skyview.astronomiemuseum.de/public/py/vendor/skyfield/framelib.py

# -*- coding: utf-8 -*-
"""Raw transforms between coordinate frames, as NumPy matrices."""

from numpy import array
from .constants import ANGVEL, ASEC2RAD, DAY_S, tau
from .data.spice import inertial_frames as _inertial_frames
from .functions import mxm, rot_x, rot_z

def build_matrix():
    # 'xi0', 'eta0', and 'da0' are ICRS frame biases in arcseconds taken
    # from IERS (2003) Conventions, Chapter 5.

    xi0  = -0.0166170 * ASEC2RAD
    eta0 = -0.0068192 * ASEC2RAD
    da0  = -0.01460   * ASEC2RAD

    # Compute elements of rotation matrix.

    yx = -da0
    zx =  xi0
    xy =  da0
    zy =  eta0
    xz = -xi0
    yz = -eta0

    # Include second-order corrections to diagonal elements.

    xx = 1.0 - 0.5 * (yx * yx + zx * zx)
    yy = 1.0 - 0.5 * (yx * yx + zy * zy)
    zz = 1.0 - 0.5 * (zy * zy + zx * zx)

    return array(((xx, xy, xz), (yx, yy, yz), (zx, zy, zz)))

ICRS_to_J2000 = build_matrix()
del build_matrix

_identity = array([(1,0,0), (0,1,0), (0,0,1)])

class ICRS(object):
    """The International Celestial Reference System (ICRS).

    The ICRS is a permanent reference frame which has replaced J2000,
    with which its axes agree to within 0.02 arcseconds (closer than the
    precision of J2000 itself).  The ICRS also supersedes older
    equinox-based systems like B1900 and B1950.

    """
    @staticmethod
    def rotation_at(t):
        return _identity

class mean_equator_and_equinox_of_date(object):
    """The coordinate frame of Earth’s mean equator and equinox.

    This frame is used for measuring right ascension and declination.
    It tracks the Earth’s ‘mean’ equator and equinox which shift slowly
    across the sky due to precession, but ignores the smaller effects of
    nutation.

    """
    @staticmethod
    def rotation_at(t):
        return mxm(t.P, ICRS_to_J2000)

class true_equator_and_equinox_of_date(object):
    """The dynamical frame of Earth’s true equator and true equinox of date.

    This frame is used for measuring right ascension and declination.
    Unlike the fixed reference frames J2000 and the ICRS, this ‘TETE’
    frame rotates slowly as the Earth’s precession and nutation shift
    the equinox point.  Unlike the :class:`~skyfield.sgp4lib.TEME`
    frame, this frame doesn’t ignore nutation.

    This is supplied as an explicit reference frame in case you want
    |xyz| coordinates; if you want angles, it’s better to use the
    standard position method ``radec(epoch='date')`` since that will
    return the conventional units of hours-of-right-ascension instead of
    the degrees-of-longitude that ``frame_latlon()`` would return.

    This reference frame combines current theories of the Earth’s
    precession and nutation with a small offset between the ITRS and
    J2000 systems to produce right ascension and declination for a given
    date relative to the Earth’s axis and equator of rotation.

    """
    @staticmethod
    def rotation_at(t):
        return t.M

_itrs_angvel_matrix = array((
    (0.0, DAY_S * ANGVEL, 0.0),
    (-DAY_S * ANGVEL, 0.0, 0.0),
    (0.0, 0.0, 0.0),
))

class tirs(object):
    """The Terrestrial Intermediate Reference System (TIRS).

    Coordinates in this Earth-centered Earth-fixed (ECEF) system are
    measured from the axis and equator of the Earth’s rotation, ignoring
    the few tenths of an arcsecond by which the Earth’s actual crust and
    continents might be askance from the axis.  (More precisely: like
    the ITRS this frame accounts for precession and nutation, but
    neglects polar motion and the TIO locator.)

    """
    @staticmethod
    def rotation_at(t):
        return mxm(rot_z(-t.gast * tau / 24.0), t.M)

    @staticmethod
    def _dRdt_times_RT_at(t):
        # TODO: taking the derivative of the instantaneous angular
        # velocity provides a more accurate transform.
        return _itrs_angvel_matrix

tirs = tirs()

class itrs(object):
    """The International Terrestrial Reference System (ITRS).

    This is the IAU standard for an Earth-centered Earth-fixed (ECEF)
    coordinate system, anchored to the Earth’s crust and continents.
    This reference frame combines three other reference frames: the
    Earth’s true equator and equinox of date, the Earth’s rotation with
    respect to the stars, and (if your ``Timescale`` has polar offsets
    loaded) the polar wobble of the crust with respect to the Earth’s
    pole of rotation.

    .. versionadded:: 1.34

    """
    @staticmethod
    def rotation_at(t):
        R = mxm(rot_z(-t.gast * tau / 24.0), t.M)
        if t.ts.polar_motion_table is not None:
            R = mxm(t.polar_motion_matrix(), R)
        return R

    @staticmethod
    def _dRdt_times_RT_at(t):
        # TODO: taking the derivative of the instantaneous angular
        # velocity provides a more accurate transform.
        return _itrs_angvel_matrix

itrs = itrs()

def build_ecliptic_matrix(t):
    # Build the matrix to rotate an ICRF vector into ecliptic coordinates.
    _, d_eps = t._nutation_angles_radians
    true_obliquity = t._mean_obliquity_radians + d_eps
    return mxm(rot_x(- true_obliquity), t.M)

class ecliptic_frame(object):
    """Reference frame of the true ecliptic and equinox of date."""
    @staticmethod
    def rotation_at(t):
        return build_ecliptic_matrix(t)

ecliptic_frame = ecliptic_frame()

class InertialFrame(object):
    def __init__(self, doc, matrix):
        self.__doc__ = doc
        self._matrix = matrix

    def rotation_at(self, t):
        return self._matrix

equatorial_B1950_frame = InertialFrame(
    'Reference frame of the Earth’s mean equator and equinox at B1950.',
    _inertial_frames['B1950'],
)

ecliptic_J2000_frame = InertialFrame(
    'Reference frame of the true ecliptic and equinox at J2000.',
    _inertial_frames['ECLIPJ2000'],
)
galactic_frame = InertialFrame(
    'Galactic System II reference frame.',
    _inertial_frames['GALACTIC'],
)