Examples with FieldKeplerianOrbit org.orekit.orbits.FieldKeplerianOrbit used on opensource projects

Example 6 with FieldKeplerianOrbit

use of org.orekit.orbits.FieldKeplerianOrbit in project Orekit by CS-SI.

the class FieldPropagation method main.

/**
 * Program entry point.
 * @param args program arguments (unused here)
 * @throws IOException
 * @throws OrekitException
 */
public static void main(String[] args) throws IOException, OrekitException {
    // the goal of this example is to make a Montecarlo simulation giving an error on the semiaxis,
    // the inclination and the RAAN. The interest of doing it with Orekit based on the
    // DerivativeStructure is that instead of doing a large number of propagation around the initial
    // point we will do a single propagation of the initial state, and thanks to the Taylor expansion
    // we will see the evolution of the std deviation of the position, which is divided in the
    // CrossTrack, the LongTrack and the Radial error.
    // configure Orekit
    File home = new File(System.getProperty("user.home"));
    File orekitData = new File(home, "orekit-data");
    if (!orekitData.exists()) {
        System.err.format(Locale.US, "Failed to find %s folder%n", orekitData.getAbsolutePath());
        System.err.format(Locale.US, "You need to download %s from the %s page and unzip it in %s for this tutorial to work%n", "orekit-data.zip", "https://www.orekit.org/forge/projects/orekit/files", home.getAbsolutePath());
        System.exit(1);
    }
    DataProvidersManager manager = DataProvidersManager.getInstance();
    manager.addProvider(new DirectoryCrawler(orekitData));
    // output file in user's home directory
    File workingDir = new File(System.getProperty("user.home"));
    File errorFile = new File(workingDir, "error.txt");
    System.out.println("Output file is in : " + errorFile.getAbsolutePath());
    PrintWriter PW = new PrintWriter(errorFile, "UTF-8");
    PW.printf("time \t\tCrossTrackErr \tLongTrackErr  \tRadialErr \tTotalErr%n");
    // setting the parameters of the simulation
    // Order of derivation of the DerivativeStructures
    int params = 3;
    int order = 3;
    DSFactory factory = new DSFactory(params, order);
    // number of samples of the montecarlo simulation
    int montecarlo_size = 100;
    // nominal values of the Orbital parameters
    double a_nominal = 7.278E6;
    double e_nominal = 1e-3;
    double i_nominal = FastMath.toRadians(98.3);
    double pa_nominal = FastMath.PI / 2;
    double raan_nominal = 0.0;
    double ni_nominal = 0.0;
    // mean of the gaussian curve for each of the errors around the nominal values
    // {a, i, RAAN}
    double[] mean = { 0, 0, 0 };
    // standard deviation of the gaussian curve for each of the errors around the nominal values
    // {dA, dI, dRaan}
    double[] dAdIdRaan = { 5, FastMath.toRadians(1e-3), FastMath.toRadians(1e-3) };
    // time of integration
    double final_Dt = 1 * 60 * 60;
    // number of steps per orbit
    double num_step_orbit = 10;
    DerivativeStructure a_0 = factory.variable(0, a_nominal);
    DerivativeStructure e_0 = factory.constant(e_nominal);
    DerivativeStructure i_0 = factory.variable(1, i_nominal);
    DerivativeStructure pa_0 = factory.constant(pa_nominal);
    DerivativeStructure raan_0 = factory.variable(2, raan_nominal);
