Package gaia.cu9.ari.gaiaorbit.util.coord

Class Coordinates

  • public class Coordinates
extends java.lang.Object
    Provides utility coordinate conversions between some astronomical coordinate systems and to Cartesian coordinates. All angles are in radians.

    • Field Detail

      • OBLIQUITY_DEG_J2000

        public static final double OBLIQUITY_DEG_J2000
        Obliquity for low precision calculations in degrees and radians. J2000 with T=0
        See Also:
        Constant Field Values

      • OBLIQUITY_RAD_J2000

        public static final double OBLIQUITY_RAD_J2000

      • OBLIQUITY_ARCSEC_J2000

        public static final double OBLIQUITY_ARCSEC_J2000
        Obliquity of ecliptic in J2000 in arcsec
        See Also:
        Constant Field Values

    • Constructor Detail

      • Coordinates

        public Coordinates()

    • Method Detail

      • getRotationMatrix

        public static Matrix4d getRotationMatrix​(double alpha,
                                         double beta,
                                         double gamma)
        Gets the rotation matrix to apply for the given Euler angles α, β and γ. It applies Ry(γ)*Rz(β)*Ry(α), so that it rotates the fixed xyz system to make it coincide with the XYZ, where α is the angle between the axis z and the line of nodes N, β is the angle between the y axis and the Y axis, and γ is the angle between the Z axis and the line of nodes N.
        The assumed reference system is as follows:
        • ZX is the fundamental plane.
        • Z points to the origin of the reference plane (the line of nodes N).
        • Y points upwards.
        Parameters:
        alpha - The α angle in degrees, between z and N.
        beta - The β angle in degrees, between y and Y.
        gamma - The γ angle in degrees, Z and N.
        Returns:
        The rotation matrix.

      • eclToEq

        public static Matrix4d eclToEq()
        Gets the rotation matrix to transform equatorial to the ecliptic coordinates. Since the zero point in both systems is the same (the vernal equinox, γ, defined as the intersection between the equator and the ecliptic), α and γ are zero. β, the angle between the up directions of both systems, is precisely the obliquity of the ecliptic, ε. So we have the Euler angles α=0°, β=ε;, γ=0°.
        Returns:
        The matrix to transform from equatorial coordinates to ecliptic coordinates.

      • eclipticToEquatorial

        public static Matrix4d eclipticToEquatorial()

      • eclToEqF

        public static com.badlogic.gdx.math.Matrix4 eclToEqF()

      • eclipticToEquatorialF

        public static com.badlogic.gdx.math.Matrix4 eclipticToEquatorialF()

      • eclToEq

        public static Matrix4d eclToEq​(double julianDate)
        Gets the rotation matrix to transform from the ecliptic system to the equatorial system. See equatorialToEcliptic() for more information, for this is the inverse transformation.
        Returns:
        The transformation matrix.

      • eclipticToEquatorial

        public static Matrix4d eclipticToEquatorial​(double jd)

      • eqToEcl

        public static Matrix4d eqToEcl()
        Gets the rotation matrix to transform from the ecliptic system to the equatorial system. See eclToEq() for more information, for this is the inverse transformation.
        Returns:
        The transformation matrix.

      • equatorialToEcliptic

        public static Matrix4d equatorialToEcliptic()

      • eqToEclF

        public static com.badlogic.gdx.math.Matrix4 eqToEclF()

      • equatorialToEclipticF

        public static com.badlogic.gdx.math.Matrix4 equatorialToEclipticF()

      • eqToEcl

        public static Matrix4d eqToEcl​(double julianDate)
        Gets the rotation matrix to transform equatorial to the ecliptic coordinates. Since the zero point in both systems is the same (the vernal equinox, γ, defined as the intersection between the equator and the ecliptic), α and γ are zero. β, the angle between the up directions of both systems, is precisely the obliquity of the ecliptic, ε. So we have the Euler angles α=0°, β=ε;, γ=0°.
        Returns:
        The matrix to transform from equatorial coordinates to ecliptic coordinates.

      • equatorialToEcliptic

        public static Matrix4d equatorialToEcliptic​(double jd)

      • galToEq

        public static Matrix4d galToEq()
        Gets the rotation matrix to transform from the galactic system to the equatorial system. See galToEq() for more information, since this is the inverse transformation. Use this matrix if you need to convert equatorial cartesian coordinates to galactic cartesian coordinates.
        Returns:
        The transformation matrix.

