def apparent_longitude(t='now'):
"""
Returns the Sun's apparent longitude, referred to the true equinox of date. Corrections for
nutation and aberration (for Earth motion) are included.
Parameters
----------
t : {parse_time_types}
A time (usually the start time) specified as a parse_time-compatible
time string, number, or a datetime object.
Notes
-----
The nutation model is IAU 2000A nutation with adjustments to match IAU 2006 precession.
"""
time = parse_time(t)
sun = SkyCoord(0*u.deg, 0*u.deg, 0*u.AU, frame='hcrs', obstime=time)
coord = sun.transform_to(GeocentricMeanEcliptic(equinox=time))
# Astropy's GeocentricMeanEcliptic already includes aberration, so only add nutation
jd1, jd2 = get_jd12(time, 'tt')
nut_lon, _ = erfa.nut06a(jd1, jd2)*u.radian
lon = coord.lon + nut_lon
return Longitude(lon)
def _true_ecliptic_rotation_matrix(equinox):
# This code calls pnm06a from ERFA, which retrieves the precession
# matrix (including frame bias) according to the IAU 2006 model, and
# including the nutation. This family of systems is less popular
# (see https://github.com/astropy/astropy/pull/6508).
jd1, jd2 = get_jd12(equinox, 'tt')
rnpb = erfa.pnm06a(jd1, jd2)
_, nut_obl = erfa.nut06a(jd1, jd2) * u.radian
obl = erfa.obl06(
jd1, jd2
) * u.radian + nut_obl # calculate the true obliquity of the ecliptic
return matrix_product(rotation_matrix(obl, 'x'), rnpb)
def true_obliquity_of_ecliptic(t='now'):
"""
Returns the true obliquity of the ecliptic, using the IAU 2006 definition. Correction for
nutation is included.
Parameters
----------
t : {parse_time_types}
Time to use in a parse-time-compatible format
Notes
-----
The nutation model is IAU 2000A nutation with adjustments to match IAU 2006 precession.
"""
time = parse_time(t)
jd1, jd2 = get_jd12(time, 'tt')
obl = erfa.obl06(jd1, jd2) * u.radian
_, nut_obl = erfa.nut06a(jd1, jd2) * u.radian
obl += nut_obl
return Angle(obl, u.arcsec)
def true_obliquity_of_ecliptic(t='now'):
"""
Returns the true obliquity of the ecliptic, using the IAU 2006 definition. Correction for
nutation is included.
Parameters
----------
t : {parse_time_types}
A time (usually the start time) specified as a parse_time-compatible
time string, number, or a datetime object.
Notes
-----
The nutation model is IAU 2000A nutation with adjustments to match IAU 2006 precession.
"""
time = parse_time(t)
jd1, jd2 = get_jd12(time, 'tt')
obl = erfa.obl06(jd1, jd2)*u.radian
_, nut_obl = erfa.nut06a(jd1, jd2)*u.radian
obl += nut_obl
return Angle(obl, u.arcsec)
def calc_moon(t):
"""
Lunar position model ELP2000-82 of (Chapront-Touze' and Chapront, 1983, 124, 50)
This is the simplified version of Jean Meeus, Astronomical Algorithms,
second edition, 1998, Willmann-Bell. Meeus claims approximate accuracy of 10"
in longitude and 4" in latitude, with no specified time range.
Tests against JPL ephemerides show accuracy of 10 arcseconds and 50 km over the
date range CE 1950-2050.
Parameters
-----------
t : `~astropy.time.Time`
Time of observation.
Returns
--------
skycoord : `~astropy.coordinates.SkyCoord`
ICRS Coordinate for the body
"""
# number of centuries since J2000.0.
# This should strictly speaking be in Ephemeris Time, but TDB or TT
# will introduce error smaller than intrinsic accuracy of algorithm.
T = (t.tdb.jyear-2000.0)/100.
