Package org.orekit.orbits

Class FieldCircularOrbit<T extends CalculusFieldElement<T>>

java.lang.Object
org.orekit.orbits.FieldOrbit<T>
org.orekit.orbits.FieldCircularOrbit<T>
Type Parameters:
T - type of the field elements
All Implemented Interfaces:
PositionAngleBased<FieldCircularOrbit<T>>, FieldTimeShiftable<ShiftableFieldPVCoordinatesHolder<FieldOrbit<T>,T>,T>, FieldTimeStamped<T>, TimeShiftable<ShiftableFieldPVCoordinatesHolder<FieldOrbit<T>,T>>, FieldPVCoordinatesProvider<T>, ShiftableFieldPVCoordinatesHolder<FieldOrbit<T>,T>
public class FieldCircularOrbit<T extends CalculusFieldElement<T>> extends FieldOrbit<T> implements PositionAngleBased<FieldCircularOrbit<T>>
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.

Since:
9.0
Author:
Luc Maisonobe, Fabien Maussion, Véronique Pommier-Maurussane
See Also:

  • Constructor Details

    • FieldCircularOrbit

      public FieldCircularOrbit(T a, T ex, T ey, T i, T raan, T alpha, PositionAngleType type, PositionAngleType cachedPositionAngleType, Frame frame, FieldAbsoluteDate<T> date, T 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

    • FieldCircularOrbit

      public FieldCircularOrbit(T a, T ex, T ey, T i, T raan, T alpha, PositionAngleType type, Frame frame, FieldAbsoluteDate<T> date, T 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

    • FieldCircularOrbit

      public FieldCircularOrbit(T a, T ex, T ey, T i, T raan, T alpha, T aDot, T exDot, T eyDot, T iDot, T raanDot, T alphaDot, PositionAngleType type, Frame frame, FieldAbsoluteDate<T> date, T 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

    • FieldCircularOrbit

      public FieldCircularOrbit(T a, T ex, T ey, T i, T raan, T alpha, T aDot, T exDot, T eyDot, T iDot, T raanDot, T alphaDot, PositionAngleType type, PositionAngleType cachedPositionAngleType, Frame frame, FieldAbsoluteDate<T> date, T 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

    • FieldCircularOrbit

      public FieldCircularOrbit(TimeStampedFieldPVCoordinates<T> pvCoordinates, Frame frame, T mu) throws IllegalArgumentException
      Constructor from Cartesian parameters.

      The acceleration provided in FieldPVCoordinates is accessible using FieldOrbit.getPVCoordinates() and FieldOrbit.getPVCoordinates(Frame). All other methods use mu and the position to compute the acceleration, including shiftedBy(CalculusFieldElement) and FieldOrbit.getPVCoordinates(FieldAbsoluteDate, Frame).

      Parameters:
      pvCoordinates - the FieldPVCoordinates in inertial frame
      frame - the frame in which are defined the FieldPVCoordinates (must be a pseudo-inertial frame)
      mu - central attraction coefficient (m³/s²)
      Throws:
      IllegalArgumentException - if frame is not a pseudo-inertial frame

    • FieldCircularOrbit

      public FieldCircularOrbit(FieldPVCoordinates<T> PVCoordinates, Frame frame, FieldAbsoluteDate<T> date, T mu) throws IllegalArgumentException
      Constructor from Cartesian parameters.

      The acceleration provided in FieldPVCoordinates is accessible using FieldOrbit.getPVCoordinates() and FieldOrbit.getPVCoordinates(Frame). All other methods use mu and the position to compute the acceleration, including shiftedBy(CalculusFieldElement) and FieldOrbit.getPVCoordinates(FieldAbsoluteDate, Frame).

      Parameters:
      PVCoordinates - the FieldPVCoordinates in inertial frame
      frame - the frame in which are defined the FieldPVCoordinates (must be a pseudo-inertial frame)
      date - date of the orbital parameters
      mu - central attraction coefficient (m³/s²)
      Throws:
      IllegalArgumentException - if frame is not a pseudo-inertial frame

    • FieldCircularOrbit

      public FieldCircularOrbit(FieldOrbit<T> op)
      Constructor from any kind of orbital parameters.
      Parameters:
      op - orbital parameters to copy

    • FieldCircularOrbit

      public FieldCircularOrbit(Field<T> field, CircularOrbit op)
      Constructor from Field and CircularOrbit.

      Build a FieldCircularOrbit from non-Field CircularOrbit.

      Parameters:
      field - CalculusField to base object on
      op - non-field orbit with only "constant" terms
      Since:
      12.0

    • FieldCircularOrbit

      public FieldCircularOrbit(Field<T> field, Orbit op)
      Constructor from Field and Orbit.

      Build a FieldCircularOrbit from any non-Field Orbit.

