
      public static final String B_STAR = "BSTAR";
  
      /** Default value for epsilon. */
      private static final double EPSILON_DEFAULT = 1.0e-10;
  
      /** Default value for maxIterations. */
      private static final int MAX_ITERATIONS_DEFAULT = 100;
  
      /** B* scaling factor.
       * <p>
       * We use a power of 2 to avoid numeric noise introduction
      * in the multiplications/divisions sequences.
      * </p>
      */
     private static final double B_STAR_SCALE = FastMath.scalb(1.0, -20);
 
     /** Name of the mean motion parameter. */
     private static final String MEAN_MOTION = "meanMotion";
 
     /** Name of the inclination parameter. */
     private static final String INCLINATION = "inclination";
 
     /** Name of the eccentricity parameter. */
     private static final String ECCENTRICITY = "eccentricity";
 
     /** Pattern for line 1. */
     private static final Pattern LINE_1_PATTERN =
         Pattern.compile("1 [ 0-9A-Z&&[^IO]][ 0-9]{4}[A-Z] [ 0-9]{5}[ A-Z]{3} [ 0-9]{5}[.][ 0-9]{8} (?:(?:[ 0+-][.][ 0-9]{8})|(?: [ +-][.][ 0-9]{7})) " +
                         "[ +-][ 0-9]{5}[+-][ 0-9] [ +-][ 0-9]{5}[+-][ 0-9] [ 0-9] [ 0-9]{4}[ 0-9]");
 
     /** Pattern for line 2. */
     private static final Pattern LINE_2_PATTERN =
         Pattern.compile("2 [ 0-9A-Z&&[^IO]][ 0-9]{4} [ 0-9]{3}[.][ 0-9]{4} [ 0-9]{3}[.][ 0-9]{4} [ 0-9]{7} " +
                         "[ 0-9]{3}[.][ 0-9]{4} [ 0-9]{3}[.][ 0-9]{4} [ 0-9]{2}[.][ 0-9]{13}[ 0-9]");
 
     /** International symbols for parsing. */
     private static final DecimalFormatSymbols SYMBOLS =
         new DecimalFormatSymbols(Locale.US);
 
     /** Serializable UID. */
     private static final long serialVersionUID = -1596648022319057689L;
 
     /** The satellite number. */
     private final int satelliteNumber;
 
     /** Classification (U for unclassified). */
     private final char classification;
 
     /** Launch year. */
     private final int launchYear;
 
     /** Launch number. */
     private final int launchNumber;
 
     /** Piece of launch (from "A" to "ZZZ"). */
     private final String launchPiece;
 
     /** Type of ephemeris. */
     private final int ephemerisType;
 
     /** Element number. */
     private final int elementNumber;
 
     /** the TLE current date. */
     private final AbsoluteDate epoch;
 
     /** Mean motion (rad/s). */
     private final double meanMotion;
 
     /** Mean motion first derivative (rad/s²). */
     private final double meanMotionFirstDerivative;
 
     /** Mean motion second derivative (rad/s³). */
     private final double meanMotionSecondDerivative;
 
     /** Eccentricity. */
     private final double eccentricity;
 
     /** Inclination (rad). */
     private final double inclination;
 
     /** Argument of perigee (rad). */
     private final double pa;
 
     /** Right Ascension of the Ascending node (rad). */
     private final double raan;
 
     /** Mean anomaly (rad). */
     private final double meanAnomaly;
 
     /** Revolution number at epoch. */
     private final int revolutionNumberAtEpoch;
 
     /** First line. */
     private String line1;
 
     /** Second line. */
     private String line2;
 
     /** The UTC scale. */
     private final TimeScale utc;
 
     /** Driver for ballistic coefficient parameter. */
     private final transient ParameterDriver bStarParameterDriver;
 
 
     /** Simple constructor from unparsed two lines. This constructor uses the {@link
      * DataContext#getDefault() default data context}.
      *
      * <p>The static method {@link #isFormatOK(String, String)} should be called
      * before trying to build this object.<p>
      * @param line1 the first element (69 char String)
      * @param line2 the second element (69 char String)
      * @see #TLE(String, String, TimeScale)
      */
     @DefaultDataContext
     public TLE(final String line1, final String line2) {
         this(line1, line2, DataContext.getDefault().getTimeScales().getUTC());
     }
 
     /** Simple constructor from unparsed two lines using the given time scale as UTC.
      *
      * <p>The static method {@link #isFormatOK(String, String)} should be called
      * before trying to build this object.<p>
      * @param line1 the first element (69 char String)
      * @param line2 the second element (69 char String)
      * @param utc the UTC time scale.
      * @since 10.1
      */
     public TLE(final String line1, final String line2, final TimeScale utc) {
 
