def gei_to_hme(geicoord, hmeframe):
"""
Convert from Geocentric Earth Equatorial to Heliocentric Mean Ecliptic
"""
if geicoord.obstime is None:
raise ConvertError("To perform this transformation, the coordinate"
" frame needs a specified `obstime`.")
# Use an intermediate frame of HME at the GEI observation time
int_frame = HeliocentricMeanEcliptic(obstime=geicoord.obstime, equinox=geicoord.equinox)
# Get the Sun-Earth vector in the intermediate frame
sun_earth = HCRS(_sun_earth_icrf(int_frame.obstime), obstime=int_frame.obstime)
sun_earth_int = sun_earth.transform_to(int_frame).cartesian
# Rotate from Earth equatorial to ecliptic
rot_matrix = _rotation_matrix_obliquity(int_frame.equinox)
earth_object_int = geicoord.cartesian.transform(rot_matrix)
# Find the Sun-object vector in the intermediate frame
sun_object_int = sun_earth_int + earth_object_int
int_coord = int_frame.realize_frame(sun_object_int)
# Convert to the final frame through HCRS
return int_coord.transform_to(HCRS(obstime=int_coord.obstime)).transform_to(hmeframe)
def test_hme_hee_sunspice():
# Compare our HME->HEE transformation against SunSPICE
# "HAE" is equivalent to Astropy's Heliocentric Mean Ecliptic, and defaults to J2000.0
#
# IDL> coord = [1.d, 0.d, 10.d]
# IDL> convert_sunspice_lonlat, '2019-06-01', coord, 'HAE', 'HEE', /au, /degrees
# IDL> print, coord
# 1.0000000 110.01610 10.000300
old = SkyCoord(0*u.deg, 10*u.deg, 1*u.AU, frame=HeliocentricMeanEcliptic(obstime='2019-06-01'))
new = old.transform_to(HeliocentricEarthEcliptic)
assert_quantity_allclose(new.lon, Longitude(110.01610*u.deg), atol=0.01*u.arcsec, rtol=0)
assert_quantity_allclose(new.lat, 10.000300*u.deg, atol=0.01*u.arcsec, rtol=0)
assert_quantity_allclose(new.distance, old.distance)
# Transform from HAE precessed to the mean ecliptic of date instead of J2000.0
# IDL> coord = [1.d, 0.d, 10.d]
# IDL> convert_sunspice_lonlat, '2019-06-01', coord, 'HAE', 'HEE', /au, /degrees, /precess
# IDL> print, coord
# 1.0000000 109.74535 10.000070
old = SkyCoord(0*u.deg, 10*u.deg, 1*u.AU, frame=HeliocentricMeanEcliptic(obstime='2019-06-01',
equinox='2019-06-01'))
new = old.transform_to(HeliocentricEarthEcliptic)
assert_quantity_allclose(new.lon, Longitude(109.74535*u.deg), atol=0.05*u.arcsec, rtol=0)
assert_quantity_allclose(new.lat, 10.000070*u.deg, atol=0.01*u.arcsec, rtol=0)
assert_quantity_allclose(new.distance, old.distance)
def test_hme_gei_sunspice():
# Compare our HME->GEI transformation against SunSPICE
# "HAE" is equivalent to Astropy's Heliocentric Mean Ecliptic, and defaults to J2000.0
#
# IDL> coord = [1.d, 120.d, 10.d]
# IDL> convert_sunspice_lonlat, '2019-06-01', coord, 'HAE', 'GEI', /au, /degrees
# IDL> print, coord
# 1.8197210 95.230617 28.830109
old = SkyCoord(120*u.deg, 10*u.deg, 1*u.AU,
frame=HeliocentricMeanEcliptic(obstime='2019-06-01'))
new = old.transform_to(GeocentricEarthEquatorial)
assert_quantity_allclose(new.lon, Longitude(95.230617*u.deg), atol=0.01*u.arcsec, rtol=0)
assert_quantity_allclose(new.lat, 28.830109*u.deg, atol=0.05*u.arcsec, rtol=0)
assert_quantity_allclose(new.distance, 1.8197210*u.AU)
# Transform from HAE precessed to the mean ecliptic of date instead of J2000.0
# IDL> coord = [1.d, 120.d, 10.d]
# IDL> convert_sunspice_lonlat, '2019-06-01', coord, 'HAE', 'GEI', /au, /degrees, /precess
# IDL> print, coord
# 1.8217103 95.079030 28.827750
old = SkyCoord(120*u.deg, 10*u.deg, 1*u.AU,
frame=HeliocentricMeanEcliptic(obstime='2019-06-01', equinox='2019-06-01'))
