Nutze Skyfield fuer praezisere Daemmerungsberechnung

public/py/vendor/skyfield/framelib.py

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+# -*- 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'],
+)