# constants that are needed for all calculations
Lc = u.Quantity(polyval(T, _coLc), u.deg)
D = u.Quantity(polyval(T, _coD), u.deg)
M = u.Quantity(polyval(T, _coM), u.deg)
Mc = u.Quantity(polyval(T, _coMc), u.deg)
F = u.Quantity(polyval(T, _coF), u.deg)
A1 = u.Quantity(polyval(T, _coA1), u.deg)
A2 = u.Quantity(polyval(T, _coA2), u.deg)
A3 = u.Quantity(polyval(T, _coA3), u.deg)
E = polyval(T, _coE)
suml = sumr = 0.0
for DNum, MNum, McNum, FNum, LFac, RFac in _MOON_L_R:
corr = E ** abs(MNum)
suml += LFac*corr*np.sin(D*DNum+M*MNum+Mc*McNum+F*FNum)
sumr += RFac*corr*np.cos(D*DNum+M*MNum+Mc*McNum+F*FNum)
sumb = 0.0
for DNum, MNum, McNum, FNum, BFac in _MOON_B:
corr = E ** abs(MNum)
sumb += BFac*corr*np.sin(D*DNum+M*MNum+Mc*McNum+F*FNum)
suml += (3958*np.sin(A1) + 1962*np.sin(Lc-F) + 318*np.sin(A2))
sumb += (-2235*np.sin(Lc) + 382*np.sin(A3) + 175*np.sin(A1-F) +
175*np.sin(A1+F) + 127*np.sin(Lc-Mc) - 115*np.sin(Lc+Mc))
# ensure units
suml = suml*u.microdegree
sumb = sumb*u.microdegree
# nutation of longitude
jd1, jd2 = get_jd12(t, 'tt')
nut, _ = erfa.nut06a(jd1, jd2)
nut = nut*u.rad
# calculate ecliptic coordinates
lon = Lc + suml + nut
lat = sumb
dist = (385000.56+sumr/1000)*u.km
# Meeus algorithm gives GeocentricTrueEcliptic coordinates
ecliptic_coo = GeocentricTrueEcliptic(lon, lat, distance=dist,
obstime=t, equinox=t)
return SkyCoord(ecliptic_coo.transform_to(ICRS))
def calc_moon(t):
"""
Lunar position model ELP2000-82 of (Chapront-Touze' and Chapront, 1983, 124, 50)
This is the simplified version of Jean Meeus, Astronomical Algorithms,
second edition, 1998, Willmann-Bell. Meeus claims approximate accuracy of 10"
in longitude and 4" in latitude, with no specified time range.
Tests against JPL ephemerides show accuracy of 10 arcseconds and 50 km over the
date range CE 1950-2050.
Parameters
-----------
t : `~astropy.time.Time`
Time of observation.
Returns
--------
skycoord : `~astropy.coordinates.SkyCoord`
ICRS Coordinate for the body
"""
# number of centuries since J2000.0.
# This should strictly speaking be in Ephemeris Time, but TDB or TT
# will introduce error smaller than intrinsic accuracy of algorithm.
T = (t.tdb.jyear - 2000.0) / 100.
# constants that are needed for all calculations
Lc = u.Quantity(polyval(T, _coLc), u.deg)
D = u.Quantity(polyval(T, _coD), u.deg)
M = u.Quantity(polyval(T, _coM), u.deg)
Mc = u.Quantity(polyval(T, _coMc), u.deg)
F = u.Quantity(polyval(T, _coF), u.deg)
A1 = u.Quantity(polyval(T, _coA1), u.deg)
A2 = u.Quantity(polyval(T, _coA2), u.deg)
A3 = u.Quantity(polyval(T, _coA3), u.deg)
E = polyval(T, _coE)
suml = sumr = 0.0
for DNum, MNum, McNum, FNum, LFac, RFac in _MOON_L_R:
corr = E**abs(MNum)
suml += LFac * corr * np.sin(D * DNum + M * MNum + Mc * McNum +
F * FNum)
sumr += RFac * corr * np.cos(D * DNum + M * MNum + Mc * McNum +
F * FNum)
sumb = 0.0
for DNum, MNum, McNum, FNum, BFac in _MOON_B:
corr = E**abs(MNum)
sumb += BFac * corr * np.sin(D * DNum + M * MNum + Mc * McNum +
F * FNum)
suml += (3958 * np.sin(A1) + 1962 * np.sin(Lc - F) + 318 * np.sin(A2))
sumb += (-2235 * np.sin(Lc) + 382 * np.sin(A3) + 175 * np.sin(A1 - F) +
175 * np.sin(A1 + F) + 127 * np.sin(Lc - Mc) -
115 * np.sin(Lc + Mc))
# ensure units
suml = suml * u.microdegree
sumb = sumb * u.microdegree
# nutation of longitude
jd1, jd2 = get_jd12(t, 'tt')
nut, _ = erfa.nut06a(jd1, jd2)
nut = nut * u.rad
# calculate ecliptic coordinates
lon = Lc + suml + nut
lat = sumb
dist = (385000.56 + sumr / 1000) * u.km
# Meeus algorithm gives GeocentricTrueEcliptic coordinates
ecliptic_coo = GeocentricTrueEcliptic(lon,
lat,
distance=dist,
obstime=t,
equinox=t)
return SkyCoord(ecliptic_coo.transform_to(ICRS))
