Package org.orekit.orbits

Class CircularOrbit

  • All Implemented Interfaces:
    Serializable, TimeInterpolable<Orbit>, TimeShiftable<Orbit>, TimeStamped, PVCoordinatesProvider
    public class CircularOrbit
extends Orbit
    This class handles circular orbital parameters.

    The parameters used internally are the circular elements which can be related to Keplerian elements as follows:

    • a
    • ex = e cos(ω)
    • ey = e sin(ω)
    • i
    • Ω
    • αv = v + ω
    where Ω stands for the Right Ascension of the Ascending Node and αv stands for the true latitude argument

    The conversion equations from and to Keplerian elements given above hold only when both sides are unambiguously defined, i.e. when orbit is neither equatorial nor circular. When orbit is circular (but not equatorial), the circular parameters are still unambiguously defined whereas some Keplerian elements (more precisely ω and Ω) become ambiguous. When orbit is equatorial, neither the Keplerian nor the circular parameters can be defined unambiguously. equinoctial orbits is the recommended way to represent orbits.

    The instance CircularOrbit is guaranteed to be immutable.

    Author:
    Luc Maisonobe, Fabien Maussion, Véronique Pommier-Maurussane
    See Also:
    Orbit, KeplerianOrbit, CartesianOrbit, EquinoctialOrbit, Serialized Form

    • Constructor Detail

      • CircularOrbit

        public CircularOrbit​(double a,
                     double ex,
                     double ey,
                     double i,
                     double raan,
                     double alpha,
                     PositionAngle type,
                     Frame frame,
                     AbsoluteDate date,
                     double mu)
              throws IllegalArgumentException
        Creates a new instance.
        Parameters:
        a - semi-major axis (m)
        ex - e cos(ω), first component of circular eccentricity vector
        ey - e sin(ω), second component of circular eccentricity vector
        i - inclination (rad)
        raan - right ascension of ascending node (Ω, rad)
        alpha - an + ω, mean, eccentric or true latitude argument (rad)
        type - type of latitude argument
        frame - the frame in which are defined the parameters (must be a pseudo-inertial frame)
        date - date of the orbital parameters
        mu - central attraction coefficient (m³/s²)
        Throws:
        IllegalArgumentException - if eccentricity is equal to 1 or larger or if frame is not a pseudo-inertial frame

      • CircularOrbit

        public CircularOrbit​(double a,
                     double ex,
                     double ey,
                     double i,
                     double raan,
                     double alpha,
                     double aDot,
                     double exDot,
                     double eyDot,
                     double iDot,
                     double raanDot,
                     double alphaDot,
                     PositionAngle type,
                     Frame frame,
                     AbsoluteDate date,
                     double mu)
              throws IllegalArgumentException
        Creates a new instance.
        Parameters:
        a - semi-major axis (m)
        ex - e cos(ω), first component of circular eccentricity vector
        ey - e sin(ω), second component of circular eccentricity vector
        i - inclination (rad)
        raan - right ascension of ascending node (Ω, rad)
        alpha - an + ω, mean, eccentric or true latitude argument (rad)
        aDot - semi-major axis derivative (m/s)
        exDot - d(e cos(ω))/dt, first component of circular eccentricity vector derivative
        eyDot - d(e sin(ω))/dt, second component of circular eccentricity vector derivative
        iDot - inclination derivative(rad/s)
        raanDot - right ascension of ascending node derivative (rad/s)
        alphaDot - d(an + ω), mean, eccentric or true latitude argument derivative (rad/s)
        type - type of latitude argument
        frame - the frame in which are defined the parameters (must be a pseudo-inertial frame)
        date - date of the orbital parameters
        mu - central attraction coefficient (m³/s²)
        Throws:
        IllegalArgumentException - if eccentricity is equal to 1 or larger or if frame is not a pseudo-inertial frame

      • CircularOrbit

        public CircularOrbit​(Orbit op)
        Constructor from any kind of orbital parameters.
        Parameters:
        op - orbital parameters to copy

    • Method Detail

      • getType

        public OrbitType getType()
        Get the orbit type.
        Specified by:
        getType in class Orbit
        Returns:
        orbit type

      • getA

        public double getA()
        Get the semi-major axis.

        Note that the semi-major axis is considered negative for hyperbolic orbits.

        Specified by:
        getA in class Orbit
        Returns:
        semi-major axis (m)

      • getADot

        public double getADot()
        Get the semi-major axis derivative.