         // identification
         satelliteNumber = ParseUtils.parseSatelliteNumber(line1, 2, 5);
         final int satNum2 = ParseUtils.parseSatelliteNumber(line2, 2, 5);
         if (satelliteNumber != satNum2) {
             throw new OrekitException(OrekitMessages.TLE_LINES_DO_NOT_REFER_TO_SAME_OBJECT,
                                       line1, line2);
         }
         classification  = line1.charAt(7);
         launchYear      = ParseUtils.parseYear(line1, 9);
         launchNumber    = ParseUtils.parseInteger(line1, 11, 3);
         launchPiece     = line1.substring(14, 17).trim();
         ephemerisType   = ParseUtils.parseInteger(line1, 62, 1);
         elementNumber   = ParseUtils.parseInteger(line1, 64, 4);
 
         // Date format transform (nota: 27/31250 == 86400/100000000)
         final int    year      = ParseUtils.parseYear(line1, 18);
         final int    dayInYear = ParseUtils.parseInteger(line1, 20, 3);
         final long   df        = 27l * ParseUtils.parseInteger(line1, 24, 8);
         final int    secondsA  = (int) (df / 31250l);
         final double secondsB  = (df % 31250l) / 31250.0;
         epoch = new AbsoluteDate(new DateComponents(year, dayInYear),
                                  new TimeComponents(secondsA, secondsB),
                                  utc);
 
         // mean motion development
         // converted from rev/day, 2 * rev/day^2 and 6 * rev/day^3 to rad/s, rad/s^2 and rad/s^3
         meanMotion                 = ParseUtils.parseDouble(line2, 52, 11) * FastMath.PI / 43200.0;
         meanMotionFirstDerivative  = ParseUtils.parseDouble(line1, 33, 10) * FastMath.PI / 1.86624e9;
         meanMotionSecondDerivative = Double.parseDouble((line1.substring(44, 45) + '.' +
                                                          line1.substring(45, 50) + 'e' +
                                                          line1.substring(50, 52)).replace(' ', '0')) *
                                      FastMath.PI / 5.3747712e13;
 
         eccentricity = Double.parseDouble("." + line2.substring(26, 33).replace(' ', '0'));
         inclination  = FastMath.toRadians(ParseUtils.parseDouble(line2, 8, 8));
         pa           = FastMath.toRadians(ParseUtils.parseDouble(line2, 34, 8));
         raan         = FastMath.toRadians(Double.parseDouble(line2.substring(17, 25).replace(' ', '0')));
         meanAnomaly  = FastMath.toRadians(ParseUtils.parseDouble(line2, 43, 8));
 
         revolutionNumberAtEpoch = ParseUtils.parseInteger(line2, 63, 5);
         final double bStarValue = Double.parseDouble((line1.substring(53, 54) + '.' +
                                     line1.substring(54, 59) + 'e' +
                                     line1.substring(59, 61)).replace(' ', '0'));
 
         // save the lines
         this.line1 = line1;
         this.line2 = line2;
         this.utc = utc;
 
         // create model parameter drivers
         this.bStarParameterDriver = new ParameterDriver(B_STAR, bStarValue, B_STAR_SCALE,
                                                         Double.NEGATIVE_INFINITY,
                                                         Double.POSITIVE_INFINITY);
 
     }
 
     /**
      * <p>
      * Simple constructor from already parsed elements. This constructor uses the
      * {@link DataContext#getDefault() default data context}.
      * </p>
      *
      * <p>
      * The mean anomaly, the right ascension of ascending node Ω and the argument of
      * perigee ω are normalized into the [0, 2π] interval as they can be negative.
      * After that, a range check is performed on some of the orbital elements:
      *
      * <pre>
      *     meanMotion &gt;= 0
      *     0 &lt;= i &lt;= π
      *     0 &lt;= Ω &lt;= 2π
      *     0 &lt;= e &lt;= 1
      *     0 &lt;= ω &lt;= 2π
      *     0 &lt;= meanAnomaly &lt;= 2π
      * </pre>
      *
      * @param satelliteNumber satellite number
      * @param classification classification (U for unclassified)
      * @param launchYear launch year (all digits)
      * @param launchNumber launch number
      * @param launchPiece launch piece (3 char String)
      * @param ephemerisType type of ephemeris
      * @param elementNumber element number
      * @param epoch elements epoch
      * @param meanMotion mean motion (rad/s)
      * @param meanMotionFirstDerivative mean motion first derivative (rad/s²)
      * @param meanMotionSecondDerivative mean motion second derivative (rad/s³)
      * @param e eccentricity
      * @param i inclination (rad)
      * @param pa argument of perigee (rad)
      * @param raan right ascension of ascending node (rad)
      * @param meanAnomaly mean anomaly (rad)
      * @param revolutionNumberAtEpoch revolution number at epoch
      * @param bStar ballistic coefficient
      * @see #TLE(int, char, int, int, String, int, int, AbsoluteDate, double, double,
      * double, double, double, double, double, double, int, double, TimeScale)
      */
     @DefaultDataContext
     public TLE(final int satelliteNumber, final char classification,
                final int launchYear, final int launchNumber, final String launchPiece,
                final int ephemerisType, final int elementNumber, final AbsoluteDate epoch,
                final double meanMotion, final double meanMotionFirstDerivative,
                final double meanMotionSecondDerivative, final double e, final double i,
                final double pa, final double raan, final double meanAnomaly,
                final int revolutionNumberAtEpoch, final double bStar) {
         this(satelliteNumber, classification, launchYear, launchNumber, launchPiece,
                 ephemerisType, elementNumber, epoch, meanMotion,
                 meanMotionFirstDerivative, meanMotionSecondDerivative, e, i, pa, raan,
                 meanAnomaly, revolutionNumberAtEpoch, bStar,
                 DataContext.getDefault().getTimeScales().getUTC());
     }
 