new = old.transform_to(GeocentricEarthEquatorial(equinox=_J2000))
assert_quantity_allclose(new.lon, Longitude(95.079030*u.deg), atol=0.05*u.arcsec, rtol=0)
assert_quantity_allclose(new.lat, 28.827750*u.deg, atol=0.05*u.arcsec, rtol=0)
assert_quantity_allclose(new.distance, 1.8217103*u.AU)
def hee_to_hme(heecoord, hmeframe):
"""
Convert from Heliocentric Earth Ecliptic to Heliocentric Mean Ecliptic
"""
int_frame = HeliocentricMeanEcliptic(obstime=heecoord.obstime, equinox=heecoord.obstime)
# Rotate the HEE coord to the intermediate frame
total_matrix = matrix_transpose(_rotation_matrix_hme_to_hee(int_frame))
int_repr = heecoord.cartesian.transform(total_matrix)
int_coord = int_frame.realize_frame(int_repr)
# Convert to the HME frame through HCRS
return int_coord.transform_to(HCRS).transform_to(hmeframe)
def test_hgs_hcrs():
# This test checks the HGS->HCRS transformation by transforming from HGS to
# HeliocentricMeanEcliptic (HME). It will fail if there are errors in Astropy's
# HCRS->ICRS or ICRS->HME transformations.
# Use published HGS coordinates in the Astronomical Almanac (2013), pages C6-C7
obstime = Time('2013-01-28')
earth_hgs = SkyCoord(0 * u.deg,
-5.73 * u.deg,
0.9848139 * u.AU,
frame=HeliographicStonyhurst,
obstime=obstime)
# Transform to HME at observation-time equinox
earth_hme = earth_hgs.transform_to(
HeliocentricMeanEcliptic(equinox=obstime))
# Validate against published values from the Astronomical Almanac (2013), page C6 per page E2
# The dominant source of inaccuracy is the limited precision of the published B0 used above
assert quantity_allclose(earth_hme.lon,
Angle('308d13m30.51s') - 180 * u.deg,
atol=5 * u.arcsec)
assert quantity_allclose(earth_hme.lat,
-Angle('-0.27s'),
atol=10 * u.arcsec)
assert quantity_allclose(earth_hme.distance,
0.9848139 * u.AU,
atol=5e-7 * u.AU)
def test_hgs_hcrs_sunspice():
# Compare our HGS->HCRS transformation against SunSPICE by transforming beyond it
# "HEQ" is another name for HEEQ, which is equivalent to Heliographic Stonyhurst
# "HAE" is equivalent to Astropy's Heliocentric Mean Ecliptic, and defaults to J2000.0
#
# IDL> coord = [1.d, 0.d, 10.d]
# IDL> convert_sunspice_lonlat, '2019-06-01', coord, 'HEQ', 'HAE', /au, /degrees
# IDL> print, coord
# 1.0000000 -108.65371 10.642778
old = SkyCoord(0*u.deg, 10*u.deg, 1*u.AU, frame=HeliographicStonyhurst(obstime='2019-06-01'))
new = old.transform_to(HeliocentricMeanEcliptic)
assert_quantity_allclose(new.lon, Longitude(-108.65371*u.deg), atol=0.1*u.arcsec, rtol=0)
assert_quantity_allclose(new.lat, 10.642778*u.deg, atol=0.1*u.arcsec, rtol=0)
assert_quantity_allclose(new.distance, old.radius)
# Transform to HAE precessed to the mean ecliptic of date instead of J2000.0
# IDL> coord = [1.d, 0.d, 10.d]
# IDL> convert_sunspice_lonlat, '2019-06-01', coord, 'HEQ', 'HAE', /precess, /au, /degrees
# IDL> print, coord
# 1.0000000 -108.38240 10.640314
new = old.transform_to(HeliocentricMeanEcliptic(equinox='2019-06-01'))
assert_quantity_allclose(new.lon, Longitude(-108.38240*u.deg), atol=0.1*u.arcsec, rtol=0)
assert_quantity_allclose(new.lat, 10.640314*u.deg, atol=0.1*u.arcsec, rtol=0)
assert_quantity_allclose(new.distance, old.radius)
def hme_to_gei(hmecoord, geiframe):
"""
Convert from Heliocentric Mean Ecliptic to Geocentric Earth Equatorial
"""
if geiframe.obstime is None:
raise ConvertError("To perform this transformation, the coordinate"
" frame needs a specified `obstime`.")