      Parameters:
      field - CalculusField to base object on
      op - non-field orbit with only "constant" terms
      Since:
      12.0

  • Method Details

    • getType

      public OrbitType getType()
      Get the orbit type.
      Specified by:
      getType in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      orbit type

    • getA

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

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

      Specified by:
      getA in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      semi-major axis (m)

    • getADot

      public T 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 null.

      Specified by:
      getADot in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      semi-major axis derivative (m/s)

    • getEquinoctialEx

      public T getEquinoctialEx()
      Get the first component of the equinoctial eccentricity vector.
      Specified by:
      getEquinoctialEx in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      first component of the equinoctial eccentricity vector

    • getEquinoctialExDot

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

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

      Specified by:
      getEquinoctialExDot in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      first component of the equinoctial eccentricity vector derivative

    • getEquinoctialEy

      public T getEquinoctialEy()
      Get the second component of the equinoctial eccentricity vector.
      Specified by:
      getEquinoctialEy in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      second component of the equinoctial eccentricity vector

    • getEquinoctialEyDot

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

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

      Specified by:
      getEquinoctialEyDot in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      second component of the equinoctial eccentricity vector derivative

    • getCircularEx

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

    • getCircularExDot

      public T getCircularExDot()
      Get the first component of the circular eccentricity vector derivative.
      Returns:
      d(ex)/dt = d(e cos(ω))/dt, first component of the circular eccentricity vector derivative

    • getCircularEy

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

    • getCircularEyDot

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

    • getHx

      public T getHx()
      Get the first component of the inclination vector.
      Specified by:
      getHx in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      first component of the inclination vector

    • getHxDot

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

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

      Specified by:
      getHxDot in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      first component of the inclination vector derivative

    • getHy

      public T getHy()
      Get the second component of the inclination vector.
      Specified by:
      getHy in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      second component of the inclination vector

    • getHyDot

      public T getHyDot()
      Get the second component of the inclination vector derivative.
      Specified by:
      getHyDot in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      second component of the inclination vector derivative

    • getAlphaV

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

    • getAlphaVDot

      public T getAlphaVDot()
      Get the true latitude argument derivative.
      Returns:
      d(v + ω)/dt true latitude argument derivative (rad/s)

    • getAlphaE

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

    • getAlphaEDot

      public T getAlphaEDot()
      Get the eccentric latitude argument derivative.
      Returns:
      d(E + ω)/dt eccentric latitude argument derivative (rad/s)

    • getAlphaM

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

    • getAlphaMDot

      public T getAlphaMDot()
      Get the mean latitude argument derivative.
      Returns:
      d(M + ω)/dt mean latitude argument derivative (rad/s)

    • getAlpha

      public T getAlpha(PositionAngleType type)
      Get the latitude argument.
      Parameters:
      type - type of the angle
      Returns:
      latitude argument (rad)

    • getAlphaDot

      public T getAlphaDot(PositionAngleType type)
      Get the latitude argument derivative.
      Parameters:
      type - type of the angle
      Returns:
      latitude argument derivative (rad/s)

    • getE

      public T getE()
      Get the eccentricity.
      Specified by:
      getE in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      eccentricity

    • getEDot

      public T getEDot()
      Get the eccentricity derivative.

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

      Specified by:
      getEDot in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      eccentricity derivative

    • getI

      public T getI()
      Get the inclination.

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

      Specified by:
      getI in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      inclination (rad)

    • getIDot

      public T getIDot()
      Get the inclination derivative.
      Specified by:
      getIDot in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      inclination derivative (rad/s)

    • getRightAscensionOfAscendingNode

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

    • getRightAscensionOfAscendingNodeDot

      public T getRightAscensionOfAscendingNodeDot()
      Get the right ascension of the ascending node derivative.
      Returns:
      right ascension of the ascending node derivative (rad/s)

    • getLv

      public T getLv()
      Get the true longitude argument.
      Specified by:
      getLv in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      v + ω + Ω true longitude argument (rad)

    • getLvDot

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

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

      Specified by:
      getLvDot in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      d(v + ω + Ω)/dt true longitude argument derivative (rad/s)

    • getLE

      public T getLE()
      Get the eccentric longitude argument.
      Specified by:
      getLE in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      E + ω + Ω eccentric longitude argument (rad)

    • getLEDot

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

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

      Specified by:
      getLEDot in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      d(E + ω + Ω)/dt eccentric longitude argument derivative (rad/s)

    • getLM

      public T getLM()
      Get the mean longitude argument.
      Specified by:
      getLM in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      M + ω + Ω mean longitude argument (rad)

    • getLMDot

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

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

      Specified by:
      getLMDot in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      d(M + ω + Ω)/dt mean longitude argument derivative (rad/s)