     /**
      * <p>
      * Simple constructor from already parsed elements using the given time scale as
      * UTC.
      * </p>
      *
      * <p>
      * The mean anomaly, the right ascension of ascending node Ω and the argument of
      * perigee ω are normalized into the [0, 2π] interval as they can be negative.
      * After that, a range check is performed on some of the orbital elements:
      *
      * <pre>
      *     meanMotion &gt;= 0
      *     0 &lt;= i &lt;= π
      *     0 &lt;= Ω &lt;= 2π
      *     0 &lt;= e &lt;= 1
      *     0 &lt;= ω &lt;= 2π
      *     0 &lt;= meanAnomaly &lt;= 2π
      * </pre>
      *
      * @param satelliteNumber satellite number
      * @param classification classification (U for unclassified)
      * @param launchYear launch year (all digits)
      * @param launchNumber launch number
      * @param launchPiece launch piece (3 char String)
      * @param ephemerisType type of ephemeris
      * @param elementNumber element number
      * @param epoch elements epoch
      * @param meanMotion mean motion (rad/s)
      * @param meanMotionFirstDerivative mean motion first derivative (rad/s²)
      * @param meanMotionSecondDerivative mean motion second derivative (rad/s³)
      * @param e eccentricity
      * @param i inclination (rad)
      * @param pa argument of perigee (rad)
      * @param raan right ascension of ascending node (rad)
      * @param meanAnomaly mean anomaly (rad)
      * @param revolutionNumberAtEpoch revolution number at epoch
      * @param bStar ballistic coefficient
      * @param utc the UTC time scale.
      * @since 10.1
      */
     public TLE(final int satelliteNumber, final char classification,
                final int launchYear, final int launchNumber, final String launchPiece,
                final int ephemerisType, final int elementNumber, final AbsoluteDate epoch,
                final double meanMotion, final double meanMotionFirstDerivative,
                final double meanMotionSecondDerivative, final double e, final double i,
                final double pa, final double raan, final double meanAnomaly,
                final int revolutionNumberAtEpoch, final double bStar,
                final TimeScale utc) {
 
         // identification
         this.satelliteNumber = satelliteNumber;
         this.classification  = classification;
         this.launchYear      = launchYear;
         this.launchNumber    = launchNumber;
         this.launchPiece     = launchPiece;
         this.ephemerisType   = ephemerisType;
         this.elementNumber   = elementNumber;
 
         // orbital parameters
         this.epoch = epoch;
         // Checking mean motion range
         this.meanMotion = meanMotion;
         this.meanMotionFirstDerivative = meanMotionFirstDerivative;
         this.meanMotionSecondDerivative = meanMotionSecondDerivative;
 
         // Checking inclination range
         this.inclination = i;
 
         // Normalizing RAAN in [0,2pi] interval
         this.raan = MathUtils.normalizeAngle(raan, FastMath.PI);
 
         // Checking eccentricity range
         this.eccentricity = e;
 
         // Normalizing PA in [0,2pi] interval
         this.pa = MathUtils.normalizeAngle(pa, FastMath.PI);
 
         // Normalizing mean anomaly in [0,2pi] interval
         this.meanAnomaly = MathUtils.normalizeAngle(meanAnomaly, FastMath.PI);
 
         this.revolutionNumberAtEpoch = revolutionNumberAtEpoch;
 
 
         // don't build the line until really needed
         this.line1 = null;
         this.line2 = null;
         this.utc = utc;
 
         // create model parameter drivers
         this.bStarParameterDriver = new ParameterDriver(B_STAR, bStar, B_STAR_SCALE,
                                                         Double.NEGATIVE_INFINITY,
                                                         Double.POSITIVE_INFINITY);
 
     }
 
     /**
      * Get the UTC time scale used to create this TLE.
      *
      * @return UTC time scale.
      */
     public TimeScale getUtc() {
         return utc;
     }
 
     /** Get the first line.
      * @return first line
      */
     public String getLine1() {
         if (line1 == null) {
             buildLine1();
         }
         return line1;
     }
 
     /** Get the second line.
      * @return second line
      */
     public String getLine2() {
         if (line2 == null) {
             buildLine2();
         }
         return line2;
     }
 