    DerivativeStructure ni_0 = factory.constant(ni_nominal);
    // sometimes we will need the field of the DerivativeStructure to build new instances
    Field<DerivativeStructure> field = a_0.getField();
    // sometimes we will need the zero of the DerivativeStructure to build new instances
    DerivativeStructure zero = field.getZero();
    // initializing the FieldAbsoluteDate with only the field it will generate the day J2000
    FieldAbsoluteDate<DerivativeStructure> date_0 = new FieldAbsoluteDate<>(field);
    // initialize a basic frame
    Frame frame = FramesFactory.getEME2000();
    // initialize the orbit
    double mu = 3.9860047e14;
    FieldKeplerianOrbit<DerivativeStructure> KO = new FieldKeplerianOrbit<>(a_0, e_0, i_0, pa_0, raan_0, ni_0, PositionAngle.ECCENTRIC, frame, date_0, mu);
    // step of integration (how many times per orbit we take the mesures)
    double int_step = KO.getKeplerianPeriod().getReal() / num_step_orbit;
    // random generator to conduct an
    long number = 23091991;
    RandomGenerator RG = new Well19937a(number);
    GaussianRandomGenerator NGG = new GaussianRandomGenerator(RG);
    UncorrelatedRandomVectorGenerator URVG = new UncorrelatedRandomVectorGenerator(mean, dAdIdRaan, NGG);
    double[][] rand_gen = new double[montecarlo_size][3];
    for (int jj = 0; jj < montecarlo_size; jj++) {
        rand_gen[jj] = URVG.nextVector();
    }
    // 
    FieldSpacecraftState<DerivativeStructure> SS_0 = new FieldSpacecraftState<>(KO);
    // adding force models
    ForceModel fModel_Sun = new ThirdBodyAttraction(CelestialBodyFactory.getSun());
    ForceModel fModel_Moon = new ThirdBodyAttraction(CelestialBodyFactory.getMoon());
    ForceModel fModel_HFAM = new HolmesFeatherstoneAttractionModel(FramesFactory.getITRF(IERSConventions.IERS_2010, true), GravityFieldFactory.getNormalizedProvider(18, 18));
    // setting an hipparchus field integrator
    OrbitType type = OrbitType.CARTESIAN;
    double[][] tolerance = NumericalPropagator.tolerances(0.001, KO.toOrbit(), type);
    AdaptiveStepsizeFieldIntegrator<DerivativeStructure> integrator = new DormandPrince853FieldIntegrator<>(field, 0.001, 200, tolerance[0], tolerance[1]);
    integrator.setInitialStepSize(zero.add(60));
    // setting of the field propagator, we used the numerical one in order to add the third body attraction
    // and the holmes featherstone force models
    FieldNumericalPropagator<DerivativeStructure> numProp = new FieldNumericalPropagator<>(field, integrator);
    numProp.setOrbitType(type);
    numProp.setInitialState(SS_0);
    numProp.addForceModel(fModel_Sun);
    numProp.addForceModel(fModel_Moon);
    numProp.addForceModel(fModel_HFAM);
    // with the master mode we will calulcate and print the error on every fixed step on the file error.txt
    // we defined the StepHandler to do that giving him the random number generator,
    // the size of the montecarlo simulation and the initial date
    numProp.setMasterMode(zero.add(int_step), new MyStepHandler<DerivativeStructure>(rand_gen, montecarlo_size, date_0, PW));
    // 
    long START = System.nanoTime();
    FieldSpacecraftState<DerivativeStructure> finalState = numProp.propagate(date_0.shiftedBy(final_Dt));
    long STOP = System.nanoTime();
    System.out.println((STOP - START) / 1E6 + " ms");
    System.out.println(finalState.getDate());
    PW.close();
}

