Source code for astropy.coordinates.builtin_frames.fk4

# -*- coding: utf-8 -*-
# Licensed under a 3-clause BSD style license - see LICENSE.rst

import numpy as np

from astropy import units as u
from astropy.utils.decorators import format_doc
from astropy.coordinates.baseframe import frame_transform_graph, base_doc
from astropy.coordinates.attributes import TimeAttribute
from astropy.coordinates.transformations import (
    FunctionTransformWithFiniteDifference, DynamicMatrixTransform)
from astropy.coordinates.representation import (CartesianRepresentation,
                                                UnitSphericalRepresentation)
from astropy.coordinates import earth_orientation as earth

from .utils import EQUINOX_B1950
from .baseradec import doc_components, BaseRADecFrame

__all__ = ['FK4', 'FK4NoETerms']


doc_footer_fk4 = """
    Other parameters
    ----------------
    equinox : `~astropy.time.Time`
        The equinox of this frame.
    obstime : `~astropy.time.Time`
        The time this frame was observed.  If ``None``, will be the same as
        ``equinox``.
"""


[docs]@format_doc(base_doc, components=doc_components, footer=doc_footer_fk4) class FK4(BaseRADecFrame): """ A coordinate or frame in the FK4 system. Note that this is a barycentric version of FK4 - that is, the origin for this frame is the Solar System Barycenter, *not* the Earth geocenter. The frame attributes are listed under **Other Parameters**. """ equinox = TimeAttribute(default=EQUINOX_B1950) obstime = TimeAttribute(default=None, secondary_attribute='equinox')
# the "self" transform @frame_transform_graph.transform(FunctionTransformWithFiniteDifference, FK4, FK4) def fk4_to_fk4(fk4coord1, fk4frame2): # deceptively complicated: need to transform to No E-terms FK4, precess, and # then come back, because precession is non-trivial with E-terms fnoe_w_eqx1 = fk4coord1.transform_to(FK4NoETerms(equinox=fk4coord1.equinox)) fnoe_w_eqx2 = fnoe_w_eqx1.transform_to(FK4NoETerms(equinox=fk4frame2.equinox)) return fnoe_w_eqx2.transform_to(fk4frame2)
[docs]@format_doc(base_doc, components=doc_components, footer=doc_footer_fk4) class FK4NoETerms(BaseRADecFrame): """ A coordinate or frame in the FK4 system, but with the E-terms of aberration removed. The frame attributes are listed under **Other Parameters**. """ equinox = TimeAttribute(default=EQUINOX_B1950) obstime = TimeAttribute(default=None, secondary_attribute='equinox') @staticmethod def _precession_matrix(oldequinox, newequinox): """ Compute and return the precession matrix for FK4 using Newcomb's method. Used inside some of the transformation functions. Parameters ---------- oldequinox : `~astropy.time.Time` The equinox to precess from. newequinox : `~astropy.time.Time` The equinox to precess to. Returns ------- newcoord : array The precession matrix to transform to the new equinox """ return earth._precession_matrix_besselian(oldequinox.byear, newequinox.byear)
# the "self" transform @frame_transform_graph.transform(DynamicMatrixTransform, FK4NoETerms, FK4NoETerms) def fk4noe_to_fk4noe(fk4necoord1, fk4neframe2): return fk4necoord1._precession_matrix(fk4necoord1.equinox, fk4neframe2.equinox) # FK4-NO-E to/from FK4 -----------------------------> # Unlike other frames, this module include *two* frame classes for FK4 # coordinates - one including the E-terms of aberration (FK4), and # one not including them (FK4NoETerms). The following functions # implement the transformation between these two. def fk4_e_terms(equinox): """ Return the e-terms of aberation vector Parameters ---------- equinox : Time object The equinox for which to compute the e-terms """ # Constant of aberration at J2000; from Explanatory Supplement to the # Astronomical Almanac (Seidelmann, 2005). k = 0.0056932 # in degrees (v_earth/c ~ 1e-4 rad ~ 0.0057 deg) k = np.radians(k) # Eccentricity of the Earth's orbit e = earth.eccentricity(equinox.jd) # Mean longitude of perigee of the solar orbit g = earth.mean_lon_of_perigee(equinox.jd) g = np.radians(g) # Obliquity of the ecliptic o = earth.obliquity(equinox.jd, algorithm=1980) o = np.radians(o) return (e * k * np.sin(g), -e * k * np.cos(g) * np.cos(o), -e * k * np.cos(g) * np.sin(o)) @frame_transform_graph.transform(FunctionTransformWithFiniteDifference, FK4, FK4NoETerms) def fk4_to_fk4_no_e(fk4coord, fk4noeframe): # Extract cartesian vector rep = fk4coord.cartesian # Find distance (for re-normalization) d_orig = rep.norm() rep /= d_orig # Apply E-terms of aberration. Note that this depends on the equinox (not # the observing time/epoch) of the coordinates. See issue #1496 for a # discussion of this. eterms_a = CartesianRepresentation( u.Quantity(fk4_e_terms(fk4coord.equinox), u.dimensionless_unscaled, copy=False), copy=False) rep = rep - eterms_a + eterms_a.dot(rep) * rep # Find new distance (for re-normalization) d_new = rep.norm() # Renormalize rep *= d_orig / d_new # now re-cast into an appropriate Representation, and precess if need be if isinstance(fk4coord.data, UnitSphericalRepresentation): rep = rep.represent_as(UnitSphericalRepresentation) # if no obstime was given in the new frame, use the old one for consistency newobstime = fk4coord._obstime if fk4noeframe._obstime is None else fk4noeframe._obstime fk4noe = FK4NoETerms(rep, equinox=fk4coord.equinox, obstime=newobstime) if fk4coord.equinox != fk4noeframe.equinox: # precession fk4noe = fk4noe.transform_to(fk4noeframe) return fk4noe @frame_transform_graph.transform(FunctionTransformWithFiniteDifference, FK4NoETerms, FK4) def fk4_no_e_to_fk4(fk4noecoord, fk4frame): # first precess, if necessary if fk4noecoord.equinox != fk4frame.equinox: fk4noe_w_fk4equinox = FK4NoETerms(equinox=fk4frame.equinox, obstime=fk4noecoord.obstime) fk4noecoord = fk4noecoord.transform_to(fk4noe_w_fk4equinox) # Extract cartesian vector rep = fk4noecoord.cartesian # Find distance (for re-normalization) d_orig = rep.norm() rep /= d_orig # Apply E-terms of aberration. Note that this depends on the equinox (not # the observing time/epoch) of the coordinates. See issue #1496 for a # discussion of this. eterms_a = CartesianRepresentation( u.Quantity(fk4_e_terms(fk4noecoord.equinox), u.dimensionless_unscaled, copy=False), copy=False) rep0 = rep.copy() for _ in range(10): rep = (eterms_a + rep0) / (1. + eterms_a.dot(rep)) # Find new distance (for re-normalization) d_new = rep.norm() # Renormalize rep *= d_orig / d_new # now re-cast into an appropriate Representation, and precess if need be if isinstance(fk4noecoord.data, UnitSphericalRepresentation): rep = rep.represent_as(UnitSphericalRepresentation) return fk4frame.realize_frame(rep)