     /** Build the line 1 from the parsed elements.
      */
     private void buildLine1() {
 
         final StringBuilder buffer = new StringBuilder();
 
         buffer.append('1');
 
         buffer.append(' ');
         buffer.append(ParseUtils.buildSatelliteNumber(satelliteNumber, "satelliteNumber-1"));
         buffer.append(classification);
 
         buffer.append(' ');
         buffer.append(ParseUtils.addPadding("launchYear",   launchYear % 100, '0', 2, true, satelliteNumber));
         buffer.append(ParseUtils.addPadding("launchNumber", launchNumber, '0', 3, true, satelliteNumber));
         buffer.append(ParseUtils.addPadding("launchPiece",  launchPiece, ' ', 3, false, satelliteNumber));
 
         buffer.append(' ');
         final DateTimeComponents dtc = epoch.getComponents(utc);
         buffer.append(ParseUtils.addPadding("year", dtc.getDate().getYear() % 100, '0', 2, true, satelliteNumber));
         buffer.append(ParseUtils.addPadding("day",  dtc.getDate().getDayOfYear(),  '0', 3, true, satelliteNumber));
         buffer.append('.');
         // nota: 31250/27 == 100000000/86400
         final int fraction = (int) FastMath.rint(31250 * dtc.getTime().getSecondsInUTCDay() / 27.0);
         buffer.append(ParseUtils.addPadding("fraction", fraction,  '0', 8, true, satelliteNumber));
 
         buffer.append(' ');
         final double n1 = meanMotionFirstDerivative * 1.86624e9 / FastMath.PI;
         final String sn1 = ParseUtils.addPadding("meanMotionFirstDerivative",
                                                  new DecimalFormat(".00000000", SYMBOLS).format(n1),
                                                  ' ', 10, true, satelliteNumber);
         buffer.append(sn1);
 
         buffer.append(' ');
         final double n2 = meanMotionSecondDerivative * 5.3747712e13 / FastMath.PI;
         buffer.append(formatExponentMarkerFree("meanMotionSecondDerivative", n2, 5, ' ', 8, true));
 
         buffer.append(' ');
         buffer.append(formatExponentMarkerFree("B*", getBStar(), 5, ' ', 8, true));
 
         buffer.append(' ');
         buffer.append(ephemerisType);
 
         buffer.append(' ');
         buffer.append(ParseUtils.addPadding("elementNumber", elementNumber, ' ', 4, true, satelliteNumber));
 
         buffer.append(checksum(buffer));
 
         line1 = buffer.toString();
 
     }
 
     /** Format a real number without 'e' exponent marker.
      * @param name parameter name
      * @param d number to format
      * @param mantissaSize size of the mantissa (not counting initial '-' or ' ' for sign)
      * @param c padding character
      * @param size desired size
      * @param rightJustified if true, the resulting string is
      * right justified (i.e. space are added to the left)
      * @return formatted and padded number
      */
     private String formatExponentMarkerFree(final String name, final double d, final int mantissaSize,
                                             final char c, final int size, final boolean rightJustified) {
         final double dAbs = FastMath.abs(d);
         int exponent = (dAbs < 1.0e-9) ? -9 : (int) FastMath.ceil(FastMath.log10(dAbs));
         long mantissa = FastMath.round(dAbs * FastMath.pow(10.0, mantissaSize - exponent));
         if (mantissa == 0) {
             exponent = 0;
         } else if (mantissa > (ArithmeticUtils.pow(10, mantissaSize) - 1)) {
             // rare case: if d has a single digit like d = 1.0e-4 with mantissaSize = 5
             // the above computation finds exponent = -4 and mantissa = 100000 which
             // doesn't fit in a 5 digits string
             exponent++;
             mantissa = FastMath.round(dAbs * FastMath.pow(10.0, mantissaSize - exponent));
         }
         final String sMantissa = ParseUtils.addPadding(name, (int) mantissa, '0', mantissaSize, true, satelliteNumber);
         final String sExponent = Integer.toString(FastMath.abs(exponent));
         final String formatted = (d <  0 ? '-' : ' ') + sMantissa + (exponent <= 0 ? '-' : '+') + sExponent;
 
         return ParseUtils.addPadding(name, formatted, c, size, rightJustified, satelliteNumber);
 
     }
 
     /** Build the line 2 from the parsed elements.
      */
     private void buildLine2() {
 
         final StringBuilder buffer = new StringBuilder();
         final DecimalFormat f34   = new DecimalFormat("##0.0000", SYMBOLS);
         final DecimalFormat f211  = new DecimalFormat("#0.00000000", SYMBOLS);
 
         buffer.append('2');
 
         buffer.append(' ');
         buffer.append(ParseUtils.buildSatelliteNumber(satelliteNumber, "satelliteNumber-2"));
 
