# Licensed under a 3-clause BSD style license - see LICENSE.rst
import math
import erfa
import numpy as np
from astropy import units as u
from astropy.coordinates.attributes import TimeAttribute
from astropy.coordinates.baseframe import base_doc, frame_transform_graph
from astropy.coordinates.matrix_utilities import rotation_matrix
from astropy.coordinates.representation import (
CartesianRepresentation,
UnitSphericalRepresentation,
)
from astropy.coordinates.transformations import (
DynamicMatrixTransform,
FunctionTransformWithFiniteDifference,
)
from astropy.time import Time
from astropy.utils.compat import COPY_IF_NEEDED
from astropy.utils.decorators import format_doc
from .baseradec import BaseRADecFrame, doc_components
from .utils import EQUINOX_B1950
__all__ = ["FK4", "FK4NoETerms"]
jd1950 = Time("B1950").jd
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, doc="The equinox time")
obstime = TimeAttribute(
default=None,
secondary_attribute="equinox",
doc="The reference time (e.g., time of observation)",
)
# 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, doc="The equinox time")
obstime = TimeAttribute(
default=None,
secondary_attribute="equinox",
doc="The reference time (e.g., time of observation)",
)
@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
"""
# tropical years
t1 = (oldequinox.byear - 1850.0) / 1000.0
dt = (newequinox.byear - 1850.0) / 1000.0 - t1
dt_over_3600 = dt / 3600
z1 = zeta1 = (0.060 * t1 + 139.720) * t1 + 23035.545
zeta2 = -0.27 * t1 + 30.240
zeta = ((17.995 * dt + zeta2) * dt + zeta1) * dt_over_3600
z2 = 109.480 + 0.39 * t1
z = ((18.325 * dt + z2) * dt + z1) * dt_over_3600
theta1 = (-0.37 * t1 - 85.29) * t1 + 20051.12
theta2 = -0.37 * t1 - 42.65
theta = ((-41.8 * dt + theta2) * dt + theta1) * dt_over_3600
return (
rotation_matrix(-z, "z")
@ rotation_matrix(theta, "y")
@ rotation_matrix(-zeta, "z")
)
# 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 aberration 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)
# Explanatory Supplement to the Astronomical Almanac: P. Kenneth
# Seidelmann (ed), University Science Books (1992).
T = (equinox.jd - jd1950) / 36525.0
# Eccentricity of the Earth's orbit
ek = math.radians(k) * ((-0.000000126 * T - 0.00004193) * T + 0.01673011)
# Mean longitude of perigee of the solar orbit
g = np.radians((((0.012 * T + 1.65) * T + 6190.67) * T + 1015489.951) / 3600.0)
minus_ek_cos_g = -ek * np.cos(g)
# Obliquity of the ecliptic
o = erfa.obl80(equinox.jd, 0)
return (ek * np.sin(g), minus_ek_cos_g * np.cos(o), minus_ek_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=COPY_IF_NEEDED,
),
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=COPY_IF_NEEDED,
),
copy=False,
)
eterms_a_plus_rep_ini = eterms_a + rep
for _ in range(10):
rep = eterms_a_plus_rep_ini / (1.0 + 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)