Example 7 with FieldKeplerianOrbit

use of org.orekit.orbits.FieldKeplerianOrbit in project Orekit by CS-SI.

the class RelativityTest method RealFieldExpectErrorTest.

/**
 *Same test as the previous one but not adding the ForceModel to the NumericalPropagator
 *        it is a test to validate the previous test.
 *        (to test if the ForceModel it's actually
 *        doing something in the Propagator and the FieldPropagator)
 */
@Test
public void RealFieldExpectErrorTest() throws OrekitException {
    DSFactory factory = new DSFactory(6, 0);
    DerivativeStructure a_0 = factory.variable(0, 7e7);
    DerivativeStructure e_0 = factory.variable(1, 0.4);
    DerivativeStructure i_0 = factory.variable(2, 85 * FastMath.PI / 180);
    DerivativeStructure R_0 = factory.variable(3, 0.7);
    DerivativeStructure O_0 = factory.variable(4, 0.5);
    DerivativeStructure n_0 = factory.variable(5, 0.1);
    Field<DerivativeStructure> field = a_0.getField();
    DerivativeStructure zero = field.getZero();
    FieldAbsoluteDate<DerivativeStructure> J2000 = new FieldAbsoluteDate<>(field);
    Frame EME = FramesFactory.getEME2000();
    FieldKeplerianOrbit<DerivativeStructure> FKO = new FieldKeplerianOrbit<>(a_0, e_0, i_0, R_0, O_0, n_0, PositionAngle.MEAN, EME, J2000, Constants.EIGEN5C_EARTH_MU);
    FieldSpacecraftState<DerivativeStructure> initialState = new FieldSpacecraftState<>(FKO);
    SpacecraftState iSR = initialState.toSpacecraftState();
    OrbitType type = OrbitType.KEPLERIAN;
    double[][] tolerance = NumericalPropagator.tolerances(0.001, FKO.toOrbit(), type);
    AdaptiveStepsizeFieldIntegrator<DerivativeStructure> integrator = new DormandPrince853FieldIntegrator<>(field, 0.001, 200, tolerance[0], tolerance[1]);
    integrator.setInitialStepSize(zero.add(60));
    AdaptiveStepsizeIntegrator RIntegrator = new DormandPrince853Integrator(0.001, 200, tolerance[0], tolerance[1]);
    RIntegrator.setInitialStepSize(60);
    FieldNumericalPropagator<DerivativeStructure> FNP = new FieldNumericalPropagator<>(field, integrator);
    FNP.setOrbitType(type);
    FNP.setInitialState(initialState);
    NumericalPropagator NP = new NumericalPropagator(RIntegrator);
    NP.setOrbitType(type);
    NP.setInitialState(iSR);
    final Relativity forceModel = new Relativity(Constants.EIGEN5C_EARTH_MU);
    FNP.addForceModel(forceModel);
    // NOT ADDING THE FORCE MODEL TO THE NUMERICAL PROPAGATOR   NP.addForceModel(forceModel);
    FieldAbsoluteDate<DerivativeStructure> target = J2000.shiftedBy(1000.);
    FieldSpacecraftState<DerivativeStructure> finalState_DS = FNP.propagate(target);
    SpacecraftState finalState_R = NP.propagate(target.toAbsoluteDate());
    FieldPVCoordinates<DerivativeStructure> finPVC_DS = finalState_DS.getPVCoordinates();
    PVCoordinates finPVC_R = finalState_R.getPVCoordinates();
    Assert.assertEquals(0, Vector3D.distance(finPVC_DS.toPVCoordinates().getPosition(), finPVC_R.getPosition()), 8.0e-13 * finPVC_R.getPosition().getNorm());
}

Example 8 with FieldKeplerianOrbit

use of org.orekit.orbits.FieldKeplerianOrbit in project Orekit by CS-SI.

the class ConstantThrustManeuverTest method RealFieldTest.