         buffer.append(' ');
         buffer.append(ParseUtils.addPadding(INCLINATION, f34.format(FastMath.toDegrees(inclination)), ' ', 8, true, satelliteNumber));
         buffer.append(' ');
         buffer.append(ParseUtils.addPadding("raan", f34.format(FastMath.toDegrees(raan)), ' ', 8, true, satelliteNumber));
         buffer.append(' ');
         buffer.append(ParseUtils.addPadding(ECCENTRICITY, (int) FastMath.rint(eccentricity * 1.0e7), '0', 7, true, satelliteNumber));
         buffer.append(' ');
         buffer.append(ParseUtils.addPadding("pa", f34.format(FastMath.toDegrees(pa)), ' ', 8, true, satelliteNumber));
         buffer.append(' ');
         buffer.append(ParseUtils.addPadding("meanAnomaly", f34.format(FastMath.toDegrees(meanAnomaly)), ' ', 8, true, satelliteNumber));
 
         buffer.append(' ');
         buffer.append(ParseUtils.addPadding(MEAN_MOTION, f211.format(meanMotion * 43200.0 / FastMath.PI), ' ', 11, true, satelliteNumber));
         buffer.append(ParseUtils.addPadding("revolutionNumberAtEpoch", revolutionNumberAtEpoch, ' ', 5, true, satelliteNumber));
 
         buffer.append(checksum(buffer));
 
         line2 = buffer.toString();
 
     }
 
     /** Get the satellite id.
      * @return the satellite number
      */
     public int getSatelliteNumber() {
         return satelliteNumber;
     }
 
     /** Get the classification.
      * @return classification
      */
     public char getClassification() {
         return classification;
     }
 
     /** Get the launch year.
      * @return the launch year
      */
     public int getLaunchYear() {
         return launchYear;
     }
 
     /** Get the launch number.
      * @return the launch number
      */
     public int getLaunchNumber() {
         return launchNumber;
     }
 
     /** Get the launch piece.
      * @return the launch piece
      */
     public String getLaunchPiece() {
         return launchPiece;
     }
 
     /** Get the type of ephemeris.
      * @return the ephemeris type (one of {@link #DEFAULT}, {@link #SGP},
      * {@link #SGP4}, {@link #SGP8}, {@link #SDP4}, {@link #SDP8})
      */
     public int getEphemerisType() {
         return ephemerisType;
     }
 
     /** Get the element number.
      * @return the element number
      */
     public int getElementNumber() {
         return elementNumber;
     }
 
     /** Get the TLE current date.
      * @return the epoch
      */
     public AbsoluteDate getDate() {
         return epoch;
     }
 
     /** Get the mean motion.
      * @return the mean motion (rad/s)
      */
     public double getMeanMotion() {
         return meanMotion;
     }
 
     /** Get the mean motion first derivative.
      * @return the mean motion first derivative (rad/s²)
      */
     public double getMeanMotionFirstDerivative() {
         return meanMotionFirstDerivative;
     }
 
     /** Get the mean motion second derivative.
      * @return the mean motion second derivative (rad/s³)
      */
     public double getMeanMotionSecondDerivative() {
         return meanMotionSecondDerivative;
     }
 
     /** Get the eccentricity.
      * @return the eccentricity
      */
     public double getE() {
         return eccentricity;
     }
 
     /** Get the inclination.
      * @return the inclination (rad)
      */
     public double getI() {
         return inclination;
     }
 
     /** Get the argument of perigee.
      * @return omega (rad)
      */
     public double getPerigeeArgument() {
         return pa;
     }
 
     /** Get Right Ascension of the Ascending node.
      * @return the raan (rad)
      */
     public double getRaan() {
         return raan;
     }
 
     /** Get the mean anomaly.
      * @return the mean anomaly (rad)
      */
     public double getMeanAnomaly() {
         return meanAnomaly;
     }
 
     /** Get the revolution number.
      * @return the revolutionNumberAtEpoch
      */
     public int getRevolutionNumberAtEpoch() {
         return revolutionNumberAtEpoch;
     }
 
     /** Get the ballistic coefficient.
      * @return bStar
      */
     public double getBStar() {
         return bStarParameterDriver.getValue();
     }
 
     /** Get a string representation of this TLE set.
      * <p>The representation is simply the two lines separated by the
      * platform line separator.</p>
      * @return string representation of this TLE set
      */
     public String toString() {
         return getLine1() + System.getProperty("line.separator") + getLine2();
     }
 
     /**
      * Convert Spacecraft State into TLE.
      * This converter uses Fixed Point method to reverse SGP4 and SDP4 propagation algorithm
      * and generates a usable TLE version of a state.
      * Equinocital orbital parameters are used in order to get a stiff method.
      * New TLE epoch is state epoch.
      *
      * <p>
      * This method uses the {@link DataContext#getDefault() default data context},
      * as well as {@link #EPSILON_DEFAULT} and {@link #MAX_ITERATIONS_DEFAULT} for method convergence.
      *
      * @param state Spacecraft State to convert into TLE
      * @param templateTLE first guess used to get identification and estimate new TLE
      * @return TLE matching with Spacecraft State and template identification
      * @see #stateToTLE(SpacecraftState, TLE, TimeScale, Frame)
      * @see #stateToTLE(SpacecraftState, TLE, TimeScale, Frame, double, int)
      * @since 11.0
      */
     @DefaultDataContext
     public static TLE stateToTLE(final SpacecraftState state, final TLE templateTLE) {
         return stateToTLE(state, templateTLE,
                           DataContext.getDefault().getTimeScales().getUTC(),
                           DataContext.getDefault().getFrames().getTEME());
     }
 