# Use an intermediate frame of HME at the GEI observation time, through HCRS
int_frame = HeliocentricMeanEcliptic(obstime=geiframe.obstime,
equinox=geiframe.equinox)
int_coord = hmecoord.transform_to(
HCRS(obstime=int_frame.obstime)).transform_to(int_frame)
# Get the Sun-Earth vector in the intermediate frame
sun_earth = HCRS(_sun_earth_icrf(int_frame.obstime),
obstime=int_frame.obstime)
sun_earth_int = sun_earth.transform_to(int_frame).cartesian
# Find the Earth-object vector in the intermediate frame
earth_object_int = int_coord.cartesian - sun_earth_int
# Rotate from ecliptic to Earth equatorial
rot_matrix = matrix_transpose(_rotation_matrix_obliquity(
int_frame.equinox))
newrepr = earth_object_int.transform(rot_matrix)
return geiframe.realize_frame(newrepr)
def test_observer_not_hgs_astropy(oca):
observer = HeliocentricMeanEcliptic(0*u.deg, 0*u.deg, 1*u.AU, obstime='2001-01-01')
result, converted = oca.convert_input(observer)
assert isinstance(result, HeliographicStonyhurst)
assert result.obstime == observer.obstime
assert converted
def hee_to_hme(heecoord, hmeframe):
"""
Convert from Heliocentric Earth Ecliptic to Heliocentric Mean Ecliptic
"""
if heecoord.obstime is None:
raise ConvertError("To perform this transformation, the coordinate"
" frame needs a specified `obstime`.")
int_frame = HeliocentricMeanEcliptic(obstime=heecoord.obstime, equinox=heecoord.obstime)
# Rotate the HEE coord to the intermediate frame
total_matrix = matrix_transpose(_rotation_matrix_hme_to_hee(int_frame))
int_repr = heecoord.cartesian.transform(total_matrix)
int_coord = int_frame.realize_frame(int_repr)
# Convert to the HME frame through HCRS
return int_coord.transform_to(HCRS(obstime=int_coord.obstime)).transform_to(hmeframe)
def rot_hme():
return (HeliocentricMeanEcliptic,
RotatedSunFrame(lon=1 * u.deg,
lat=2 * u.deg,
distance=3 * u.AU,
base=HeliocentricMeanEcliptic(
obstime='2001-01-01', equinox='2001-01-01'),
duration=4 * u.day))
def _rotation_matrix_hgs_to_hci(obstime):
"""
Return the rotation matrix from HGS to HCI at the same observation time
"""
z_axis = CartesianRepresentation(0, 0, 1)*u.m
if not obstime.isscalar:
z_axis = z_axis._apply('repeat', obstime.size)
# Get the ecliptic pole in HGS
ecliptic_pole = HeliocentricMeanEcliptic(z_axis, obstime=obstime, equinox=_J2000)
ecliptic_pole_hgs = ecliptic_pole.transform_to(HeliographicStonyhurst(obstime=obstime))
# Rotate the ecliptic pole to the -YZ plane, which aligns the solar ascending node with the X
# axis
rot_matrix = _rotation_matrix_reprs_to_xz_about_z(ecliptic_pole_hgs.cartesian)
xz_to_yz_matrix = rotation_matrix(-90*u.deg, 'z')
return xz_to_yz_matrix @ rot_matrix
def hme_to_hee(hmecoord, heeframe):
"""
Convert from Heliocentric Mean Ecliptic to Heliocentric Earth Ecliptic
"""
# Convert to the HME frame with mean equinox of date at the HEE obstime, through HCRS
int_frame = HeliocentricMeanEcliptic(obstime=heeframe.obstime, equinox=heeframe.obstime)
int_coord = hmecoord.transform_to(HCRS).transform_to(int_frame)
# Rotate the intermediate coord to the HEE frame
total_matrix = _rotation_matrix_hme_to_hee(int_frame)
newrepr = int_coord.cartesian.transform(total_matrix)
return heeframe.realize_frame(newrepr)
def hme_to_hee(hmecoord, heeframe):
"""
Convert from Heliocentric Mean Ecliptic to Heliocentric Earth Ecliptic
"""
if heeframe.obstime is None:
raise ConvertError("To perform this transformation, the coordinate"
" frame needs a specified `obstime`.")
