Package org.orekit.orbits

Class CircularOrbit

  • All Implemented Interfaces:
    Serializable, PositionAngleBased, TimeShiftable<Orbit>, TimeStamped, PVCoordinatesProvider
    public class CircularOrbit
extends Orbit
implements PositionAngleBased
    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,
                     PositionAngleType type,
                     PositionAngleType cachedPositionAngleType,
                     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
        cachedPositionAngleType - type of cached 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
        Since:
        12.1

      • CircularOrbit

        public CircularOrbit​(double a,
                     double ex,
                     double ey,
                     double i,
                     double raan,
                     double alpha,
                     PositionAngleType type,
                     Frame frame,
                     AbsoluteDate date,
                     double mu)
              throws IllegalArgumentException
        Creates a new instance without derivatives and with cached position angle same as value inputted.
        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,
                     PositionAngleType type,
                     PositionAngleType cachedPositionAngleType,
                     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
        cachedPositionAngleType - type of cached 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
        Since:
        12.1

      • 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,
                     PositionAngleType type,
                     Frame frame,
                     AbsoluteDate date,
                     double mu)
              throws IllegalArgumentException
        Creates a new instance with derivatives and with cached position angle same as value inputted.
        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)

      • getEquinoctialEx

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

      • getEquinoctialExDot

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

        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 derivative

      • getEquinoctialEy

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

      • getEquinoctialEyDot

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

        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 derivative

      • 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

      • 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

      • 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​(PositionAngleType type)
        Get the latitude argument.
        Parameters:
        type - type of the angle
        Returns:
        latitude argument (rad)

      • getAlphaDot

        public double getAlphaDot​(PositionAngleType 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

      • 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

      • 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)

      • 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)

      • 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)

      • 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)

      • initPosition

        protected Vector3D initPosition()
        Compute the position coordinates from the canonical parameters.
        Specified by:
        initPosition in class Orbit
        Returns:
        computed position coordinates

      • initPVCoordinates

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

      • withFrame

        public CircularOrbit withFrame​(Frame inertialFrame)
        Create a new object representing the same physical orbital state, but attached to a different reference frame. If the new frame is not inertial, an exception will be thrown.
        Specified by:
        withFrame in class Orbit
        Parameters:
        inertialFrame - reference frame of output orbit
        Returns:
        orbit with different frame

      • 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)

      • shiftedBy

        public CircularOrbit shiftedBy​(TimeOffset 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
        Returns:
        a new orbit, shifted with respect to the instance (which is immutable)

      • 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.

        The array returned by this method will not be modified.

        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.

        The array returned by this method will not be modified.

        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.

        The array returned by this method will not be modified.

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

      • addKeplerContribution

        public void addKeplerContribution​(PositionAngleType 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

      • hasNonKeplerianRates

        public boolean hasNonKeplerianRates()
        Tells whether the instance holds rates (first-order time derivatives) for dependent variables that are incompatible with Keplerian motion.
        Specified by:
        hasNonKeplerianRates in interface PositionAngleBased
        Returns:
        true if and only if holding non-Keplerian rates