     /**
      * Convert Spacecraft State into TLE.
      * This converter uses Fixed Point method to reverse SGP4 and SDP4 propagation algorithm
      * and generates a usable TLE version of a state.
      * Equinocital orbital parameters are used in order to get a stiff method.
      * New TLE epoch is state epoch.
      *
      * <p>
      * This method uses {@link #EPSILON_DEFAULT} and {@link #MAX_ITERATIONS_DEFAULT}
      * for method convergence.
      *
      * @param state Spacecraft State to convert into TLE
      * @param templateTLE first guess used to get identification and estimate new TLE
      * @param utc the UTC time scale
      * @param teme the TEME frame to use for propagation
      * @return TLE matching with Spacecraft State and template identification
      * @see #stateToTLE(SpacecraftState, TLE, TimeScale, Frame, double, int)
      * @since 11.0
      */
     public static TLE stateToTLE(final SpacecraftState state, final TLE templateTLE,
                                  final TimeScale utc, final Frame teme) {
         return stateToTLE(state, templateTLE, utc, teme, EPSILON_DEFAULT, MAX_ITERATIONS_DEFAULT);
     }
 
     /**
      * Convert Spacecraft State into TLE.
      * This converter uses Newton method to reverse SGP4 and SDP4 propagation algorithm
      * and generates a usable TLE version of a state.
      * New TLE epoch is state epoch.
      *
      * @param state Spacecraft State to convert into TLE
      * @param templateTLE first guess used to get identification and estimate new TLE
      * @param utc the UTC time scale
      * @param teme the TEME frame to use for propagation
      * @param epsilon used to compute threshold for convergence check
      * @param maxIterations maximum number of iterations for convergence
      * @return TLE matching with Spacecraft State and template identification
      * @since 11.0
      */
     public static TLE stateToTLE(final SpacecraftState state, final TLE templateTLE,
                                  final TimeScale utc, final Frame teme,
                                  final double epsilon, final int maxIterations) {
 
         // Gets equinoctial parameters in TEME frame from state
         final EquinoctialOrbit equiOrbit = convert(state.getOrbit(), teme);
         double sma = equiOrbit.getA();
         double ex  = equiOrbit.getEquinoctialEx();
         double ey  = equiOrbit.getEquinoctialEy();
         double hx  = equiOrbit.getHx();
         double hy  = equiOrbit.getHy();
         double lv  = equiOrbit.getLv();
 
         // Rough initialization of the TLE
         final KeplerianOrbit keplerianOrbit = (KeplerianOrbit) OrbitType.KEPLERIAN.convertType(equiOrbit);
         TLE current = newTLE(keplerianOrbit, templateTLE, utc);
 
         // threshold for each parameter
         final double thrA = epsilon * (1 + sma);
         final double thrE = epsilon * (1 + FastMath.hypot(ex, ey));
         final double thrH = epsilon * (1 + FastMath.hypot(hx, hy));
         final double thrV = epsilon * FastMath.PI;
 
         int k = 0;
         while (k++ < maxIterations) {
 
             // recompute the state from the current TLE
             final TLEPropagator propagator = TLEPropagator.selectExtrapolator(current, new InertialProvider(Rotation.IDENTITY, teme), state.getMass(), teme);
             final Orbit recovOrbit = propagator.getInitialState().getOrbit();
             final EquinoctialOrbit recovEquiOrbit = (EquinoctialOrbit) OrbitType.EQUINOCTIAL.convertType(recovOrbit);
 
             // adapted parameters residuals
             final double deltaSma = equiOrbit.getA() - recovEquiOrbit.getA();
             final double deltaEx  = equiOrbit.getEquinoctialEx() - recovEquiOrbit.getEquinoctialEx();
             final double deltaEy  = equiOrbit.getEquinoctialEy() - recovEquiOrbit.getEquinoctialEy();
             final double deltaHx  = equiOrbit.getHx() - recovEquiOrbit.getHx();
             final double deltaHy  = equiOrbit.getHy() - recovEquiOrbit.getHy();
             final double deltaLv  = MathUtils.normalizeAngle(equiOrbit.getLv() - recovEquiOrbit.getLv(), 0.0);
 
             // check convergence
             if (FastMath.abs(deltaSma) < thrA &&
                 FastMath.abs(deltaEx)  < thrE &&
                 FastMath.abs(deltaEy)  < thrE &&
                 FastMath.abs(deltaHx)  < thrH &&
                 FastMath.abs(deltaHy)  < thrH &&
                 FastMath.abs(deltaLv)  < thrV) {
 
