def atciqz(rc, dc, astrom):
"""
A slightly modified version of the ERFA function ``eraAtciqz``.
``eraAtciqz`` performs the transformations between two coordinate systems,
with the details of the transformation being encoded into the ``astrom`` array.
The companion function ``eraAticq`` is meant to be its inverse. However, this
is not true for directions close to the Solar centre, since the light deflection
calculations are numerically unstable and therefore not reversible.
This version sidesteps that problem by artificially reducing the light deflection
for directions which are within 90 arcseconds of the Sun's position. This is the
same approach used by the ERFA functions above, except that they use a threshold of
9 arcseconds.
Parameters
----------
rc : float or `~numpy.ndarray`
right ascension, radians
dc : float or `~numpy.ndarray`
declination, radians
astrom : eraASTROM array
ERFA astrometry context, as produced by, e.g. ``eraApci13`` or ``eraApcs13``
Returns
--------
ri : float or `~numpy.ndarray`
di : float or `~numpy.ndarray`
"""
# BCRS coordinate direction (unit vector).
pco = erfa.s2c(rc, dc)
# Light deflection by the Sun, giving BCRS natural direction.
pnat = erfa.ld(1.0, pco, pco, astrom['eh'], astrom['em'], 5e-8)
# Aberration, giving GCRS proper direction.
ppr = erfa.ab(pnat, astrom['v'], astrom['em'], astrom['bm1'])
# Bias-precession-nutation, giving CIRS proper direction.
# Has no effect if matrix is identity matrix, in which case gives GCRS ppr.
pi = erfa.rxp(astrom['bpn'], ppr)
# CIRS (GCRS) RA, Dec
ri, di = erfa.c2s(pi)
return erfa.anp(ri), di
print('''
================================================
IAU 2000A, equinox based, using classical angles
================================================
''')
# Nutation, IAU 2000A.
DP00, DE00 = erfa.nut00a(DJMJD0, TT)
# Precession-nutation quantities, IAU 2000.
EPSA, RB, RP, RPB, RN, RNPB = erfa.pn00(DJMJD0, TT, DP00, DE00)
# Transform dX,dY corrections from GCRS to mean of date.
V1 = (DX00, DY00, 0.)
V2 = erfa.rxp(RNPB, V1)
DDP00 = V2[1] / math.sin(EPSA)
DDE00 = V2[2]
# Corrected nutation.
DPSI = DP00 + DDP00
DEPS = DE00 + DDE00
# Build the rotation matrix.
RN = erfa.numat(EPSA, DPSI, DEPS)
# Combine the matrices: PN = N x P.
RNPB = erfa.rxr(RN, RPB)
print("NPB matrix, equinox based:")
pprint(RNPB)
def atciqz(srepr, astrom):
"""
A slightly modified version of the ERFA function ``eraAtciqz``.
``eraAtciqz`` performs the transformations between two coordinate systems,
with the details of the transformation being encoded into the ``astrom`` array.
There are two issues with the version of atciqz in ERFA. Both are associated
with the handling of light deflection.
The companion function ``eraAticq`` is meant to be its inverse. However, this
is not true for directions close to the Solar centre, since the light deflection
calculations are numerically unstable and therefore not reversible.
This version sidesteps that problem by artificially reducing the light deflection
for directions which are within 90 arcseconds of the Sun's position. This is the
same approach used by the ERFA functions above, except that they use a threshold of
9 arcseconds.
In addition, ERFA's atciqz assumes a distant source, so there is no difference between
the object-Sun vector and the observer-Sun vector. This can lead to errors of up to a
few arcseconds in the worst case (e.g a Venus transit).
Parameters
----------
srepr : `~astropy.coordinates.SphericalRepresentation`
Astrometric ICRS position of object from observer
astrom : eraASTROM array
ERFA astrometry context, as produced by, e.g. ``eraApci13`` or ``eraApcs13``
Returns
--------
ri : float or `~numpy.ndarray`
Right Ascension in radians
di : float or `~numpy.ndarray`
Declination in radians
"""
# ignore parallax effects if no distance, or far away
srepr_distance = srepr.distance
ignore_distance = srepr_distance.unit == u.one
# BCRS coordinate direction (unit vector).
pco = erfa.s2c(srepr.lon.radian, srepr.lat.radian)
# Find BCRS direction of Sun to object
if ignore_distance:
# No distance to object, assume a long way away
q = pco
else:
# Find BCRS direction of Sun to object.
# astrom['eh'] and astrom['em'] contain Sun to observer unit vector,
# and distance, respectively.
eh = astrom['em'][..., np.newaxis] * astrom['eh']
# unit vector from Sun to object
q = eh + srepr_distance[..., np.newaxis].to_value(u.au) * pco
sundist, q = erfa.pn(q)
sundist = sundist[..., np.newaxis]
# calculation above is extremely unstable very close to the sun
# in these situations, default back to ldsun-style behaviour,
# since this is reversible and drops to zero within stellar limb
q = np.where(sundist > 1.0e-10, q, pco)
# Light deflection by the Sun, giving BCRS natural direction.
pnat = erfa.ld(1.0, pco, q, astrom['eh'], astrom['em'], 1e-6)
# Aberration, giving GCRS proper direction.
ppr = erfa.ab(pnat, astrom['v'], astrom['em'], astrom['bm1'])
# Bias-precession-nutation, giving CIRS proper direction.
# Has no effect if matrix is identity matrix, in which case gives GCRS ppr.
pi = erfa.rxp(astrom['bpn'], ppr)
# CIRS (GCRS) RA, Dec
ri, di = erfa.c2s(pi)
return erfa.anp(ri), di
print('''
================================================
IAU 2000A, equinox based, using classical angles
================================================
''')
# Nutation, IAU 2000A.
DP00, DE00 = erfa.nut00a(DJMJD0, TT)
# Precession-nutation quantities, IAU 2000.
EPSA, RB, RP, RPB, RN, RNPB = erfa.pn00(DJMJD0, TT, DP00, DE00)
# Transform dX,dY corrections from GCRS to mean of date.
V1 = (DX00, DY00, 0.)
V2 = erfa.rxp(RNPB, V1)
DDP00 = V2[1] / math.sin(EPSA)
DDE00 = V2[2]
# Corrected nutation.
DPSI = DP00 + DDP00
DEPS = DE00 + DDE00
# Build the rotation matrix.
RN = erfa.numat(EPSA, DPSI, DEPS)
# Combine the matrices: PN = N x P.
RNPB = erfa.rxr(RN, RPB)
print("NPB matrix, equinox based:")
pprint(RNPB)