# Convert to the HME frame with mean equinox of date at the HEE obstime, through HCRS
int_frame = HeliocentricMeanEcliptic(obstime=heeframe.obstime, equinox=heeframe.obstime)
int_coord = hmecoord.transform_to(HCRS(obstime=hmecoord.obstime)).transform_to(int_frame)
# Rotate the intermediate coord to the HEE frame
total_matrix = _rotation_matrix_hme_to_hee(int_frame)
newrepr = int_coord.cartesian.transform(total_matrix)
return heeframe.realize_frame(newrepr)
def test_ephemerides():
"""
We test that using different ephemerides gives very similar results
for transformations
"""
t = Time("2014-12-25T07:00")
moon = SkyCoord(
GCRS(318.10579159 * u.deg,
-11.65281165 * u.deg,
365042.64880308 * u.km,
obstime=t))
icrs_frame = ICRS()
hcrs_frame = HCRS(obstime=t)
ecl_frame = HeliocentricMeanEcliptic(equinox=t)
cirs_frame = CIRS(obstime=t)
moon_icrs_builtin = moon.transform_to(icrs_frame)
moon_hcrs_builtin = moon.transform_to(hcrs_frame)
moon_helioecl_builtin = moon.transform_to(ecl_frame)
moon_cirs_builtin = moon.transform_to(cirs_frame)
with solar_system_ephemeris.set('jpl'):
moon_icrs_jpl = moon.transform_to(icrs_frame)
moon_hcrs_jpl = moon.transform_to(hcrs_frame)
moon_helioecl_jpl = moon.transform_to(ecl_frame)
moon_cirs_jpl = moon.transform_to(cirs_frame)
# most transformations should differ by an amount which is
# non-zero but of order milliarcsecs
sep_icrs = moon_icrs_builtin.separation(moon_icrs_jpl)
sep_hcrs = moon_hcrs_builtin.separation(moon_hcrs_jpl)
sep_helioecl = moon_helioecl_builtin.separation(moon_helioecl_jpl)
sep_cirs = moon_cirs_builtin.separation(moon_cirs_jpl)
assert_allclose([sep_icrs, sep_hcrs, sep_helioecl],
0.0 * u.deg,
atol=10 * u.mas)
assert all(sep > 10 * u.microarcsecond
for sep in (sep_icrs, sep_hcrs, sep_helioecl))
# CIRS should be the same
assert_allclose(sep_cirs, 0.0 * u.deg, atol=1 * u.microarcsecond)
def true_longitude(t='now'):
"""
Returns the Sun's true geometric longitude, referred to the mean equinox of date. No
corrections for nutation or aberration are included.
Parameters
----------
t : {parse_time_types}
Time to use in a parse-time-compatible format
"""
time = parse_time(t)
# Calculate Earth's true geometric longitude and add 180 degrees for the Sun's longitude.
# This approach is used because Astropy's GeocentricMeanEcliptic includes aberration.
earth = SkyCoord(0*u.deg, 0*u.deg, 0*u.AU, frame='gcrs', obstime=time)
coord = earth.transform_to(HeliocentricMeanEcliptic(equinox=time))
lon = coord.lon + 180*u.deg
return Longitude(lon)