/**
 *Testing if the propagation between the FieldPropagation and the propagation
 * is equivalent.
 * Also testing if propagating X+dX with the propagation is equivalent to
 * propagation X with the FieldPropagation and then applying the taylor
 * expansion of dX to the result.
 */
@Test
public void RealFieldTest() throws OrekitException {
    DSFactory factory = new DSFactory(6, 5);
    DerivativeStructure a_0 = factory.variable(0, 7e7);
    DerivativeStructure e_0 = factory.variable(1, 0.4);
    DerivativeStructure i_0 = factory.variable(2, 85 * FastMath.PI / 180);
    DerivativeStructure R_0 = factory.variable(3, 0.7);
    DerivativeStructure O_0 = factory.variable(4, 0.5);
    DerivativeStructure n_0 = factory.variable(5, 0.1);
    Field<DerivativeStructure> field = a_0.getField();
    DerivativeStructure zero = field.getZero();
    FieldAbsoluteDate<DerivativeStructure> J2000 = new FieldAbsoluteDate<>(field);
    Frame EME = FramesFactory.getEME2000();
    FieldKeplerianOrbit<DerivativeStructure> FKO = new FieldKeplerianOrbit<>(a_0, e_0, i_0, R_0, O_0, n_0, PositionAngle.MEAN, EME, J2000, Constants.EIGEN5C_EARTH_MU);
    FieldSpacecraftState<DerivativeStructure> initialState = new FieldSpacecraftState<>(FKO);
    SpacecraftState iSR = initialState.toSpacecraftState();
    final OrbitType type = OrbitType.KEPLERIAN;
    double[][] tolerance = NumericalPropagator.tolerances(10.0, FKO.toOrbit(), type);
    AdaptiveStepsizeFieldIntegrator<DerivativeStructure> integrator = new DormandPrince853FieldIntegrator<>(field, 0.001, 200, tolerance[0], tolerance[1]);
    integrator.setInitialStepSize(zero.add(60));
    AdaptiveStepsizeIntegrator RIntegrator = new DormandPrince853Integrator(0.001, 200, tolerance[0], tolerance[1]);
    RIntegrator.setInitialStepSize(60);
    FieldNumericalPropagator<DerivativeStructure> FNP = new FieldNumericalPropagator<>(field, integrator);
    FNP.setOrbitType(type);
    FNP.setInitialState(initialState);
    NumericalPropagator NP = new NumericalPropagator(RIntegrator);
    NP.setOrbitType(type);
    NP.setInitialState(iSR);
    final ConstantThrustManeuver forceModel = new ConstantThrustManeuver(J2000.toAbsoluteDate().shiftedBy(100), 100.0, 400.0, 300.0, Vector3D.PLUS_K);
    FNP.addForceModel(forceModel);
    NP.addForceModel(forceModel);
    FieldAbsoluteDate<DerivativeStructure> target = J2000.shiftedBy(1000.);
    FieldSpacecraftState<DerivativeStructure> finalState_DS = FNP.propagate(target);
    SpacecraftState finalState_R = NP.propagate(target.toAbsoluteDate());
    FieldPVCoordinates<DerivativeStructure> finPVC_DS = finalState_DS.getPVCoordinates();
    PVCoordinates finPVC_R = finalState_R.getPVCoordinates();
    Assert.assertEquals(finPVC_DS.toPVCoordinates().getPosition().getX(), finPVC_R.getPosition().getX(), FastMath.abs(finPVC_R.getPosition().getX()) * 1e-11);
    Assert.assertEquals(finPVC_DS.toPVCoordinates().getPosition().getY(), finPVC_R.getPosition().getY(), FastMath.abs(finPVC_R.getPosition().getY()) * 1e-11);
    Assert.assertEquals(finPVC_DS.toPVCoordinates().getPosition().getZ(), finPVC_R.getPosition().getZ(), FastMath.abs(finPVC_R.getPosition().getZ()) * 1e-11);
    long number = 23091991;
    RandomGenerator RG = new Well19937a(number);
    GaussianRandomGenerator NGG = new GaussianRandomGenerator(RG);
    UncorrelatedRandomVectorGenerator URVG = new UncorrelatedRandomVectorGenerator(new double[] { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }, new double[] { 1e3, 0.01, 0.01, 0.01, 0.01, 0.01 }, NGG);