        Note that the semi-major axis is considered negative for hyperbolic orbits.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Specified by:
        getADot in class Orbit
        Returns:
        semi-major axis derivative (m/s)
        See Also:
        Orbit.hasDerivatives()

      • getEquinoctialEx

        public double getEquinoctialEx()
        Get the first component of the equinoctial eccentricity vector derivative.
        Specified by:
        getEquinoctialEx in class Orbit
        Returns:
        first component of the equinoctial eccentricity vector derivative

      • getEquinoctialExDot

        public double getEquinoctialExDot()
        Get the first component of the equinoctial eccentricity vector.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Specified by:
        getEquinoctialExDot in class Orbit
        Returns:
        first component of the equinoctial eccentricity vector
        See Also:
        Orbit.hasDerivatives()

      • getEquinoctialEy

        public double getEquinoctialEy()
        Get the second component of the equinoctial eccentricity vector derivative.
        Specified by:
        getEquinoctialEy in class Orbit
        Returns:
        second component of the equinoctial eccentricity vector derivative

      • getEquinoctialEyDot

        public double getEquinoctialEyDot()
        Get the second component of the equinoctial eccentricity vector.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Specified by:
        getEquinoctialEyDot in class Orbit
        Returns:
        second component of the equinoctial eccentricity vector
        See Also:
        Orbit.hasDerivatives()

      • getCircularEx

        public double getCircularEx()
        Get the first component of the circular eccentricity vector.
        Returns:
        ex = e cos(ω), first component of the circular eccentricity vector

      • getCircularExDot

        public double getCircularExDot()
        Get the first component of the circular eccentricity vector derivative.
        Returns:
        ex = e cos(ω), first component of the circular eccentricity vector derivative
        Since:
        9.0

      • getCircularEy

        public double getCircularEy()
        Get the second component of the circular eccentricity vector.
        Returns:
        ey = e sin(ω), second component of the circular eccentricity vector

      • getCircularEyDot

        public double getCircularEyDot()
        Get the second component of the circular eccentricity vector derivative.
        Returns:
        ey = e sin(ω), second component of the circular eccentricity vector derivative

      • getHx

        public double getHx()
        Get the first component of the inclination vector.
        Specified by:
        getHx in class Orbit
        Returns:
        first component of the inclination vector

      • getHxDot

        public double getHxDot()
        Get the first component of the inclination vector derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Specified by:
        getHxDot in class Orbit
        Returns:
        first component of the inclination vector derivative
        See Also:
        Orbit.hasDerivatives()

      • getHy

        public double getHy()
        Get the second component of the inclination vector.
        Specified by:
        getHy in class Orbit
        Returns:
        second component of the inclination vector

      • getHyDot

        public double getHyDot()
        Get the second component of the inclination vector derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Specified by:
        getHyDot in class Orbit
        Returns:
        second component of the inclination vector derivative
        See Also:
        Orbit.hasDerivatives()

      • getAlphaV

        public double getAlphaV()
        Get the true latitude argument.
        Returns:
        v + ω true latitude argument (rad)

      • getAlphaVDot

        public double getAlphaVDot()
        Get the true latitude argument derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Returns:
        v + ω true latitude argument derivative (rad/s)
        Since:
        9.0

      • getAlphaE

        public double getAlphaE()
        Get the eccentric latitude argument.
        Returns:
        E + ω eccentric latitude argument (rad)

      • getAlphaEDot

        public double getAlphaEDot()
        Get the eccentric latitude argument derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Returns:
        d(E + ω)/dt eccentric latitude argument derivative (rad/s)
        Since:
        9.0

      • getAlphaM

        public double getAlphaM()
        Get the mean latitude argument.
        Returns:
        M + ω mean latitude argument (rad)

      • getAlphaMDot

        public double getAlphaMDot()
        Get the mean latitude argument derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Returns:
        d(M + ω)/dt mean latitude argument derivative (rad/s)
        Since:
        9.0

      • getAlpha

        public double getAlpha​(PositionAngle type)
        Get the latitude argument.
        Parameters:
        type - type of the angle
        Returns:
        latitude argument (rad)

      • getAlphaDot

        public double getAlphaDot​(PositionAngle type)
        Get the latitude argument derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Parameters:
        type - type of the angle
        Returns:
        latitude argument derivative (rad/s)
        Since:
        9.0

      • eccentricToTrue

        public static double eccentricToTrue​(double alphaE,
                                     double ex,
                                     double ey)
        Computes the true latitude argument from the eccentric latitude argument.
        Parameters:
        alphaE - = E + ω eccentric latitude argument (rad)
        ex - e cos(ω), first component of circular eccentricity vector
        ey - e sin(ω), second component of circular eccentricity vector
        Returns:
        the true latitude argument.