    • hasNonKeplerianAcceleration

      public boolean hasNonKeplerianAcceleration()
      Check if orbit includes non-Keplerian rates.
      Overrides:
      hasNonKeplerianAcceleration in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      true if orbit includes non-Keplerian derivatives
      See Also:

    • initPosition

      protected FieldVector3D<T> initPosition()
      Compute the position coordinates from the canonical parameters.
      Specified by:
      initPosition in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      computed position coordinates

    • initPVCoordinates

      protected TimeStampedFieldPVCoordinates<T> initPVCoordinates()
      Compute the position/velocity coordinates from the canonical parameters.
      Specified by:
      initPVCoordinates in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      computed position/velocity coordinates

    • inFrame

      public FieldCircularOrbit<T> inFrame(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:
      inFrame in class FieldOrbit<T extends CalculusFieldElement<T>>
      Parameters:
      inertialFrame - reference frame of output orbit
      Returns:
      orbit with different frame

    • withCachedPositionAngleType

      public FieldCircularOrbit<T> withCachedPositionAngleType(PositionAngleType positionAngleType)
      Creates a new instance with the provided type used for caching.
      Specified by:
      withCachedPositionAngleType in interface PositionAngleBased<T extends CalculusFieldElement<T>>
      Parameters:
      positionAngleType - position angle type to use for caching value
      Returns:
      new object

    • shiftedBy

      public FieldCircularOrbit<T> shiftedBy(double dt)
      Get a time-shifted orbit.

      The orbit can be slightly shifted to close dates. This shift is based on a simple Keplerian model. It is not intended as a replacement for proper orbit and attitude propagation but should be sufficient for small time shifts or coarse accuracy.

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

    • shiftedBy

      public FieldCircularOrbit<T> shiftedBy(T dt)
      Get a time-shifted orbit.

      The orbit can be slightly shifted to close dates. This shift is based on a simple Keplerian model. It is not intended as a replacement for proper orbit and attitude propagation but should be sufficient for small time shifts or coarse accuracy.

      Specified by:
      shiftedBy in interface FieldTimeShiftable<ShiftableFieldPVCoordinatesHolder<FieldOrbit<T extends CalculusFieldElement<T>>,T extends CalculusFieldElement<T>>,T extends CalculusFieldElement<T>>
      Specified by:
      shiftedBy in class FieldOrbit<T extends CalculusFieldElement<T>>
      Parameters:
      dt - time shift in seconds
      Returns:
      a new orbit, shifted with respect to the instance (which is immutable)

    • shiftedBy

      public FieldCircularOrbit<T> shiftedBy(TimeOffset dt)
      Get a time-shifted orbit.

      The orbit can be slightly shifted to close dates. This shift is based on a simple Keplerian model. It is not intended as a replacement for proper orbit and attitude propagation but should be sufficient for small time shifts or coarse accuracy.

      Specified by:
      shiftedBy in interface TimeShiftable<T extends CalculusFieldElement<T>>
      Specified by:
      shiftedBy in class FieldOrbit<T extends CalculusFieldElement<T>>
      Parameters:
      dt - time shift in seconds
      Returns:
      a new orbit, shifted with respect to the instance (which is immutable)
      Since:
      13.1.3

    • computeJacobianMeanWrtCartesian

      protected T[][] 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 FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      6x6 Jacobian matrix
      See Also:

    • computeJacobianEccentricWrtCartesian

      protected T[][] 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 FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      6x6 Jacobian matrix
      See Also:

    • computeJacobianTrueWrtCartesian

      protected T[][] 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 FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      6x6 Jacobian matrix
      See Also:

    • addKeplerContribution

      public void addKeplerContribution(PositionAngleType type, T gm, T[] 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 FieldOrbit<T extends CalculusFieldElement<T>>
      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

    • getCachedPositionAngleType

      public PositionAngleType getCachedPositionAngleType()
      Get the cached PositionAngleType.
      Specified by:
      getCachedPositionAngleType in interface PositionAngleBased<T extends CalculusFieldElement<T>>
      Returns:
      cached type of position angle

    • 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<T extends CalculusFieldElement<T>>
      Returns:
      true if and only if holding non-Keplerian rates

    • withKeplerianRates

      public FieldCircularOrbit<T> withKeplerianRates()
      Creates a new instance such that PositionAngleBased.hasNonKeplerianRates() is false.
      Specified by:
      withKeplerianRates in interface PositionAngleBased<T extends CalculusFieldElement<T>>
      Returns:
      new object without rates

    • toOrbit

      public CircularOrbit toOrbit()
      Transforms the FieldOrbit instance into an Orbit instance.
      Specified by:
      toOrbit in class FieldOrbit<T extends CalculusFieldElement<T>>
      Returns:
      Orbit instance with same properties