      • galacticToEquatorial

        public static Matrix4d galacticToEquatorial()

      • galToEqF

        public static com.badlogic.gdx.math.Matrix4 galToEqF()

      • galacticToEquatorialF

        public static com.badlogic.gdx.math.Matrix4 galacticToEquatorialF()

      • eqToGal

        public static Matrix4d eqToGal()
        Gets the rotation matrix to transform equatorial to galactic coordinates. The inclination of the galactic equator to the celestial equator is 62.9°. The intersection, or node line, of the two equators is at RA=282.25° DEC=0° and l=33° b=0°. So we have the Euler angles α=-33°, β=62.9°, γ=282.25°.
        Returns:
        The transformation matrix.

      • equatorialToGalactic

        public static Matrix4d equatorialToGalactic()

      • eqToGalF

        public static com.badlogic.gdx.math.Matrix4 eqToGalF()

      • equatorialToGalacticF

        public static com.badlogic.gdx.math.Matrix4 equatorialToGalacticF()

      • eclipticToEquatorial

        public static Vector2d eclipticToEquatorial​(Vector2d vec,
                                            Vector2d out)
        Transforms from ecliptic to equatorial coordinates
        Parameters:
        vec - Vector with ecliptic longitude (λ) and ecliptic latitude (β) in radians.
        out - The output vector.
        Returns:
        The output vector with ra (α) and dec (δ) in radians, for chaining.

      • eclipticToEquatorial

        public static Vector2d eclipticToEquatorial​(double lambda,
                                            double beta,
                                            Vector2d out)
        Transforms from ecliptic to equatorial coordinates
        Parameters:
        lambda - Ecliptic longitude (λ) in radians.
        beta - Ecliptic latitude (β) in radians.
        out - The output vector.
        Returns:
        The output vector with ra (α) and dec (δ) in radians, for chaining.

      • eclipticToGalactic

        public static Matrix4d eclipticToGalactic()

      • eclipticToGalacticF

        public static com.badlogic.gdx.math.Matrix4 eclipticToGalacticF()

      • galacticToEcliptic

        public static Matrix4d galacticToEcliptic()

      • galacticToEclipticF

        public static com.badlogic.gdx.math.Matrix4 galacticToEclipticF()

      • sphericalToCartesian

        public static Vector3d sphericalToCartesian​(Vector3d vec,
                                            Vector3d out)
        Converts from spherical to Cartesian coordinates, given a longitude (α), a latitude (δ) and the radius. The result is in the XYZ space, where ZX is the fundamental plane, with Z pointing to the the origin of coordinates (equinox) and Y pointing to the north pole.
        Parameters:
        vec - Vector containing the spherical coordinates.
        1. The longitude or right ascension (α), from the Z direction to the X direction, in radians.
        2. The latitude or declination (δ), in radians.
        3. The radius or distance to the point.
        out - The output vector.
        Returns:
        Output vector in Cartesian coordinates where x and z are on the horizontal plane and y is in the up direction.

      • sphericalToCartesian

        public static Vector3d sphericalToCartesian​(double longitude,
                                            double latitude,
                                            double radius,
                                            Vector3d out)
        Converts from spherical to Cartesian coordinates, given a longitude (α), a latitude (δ) and the radius.
        Parameters:
        longitude - The longitude or right ascension angle, from the z direction to the x direction, in radians.
        latitude - The latitude or declination, in radians.
        radius - The radius or distance to the point.
        out - The output vector.
        Returns:
        Output vector with the Cartesian coordinates[x, y, z] where x and z are on the horizontal plane and y is in the up direction, for chaining.

      • cartesianToSpherical

        public static Vector3d cartesianToSpherical​(Vector3d vec,
                                            Vector3d out)
        Converts from Cartesian coordinates to spherical coordinates.
        Parameters:
        vec - Vector with the Cartesian coordinates[x, y, z] where x and z are on the horizontal plane and y is in the up direction.
        out - Output vector.
        Returns:
        Output vector containing the spherical coordinates.
        1. The longitude or right ascension (α), from the z direction to the x direction.
        2. The latitude or declination (δ).
        3. The radius or distance to the point.

      • getTransformD

        public static Matrix4d getTransformD​(java.lang.String name)

      • getTransformF

        public static com.badlogic.gdx.math.Matrix4 getTransformF​(java.lang.String name)