      • trueToEccentric

        public static double trueToEccentric​(double alphaV,
                                     double ex,
                                     double ey)
        Computes the eccentric latitude argument from the true latitude argument.
        Parameters:
        alphaV - = V + ω true latitude argument (rad)
        ex - e cos(ω), first component of circular eccentricity vector
        ey - e sin(ω), second component of circular eccentricity vector
        Returns:
        the eccentric latitude argument.

      • meanToEccentric

        public static double meanToEccentric​(double alphaM,
                                     double ex,
                                     double ey)
        Computes the eccentric latitude argument from the mean latitude argument.
        Parameters:
        alphaM - = M + ω mean latitude argument (rad)
        ex - e cos(ω), first component of circular eccentricity vector
        ey - e sin(ω), second component of circular eccentricity vector
        Returns:
        the eccentric latitude argument.

      • eccentricToMean

        public static double eccentricToMean​(double alphaE,
                                     double ex,
                                     double ey)
        Computes the mean latitude argument from the eccentric latitude argument.
        Parameters:
        alphaE - = E + ω mean latitude argument (rad)
        ex - e cos(ω), first component of circular eccentricity vector
        ey - e sin(ω), second component of circular eccentricity vector
        Returns:
        the mean latitude argument.

      • getE

        public double getE()
        Get the eccentricity.
        Specified by:
        getE in class Orbit
        Returns:
        eccentricity

      • getEDot

        public double getEDot()
        Get the eccentricity derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Specified by:
        getEDot in class Orbit
        Returns:
        eccentricity derivative
        See Also:
        Orbit.hasDerivatives()

      • getI

        public double getI()
        Get the inclination.
        Specified by:
        getI in class Orbit
        Returns:
        inclination (rad)

      • getIDot

        public double getIDot()
        Get the inclination derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Specified by:
        getIDot in class Orbit
        Returns:
        inclination derivative (rad/s)
        See Also:
        Orbit.hasDerivatives()

      • getRightAscensionOfAscendingNode

        public double getRightAscensionOfAscendingNode()
        Get the right ascension of the ascending node.
        Returns:
        right ascension of the ascending node (rad)

      • getRightAscensionOfAscendingNodeDot

        public double getRightAscensionOfAscendingNodeDot()
        Get the right ascension of the ascending node derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Returns:
        right ascension of the ascending node derivative (rad/s)
        Since:
        9.0

      • getLv

        public double getLv()
        Get the true longitude argument.
        Specified by:
        getLv in class Orbit
        Returns:
        v + ω + Ω true longitude argument (rad)

      • getLvDot

        public double getLvDot()
        Get the true longitude argument derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Specified by:
        getLvDot in class Orbit
        Returns:
        d(v + ω + Ω)/dt true longitude argument derivative (rad/s)
        See Also:
        Orbit.hasDerivatives()

      • getLE

        public double getLE()
        Get the eccentric longitude argument.
        Specified by:
        getLE in class Orbit
        Returns:
        E + ω + Ω eccentric longitude argument (rad)

      • getLEDot

        public double getLEDot()
        Get the eccentric longitude argument derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Specified by:
        getLEDot in class Orbit
        Returns:
        d(E + ω + Ω)/dt eccentric longitude argument derivative (rad/s)
        See Also:
        Orbit.hasDerivatives()

      • getLM

        public double getLM()
        Get the mean longitude argument.
        Specified by:
        getLM in class Orbit
        Returns:
        M + ω + Ω mean longitude argument (rad)

      • getLMDot

        public double getLMDot()
        Get the mean longitude argument derivative.

        If the orbit was created without derivatives, the value returned is Double.NaN.

        Specified by:
        getLMDot in class Orbit
        Returns:
        d(M + ω + Ω)/dt mean longitude argument derivative (rad/s)
        See Also:
        Orbit.hasDerivatives()

      • initPVCoordinates

        protected TimeStampedPVCoordinates initPVCoordinates()
        Compute the position/velocity coordinates from the canonical parameters.
        Specified by:
        initPVCoordinates in class Orbit
        Returns:
        computed position/velocity coordinates

      • shiftedBy

        public CircularOrbit shiftedBy​(double dt)
        Get a time-shifted orbit.