    double a_R = a_0.getReal();
    double e_R = e_0.getReal();
    double i_R = i_0.getReal();
    double R_R = R_0.getReal();
    double O_R = O_0.getReal();
    double n_R = n_0.getReal();
    for (int ii = 0; ii < 1; ii++) {
        double[] rand_next = URVG.nextVector();
        double a_shift = a_R + rand_next[0];
        double e_shift = e_R + rand_next[1];
        double i_shift = i_R + rand_next[2];
        double R_shift = R_R + rand_next[3];
        double O_shift = O_R + rand_next[4];
        double n_shift = n_R + rand_next[5];
        KeplerianOrbit shiftedOrb = new KeplerianOrbit(a_shift, e_shift, i_shift, R_shift, O_shift, n_shift, PositionAngle.MEAN, EME, J2000.toAbsoluteDate(), Constants.EIGEN5C_EARTH_MU);
        SpacecraftState shift_iSR = new SpacecraftState(shiftedOrb);
        NumericalPropagator shift_NP = new NumericalPropagator(RIntegrator);
        shift_NP.setInitialState(shift_iSR);
        shift_NP.addForceModel(forceModel);
        SpacecraftState finalState_shift = shift_NP.propagate(target.toAbsoluteDate());
        PVCoordinates finPVC_shift = finalState_shift.getPVCoordinates();
        // position check
        FieldVector3D<DerivativeStructure> pos_DS = finPVC_DS.getPosition();
        double x_DS = pos_DS.getX().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double y_DS = pos_DS.getY().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double z_DS = pos_DS.getZ().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        // System.out.println(pos_DS.getX().getPartialDerivative(1));
        double x = finPVC_shift.getPosition().getX();
        double y = finPVC_shift.getPosition().getY();
        double z = finPVC_shift.getPosition().getZ();
        Assert.assertEquals(x_DS, x, FastMath.abs(x - pos_DS.getX().getReal()) * 1e-8);
        Assert.assertEquals(y_DS, y, FastMath.abs(y - pos_DS.getY().getReal()) * 1e-8);
        Assert.assertEquals(z_DS, z, FastMath.abs(z - pos_DS.getZ().getReal()) * 1e-8);
        // velocity check
        FieldVector3D<DerivativeStructure> vel_DS = finPVC_DS.getVelocity();
        double vx_DS = vel_DS.getX().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double vy_DS = vel_DS.getY().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double vz_DS = vel_DS.getZ().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double vx = finPVC_shift.getVelocity().getX();
        double vy = finPVC_shift.getVelocity().getY();
        double vz = finPVC_shift.getVelocity().getZ();
        Assert.assertEquals(vx_DS, vx, FastMath.abs(vx) * 1e-9);
        Assert.assertEquals(vy_DS, vy, FastMath.abs(vy) * 1e-9);
        Assert.assertEquals(vz_DS, vz, FastMath.abs(vz) * 1e-9);
        // acceleration check
        FieldVector3D<DerivativeStructure> acc_DS = finPVC_DS.getAcceleration();
        double ax_DS = acc_DS.getX().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double ay_DS = acc_DS.getY().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double az_DS = acc_DS.getZ().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double ax = finPVC_shift.getAcceleration().getX();
        double ay = finPVC_shift.getAcceleration().getY();
        double az = finPVC_shift.getAcceleration().getZ();
        Assert.assertEquals(ax_DS, ax, FastMath.abs(ax) * 1e-8);
        Assert.assertEquals(ay_DS, ay, FastMath.abs(ay) * 1e-8);
        Assert.assertEquals(az_DS, az, FastMath.abs(az) * 1e-8);
    }
}