                 // Verify if parameters are estimated
                 for (final ParameterDriver templateDrivers : templateTLE.getParametersDrivers()) {
                     if (templateDrivers.isSelected()) {
                         // Set to selected for the new TLE
                         current.getParameterDriver(templateDrivers.getName()).setSelected(true);
                     }
                 }
 
                 // Return
                 return current;
             }
 
             // update state
             sma += deltaSma;
             ex  += deltaEx;
             ey  += deltaEy;
             hx  += deltaHx;
             hy  += deltaHy;
             lv  += deltaLv;
             final EquinoctialOrbit newEquiOrbit =
                                     new EquinoctialOrbit(sma, ex, ey, hx, hy, lv, PositionAngle.TRUE,
                                     equiOrbit.getFrame(), equiOrbit.getDate(), equiOrbit.getMu());
             final KeplerianOrbit newKeplOrbit = (KeplerianOrbit) OrbitType.KEPLERIAN.convertType(newEquiOrbit);
 
             // update TLE
             current = newTLE(newKeplOrbit, templateTLE, utc);
         }
 
         throw new OrekitException(OrekitMessages.UNABLE_TO_COMPUTE_TLE, k);
     }
 
     /**
      * Converts an orbit into an equinoctial orbit expressed in TEME frame.
      *
      * @param orbitIn the orbit to convert
      * @param teme the TEME frame to use for propagation
      * @return the converted orbit, i.e. equinoctial in TEME frame
      */
     private static EquinoctialOrbit convert(final Orbit orbitIn, final Frame teme) {
         return new EquinoctialOrbit(orbitIn.getPVCoordinates(teme), teme, orbitIn.getMu());
     }
 
     /**
      * Builds a new TLE from Keplerian parameters and a template for TLE data.
      * @param keplerianOrbit the Keplerian parameters to build the TLE from
      * @param templateTLE TLE used to get object identification
      * @param utc the UTC time scale
      * @return TLE with template identification and new orbital parameters
      */
     private static TLE newTLE(final KeplerianOrbit keplerianOrbit, final TLE templateTLE,
                               final TimeScale utc) {
         // Keplerian parameters
         final double meanMotion  = keplerianOrbit.getKeplerianMeanMotion();
         final double e           = keplerianOrbit.getE();
         final double i           = keplerianOrbit.getI();
         final double raan        = keplerianOrbit.getRightAscensionOfAscendingNode();
         final double pa          = keplerianOrbit.getPerigeeArgument();
         final double meanAnomaly = keplerianOrbit.getMeanAnomaly();
         // TLE epoch is state epoch
         final AbsoluteDate epoch = keplerianOrbit.getDate();
         // Identification
         final int satelliteNumber = templateTLE.getSatelliteNumber();
         final char classification = templateTLE.getClassification();
         final int launchYear = templateTLE.getLaunchYear();
         final int launchNumber = templateTLE.getLaunchNumber();
         final String launchPiece = templateTLE.getLaunchPiece();
         final int ephemerisType = templateTLE.getEphemerisType();
         final int elementNumber = templateTLE.getElementNumber();
         // Updates revolutionNumberAtEpoch
         final int revolutionNumberAtEpoch = templateTLE.getRevolutionNumberAtEpoch();
         final double dt = epoch.durationFrom(templateTLE.getDate());
         final int newRevolutionNumberAtEpoch = (int) (revolutionNumberAtEpoch + FastMath.floor((MathUtils.normalizeAngle(meanAnomaly, FastMath.PI) + dt * meanMotion) / (2 * FastMath.PI)));
         // Gets B*
         final double bStar = templateTLE.getBStar();
         // Gets Mean Motion derivatives
         final double meanMotionFirstDerivative = templateTLE.getMeanMotionFirstDerivative();
         final double meanMotionSecondDerivative = templateTLE.getMeanMotionSecondDerivative();
         // Returns the new TLE
         return new TLE(satelliteNumber, classification, launchYear, launchNumber, launchPiece, ephemerisType,
                        elementNumber, epoch, meanMotion, meanMotionFirstDerivative, meanMotionSecondDerivative,
                        e, i, pa, raan, meanAnomaly, newRevolutionNumberAtEpoch, bStar, utc);
     }
 
     /** Check the lines format validity.
      * @param line1 the first element
      * @param line2 the second element
      * @return true if format is recognized (non null lines, 69 characters length,
      * line content), false if not
      */
     public static boolean isFormatOK(final String line1, final String line2) {
 
         if (line1 == null || line1.length() != 69 ||
             line2 == null || line2.length() != 69) {
             return false;
         }
 
         if (!(LINE_1_PATTERN.matcher(line1).matches() &&
               LINE_2_PATTERN.matcher(line2).matches())) {
             return false;
         }
 
         // check sums
         final int checksum1 = checksum(line1);
         if (Integer.parseInt(line1.substring(68)) != (checksum1 % 10)) {
             throw new OrekitException(OrekitMessages.TLE_CHECKSUM_ERROR,
                                       1, Integer.toString(checksum1 % 10), line1.substring(68), line1);
         }
 
         final int checksum2 = checksum(line2);
         if (Integer.parseInt(line2.substring(68)) != (checksum2 % 10)) {
             throw new OrekitException(OrekitMessages.TLE_CHECKSUM_ERROR,
                                       2, Integer.toString(checksum2 % 10), line2.substring(68), line2);
         }
 
         return true;
 