        The orbit can be slightly shifted to close dates. The shifting model is a Keplerian one if no derivatives are available in the orbit, or Keplerian plus quadratic effect of the non-Keplerian acceleration if derivatives are available. Shifting is not intended as a replacement for proper orbit propagation but should be sufficient for small time shifts or coarse accuracy.

        Specified by:
        shiftedBy in interface TimeShiftable<Orbit>
        Specified by:
        shiftedBy in class Orbit
        Parameters:
        dt - time shift in seconds
        Returns:
        a new orbit, shifted with respect to the instance (which is immutable)

      • interpolate

        public CircularOrbit interpolate​(AbsoluteDate date,
                                 Stream<Orbit> sample)
        Get an interpolated instance.

        Note that the state of the current instance may not be used in the interpolation process, only its type and non interpolable fields are used (for example central attraction coefficient or frame when interpolating orbits). The interpolable fields taken into account are taken only from the states of the sample points. So if the state of the instance must be used, the instance should be included in the sample points.

        Note that this method is designed for small samples only (say up to about 10-20 points) so it can be implemented using polynomial interpolation (typically Hermite interpolation). Using too much points may induce Runge's phenomenon and numerical problems (including NaN appearing).

        The interpolated instance is created by polynomial Hermite interpolation on circular elements, without derivatives (which means the interpolation falls back to Lagrange interpolation only).

        As this implementation of interpolation is polynomial, it should be used only with small samples (about 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).

        If orbit interpolation on large samples is needed, using the Ephemeris class is a better way than using this low-level interpolation. The Ephemeris class automatically handles selection of a neighboring sub-sample with a predefined number of point from a large global sample in a thread-safe way.

        Parameters:
        date - interpolation date
        sample - sample points on which interpolation should be done
        Returns:
        a new instance, interpolated at specified date

      • computeJacobianMeanWrtCartesian

        protected double[][] computeJacobianMeanWrtCartesian()
        Compute the Jacobian of the orbital parameters with mean angle with respect to the Cartesian parameters.

        Element jacobian[i][j] is the derivative of parameter i of the orbit with respect to Cartesian coordinate j. This means each row correspond to one orbital parameter whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.

        Specified by:
        computeJacobianMeanWrtCartesian in class Orbit
        Returns:
        6x6 Jacobian matrix
        See Also:
        Orbit.computeJacobianEccentricWrtCartesian(), Orbit.computeJacobianTrueWrtCartesian()

      • computeJacobianEccentricWrtCartesian

        protected double[][] computeJacobianEccentricWrtCartesian()
        Compute the Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian parameters.

        Element jacobian[i][j] is the derivative of parameter i of the orbit with respect to Cartesian coordinate j. This means each row correspond to one orbital parameter whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.

        Specified by:
        computeJacobianEccentricWrtCartesian in class Orbit
        Returns:
        6x6 Jacobian matrix
        See Also:
        Orbit.computeJacobianMeanWrtCartesian(), Orbit.computeJacobianTrueWrtCartesian()

      • computeJacobianTrueWrtCartesian

        protected double[][] computeJacobianTrueWrtCartesian()
        Compute the Jacobian of the orbital parameters with true angle with respect to the Cartesian parameters.

        Element jacobian[i][j] is the derivative of parameter i of the orbit with respect to Cartesian coordinate j. This means each row correspond to one orbital parameter whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.

        Specified by:
        computeJacobianTrueWrtCartesian in class Orbit
        Returns:
        6x6 Jacobian matrix
        See Also:
        Orbit.computeJacobianMeanWrtCartesian(), Orbit.computeJacobianEccentricWrtCartesian()

      • addKeplerContribution

        public void addKeplerContribution​(PositionAngle type,
                                  double gm,
                                  double[] pDot)
        Add the contribution of the Keplerian motion to parameters derivatives

        This method is used by integration-based propagators to evaluate the part of Keplerian motion to evolution of the orbital state.

        Specified by:
        addKeplerContribution in class Orbit
        Parameters:
        type - type of the position angle in the state
        gm - attraction coefficient to use
        pDot - array containing orbital state derivatives to update (the Keplerian part must be added to the array components, as the array may already contain some non-zero elements corresponding to non-Keplerian parts)

      • toString

        public String toString()
        Returns a string representation of this Orbit object.
        Overrides:
        toString in class Object
        Returns:
        a string representation of this object