Example 9 with FieldKeplerianOrbit

use of org.orekit.orbits.FieldKeplerianOrbit in project Orekit by CS-SI.

the class ConstantThrustManeuverTest method RealFieldExpectErrorTest.

/**
 *Same test as the previous one but not adding the ForceModel to the NumericalPropagator
 *    it is a test to validate the previous test.
 *    (to test if the ForceModel it's actually
 *    doing something in the Propagator and the FieldPropagator)
 */
@Test
public void RealFieldExpectErrorTest() throws OrekitException {
    DSFactory factory = new DSFactory(6, 0);
    DerivativeStructure a_0 = factory.variable(0, 7e7);
    DerivativeStructure e_0 = factory.variable(1, 0.4);
    DerivativeStructure i_0 = factory.variable(2, 85 * FastMath.PI / 180);
    DerivativeStructure R_0 = factory.variable(3, 0.7);
    DerivativeStructure O_0 = factory.variable(4, 0.5);
    DerivativeStructure n_0 = factory.variable(5, 0.1);
    Field<DerivativeStructure> field = a_0.getField();
    DerivativeStructure zero = field.getZero();
    FieldAbsoluteDate<DerivativeStructure> J2000 = new FieldAbsoluteDate<>(field);
    Frame EME = FramesFactory.getEME2000();
    FieldKeplerianOrbit<DerivativeStructure> FKO = new FieldKeplerianOrbit<>(a_0, e_0, i_0, R_0, O_0, n_0, PositionAngle.MEAN, EME, J2000, Constants.EIGEN5C_EARTH_MU);
    FieldSpacecraftState<DerivativeStructure> initialState = new FieldSpacecraftState<>(FKO);
    SpacecraftState iSR = initialState.toSpacecraftState();
    final OrbitType type = OrbitType.KEPLERIAN;
    double[][] tolerance = NumericalPropagator.tolerances(10.0, FKO.toOrbit(), type);
    AdaptiveStepsizeFieldIntegrator<DerivativeStructure> integrator = new DormandPrince853FieldIntegrator<>(field, 0.001, 200, tolerance[0], tolerance[1]);
    integrator.setInitialStepSize(zero.add(60));
    AdaptiveStepsizeIntegrator RIntegrator = new DormandPrince853Integrator(0.001, 200, tolerance[0], tolerance[1]);
    RIntegrator.setInitialStepSize(60);
    FieldNumericalPropagator<DerivativeStructure> FNP = new FieldNumericalPropagator<>(field, integrator);
    FNP.setOrbitType(type);
    FNP.setInitialState(initialState);
    NumericalPropagator NP = new NumericalPropagator(RIntegrator);
    NP.setInitialState(iSR);
    final ConstantThrustManeuver forceModel = new ConstantThrustManeuver(J2000.toAbsoluteDate().shiftedBy(100), 100.0, 400.0, 300.0, Vector3D.PLUS_K);
    FNP.addForceModel(forceModel);
    // NOT ADDING THE FORCE MODEL TO THE NUMERICAL PROPAGATOR   NP.addForceModel(forceModel);
    FieldAbsoluteDate<DerivativeStructure> target = J2000.shiftedBy(1000.);
    FieldSpacecraftState<DerivativeStructure> finalState_DS = FNP.propagate(target);
    SpacecraftState finalState_R = NP.propagate(target.toAbsoluteDate());
    FieldPVCoordinates<DerivativeStructure> finPVC_DS = finalState_DS.getPVCoordinates();
    PVCoordinates finPVC_R = finalState_R.getPVCoordinates();
    Assert.assertFalse(FastMath.abs(finPVC_DS.toPVCoordinates().getPosition().getX() - finPVC_R.getPosition().getX()) < FastMath.abs(finPVC_R.getPosition().getX()) * 1e-11);
    Assert.assertFalse(FastMath.abs(finPVC_DS.toPVCoordinates().getPosition().getY() - finPVC_R.getPosition().getY()) < FastMath.abs(finPVC_R.getPosition().getY()) * 1e-11);
    Assert.assertFalse(FastMath.abs(finPVC_DS.toPVCoordinates().getPosition().getZ() - finPVC_R.getPosition().getZ()) < FastMath.abs(finPVC_R.getPosition().getZ()) * 1e-11);
}

Example 10 with FieldKeplerianOrbit

use of org.orekit.orbits.FieldKeplerianOrbit in project Orekit by CS-SI.

the class FieldSpacecraftStateTest method doTestShiftVsEcksteinHechlerError.