     }
 
     /** Compute the checksum of the first 68 characters of a line.
      * @param line line to check
      * @return checksum
      */
     private static int checksum(final CharSequence line) {
         int sum = 0;
         for (int j = 0; j < 68; j++) {
             final char c = line.charAt(j);
             if (Character.isDigit(c)) {
                 sum += Character.digit(c, 10);
             } else if (c == '-') {
                 ++sum;
             }
         }
         return sum % 10;
     }
 
     /** Check if this tle equals the provided tle.
      * <p>Due to the difference in precision between object and string
      * representations of TLE, it is possible for this method to return false
      * even if string representations returned by {@link #toString()}
      * are equal.</p>
      * @param o other tle
      * @return true if this tle equals the provided tle
      */
     @Override
     public boolean equals(final Object o) {
         if (o == this) {
             return true;
         }
         if (!(o instanceof TLE)) {
             return false;
         }
         final TLE tle = (TLE) o;
         return satelliteNumber == tle.satelliteNumber &&
                 classification == tle.classification &&
                 launchYear == tle.launchYear &&
                 launchNumber == tle.launchNumber &&
                 Objects.equals(launchPiece, tle.launchPiece) &&
                 ephemerisType == tle.ephemerisType &&
                 elementNumber == tle.elementNumber &&
                 Objects.equals(epoch, tle.epoch) &&
                 meanMotion == tle.meanMotion &&
                 meanMotionFirstDerivative == tle.meanMotionFirstDerivative &&
                 meanMotionSecondDerivative == tle.meanMotionSecondDerivative &&
                 eccentricity == tle.eccentricity &&
                 inclination == tle.inclination &&
                 pa == tle.pa &&
                 raan == tle.raan &&
                 meanAnomaly == tle.meanAnomaly &&
                 revolutionNumberAtEpoch == tle.revolutionNumberAtEpoch &&
                 getBStar() == tle.getBStar();
     }
 
     /** Get a hashcode for this tle.
      * @return hashcode
      */
     @Override
     public int hashCode() {
         return Objects.hash(satelliteNumber,
                 classification,
                 launchYear,
                 launchNumber,
                 launchPiece,
                 ephemerisType,
                 elementNumber,
                 epoch,
                 meanMotion,
                 meanMotionFirstDerivative,
                 meanMotionSecondDerivative,
                 eccentricity,
                 inclination,
                 pa,
                 raan,
                 meanAnomaly,
                 revolutionNumberAtEpoch,
                 getBStar());
     }
 
     /** Get the drivers for TLE propagation SGP4 and SDP4.
      * @return drivers for SGP4 and SDP4 model parameters
      */
     public List<ParameterDriver> getParametersDrivers() {
         return Collections.singletonList(bStarParameterDriver);
     }
 
     /** Get parameter driver from its name.
      * @param name parameter name
      * @return parameter driver
      * @since 11.1
      */
     public ParameterDriver getParameterDriver(final String name) {
         // Loop on known drivers
         for (final ParameterDriver driver : getParametersDrivers()) {
             if (name.equals(driver.getName())) {
                 // we have found a parameter with that name
                 return driver;
             }
         }
 
         // build the list of supported parameters
         final StringBuilder sBuilder = new StringBuilder();
         for (final ParameterDriver driver : getParametersDrivers()) {
             if (sBuilder.length() > 0) {
                 sBuilder.append(", ");
             }
             sBuilder.append(driver.getName());
         }
         throw new OrekitException(OrekitMessages.UNSUPPORTED_PARAMETER_NAME,
                                   name, sBuilder.toString());
 
     }
 
     /** Replace the instance with a data transfer object for serialization.
      * @return data transfer object that will be serialized
      */
     private Object writeReplace() {
         return new DataTransferObject(line1, line2, utc);
     }
 
     /** Internal class used only for serialization. */
     private static class DataTransferObject implements Serializable {
 
         /** Serializable UID. */
         private static final long serialVersionUID = -1596648022319057689L;
 
         /** First line. */
         private String line1;
 
         /** Second line. */
         private String line2;
 
         /** The UTC scale. */
         private final TimeScale utc;
 
         /** Simple constructor.
          * @param line1 the first element (69 char String)
          * @param line2 the second element (69 char String)
          * @param utc the UTC time scale
          */
         DataTransferObject(final String line1, final String line2, final TimeScale utc) {
             this.line1 = line1;
             this.line2 = line2;
             this.utc   = utc;
         }
 
         /** Replace the deserialized data transfer object with a {@link TLE}.
          * @return replacement {@link TLE}
          */
         private Object readResolve() {
             return new TLE(line1, line2, utc);
         }
 
     }
 
 }