private <T extends RealFieldElement<T>> void doTestShiftVsEcksteinHechlerError(final Field<T> field) throws OrekitException {
    T zero = field.getZero();
    T mass = zero.add(2500.);
    T a = zero.add(rOrbit.getA());
    T e = zero.add(rOrbit.getE());
    T i = zero.add(rOrbit.getI());
    T pa = zero.add(1.9674147913622104);
    T raan = zero.add(FastMath.toRadians(261));
    T lv = zero.add(0);
    final double ae = 6.378137e6;
    final double c20 = -1.08263e-3;
    final double c30 = 2.54e-6;
    final double c40 = 1.62e-6;
    final double c50 = 2.3e-7;
    final double c60 = -5.5e-7;
    // polynomial models for interpolation error in position, velocity, acceleration and attitude
    // these models grow as follows
    // interpolation time (s)    position error (m)   velocity error (m/s)   acceleration error (m/s²)  attitude error (°)
    // 60                        2                    0.07                  0.002               0.00002
    // 120                       12                    0.3                   0.005               0.00009
    // 300                      170                    1.6                   0.012               0.0009
    // 600                     1200                    5.7                   0.024               0.006
    // 900                     3600                   10.6                   0.034               0.02
    // the expected maximum residuals with respect to these models are about 0.4m, 0.5mm/s, 8μm/s² and 3e-6°
    PolynomialFunction pModel = new PolynomialFunction(new double[] { 1.5664070631933846e-01, 7.5504722733047560e-03, -8.2460562451009510e-05, 6.9546332080305580e-06, -1.7045365367533077e-09, -4.2187860791066264e-13 });
    PolynomialFunction vModel = new PolynomialFunction(new double[] { -3.5472364019908720e-04, 1.6568103861124980e-05, 1.9637913327830596e-05, -3.4248792843039766e-09, -5.6565135131014254e-12, 1.4730170946808630e-15 });
    PolynomialFunction aModel = new PolynomialFunction(new double[] { 3.0731707577766896e-06, 3.9770746399850350e-05, 1.9779039254538660e-09, 8.0263328220724900e-12, -1.5600835252366078e-14, 1.1785257001549687e-18 });
    PolynomialFunction rModel = new PolynomialFunction(new double[] { -2.7689062063188115e-06, 1.7406542538258334e-07, 2.5109795349592287e-09, 2.0399322661074575e-11, 9.9126348912426750e-15, -3.5015638905729510e-18 });
    FieldAbsoluteDate<T> date = new FieldAbsoluteDate<>(field, new DateComponents(2004, 01, 01), TimeComponents.H00, TimeScalesFactory.getUTC());
    FieldKeplerianOrbit<T> orbit = new FieldKeplerianOrbit<>(a, e, i, pa, raan, lv, PositionAngle.TRUE, FramesFactory.getEME2000(), date, mu);
    BodyCenterPointing attitudeLaw = new BodyCenterPointing(orbit.getFrame(), earth);
    FieldPropagator<T> propagator = new FieldEcksteinHechlerPropagator<>(orbit, attitudeLaw, mass, ae, mu, c20, c30, c40, c50, c60);
    FieldAbsoluteDate<T> centerDate = orbit.getDate().shiftedBy(100.0);
    FieldSpacecraftState<T> centerState = propagator.propagate(centerDate);
    double maxResidualP = 0;
    double maxResidualV = 0;
    double maxResidualA = 0;
    double maxResidualR = 0;
    for (T dt = field.getZero(); dt.getReal() < 900.0; dt = dt.add(5)) {
        FieldSpacecraftState<T> shifted = centerState.shiftedBy(dt);
        FieldSpacecraftState<T> propagated = propagator.propagate(centerDate.shiftedBy(dt));
        FieldPVCoordinates<T> dpv = new FieldPVCoordinates<>(propagated.getPVCoordinates(), shifted.getPVCoordinates());
        double residualP = pModel.value(dt.getReal()) - dpv.getPosition().getNorm().getReal();
        double residualV = vModel.value(dt.getReal()) - dpv.getVelocity().getNorm().getReal();
        double residualA = aModel.value(dt.getReal()) - dpv.getAcceleration().getNorm().getReal();
        double residualR = rModel.value(dt.getReal()) - FastMath.toDegrees(FieldRotation.distance(shifted.getAttitude().getRotation(), propagated.getAttitude().getRotation()).getReal());
        maxResidualP = FastMath.max(maxResidualP, FastMath.abs(residualP));
        maxResidualV = FastMath.max(maxResidualV, FastMath.abs(residualV));
        maxResidualA = FastMath.max(maxResidualA, FastMath.abs(residualA));
        maxResidualR = FastMath.max(maxResidualR, FastMath.abs(residualR));
    }
    Assert.assertEquals(0.40, maxResidualP, 0.01);
    Assert.assertEquals(4.9e-4, maxResidualV, 1.0e-5);
    Assert.assertEquals(2.8e-6, maxResidualR, 1.0e-1);
}