def preprocess_star_cat(input_cata, station):
'''
Makes sure the star catalog contains all the required information: index alt-az, calculated alt-az, deltas...
input_cata: astropy Table or votable path
observer_station: EarthLocation object
'''
if isinstance(input_cata, Table):
input_table = input_cata
else:
# Read the data
input_table = Table.read(input_cata, format='votable')
# try to remove alt-az columns if they exist
possible_newcols = [alt_cata_col_,
az_cata_col_,
delta_az_cata_col_,
delta_alt_cata_col_,
alt_fitted_col_,
delta_alt_cata_col_]
for c in possible_newcols:
if c in input_table.colnames:
input_table.remove_columns(c)
times = Time(Time(input_table['jd_mid_obs'], format='jd', scale='utc').isot)
cata_data = ICRS(ra=input_table['RA_cat_deg']*u.deg, dec=input_table['DEC_cat_deg']*u.deg)
cata_data_altaz = cata_data.transform_to(AltAz(obstime=times,location=station))
fitted_data = ICRS(ra=input_table['RA_deg']*u.deg, dec=input_table['DEC_deg']*u.deg)
fitted_data_altaz = fitted_data.transform_to(AltAz(obstime=times,location=station))
alt_cata_col = Column(data=cata_data_altaz.alt, name=alt_cata_col_)
az_cata_col = Column(data=cata_data_altaz.az, name=az_cata_col_)
alt_fitted_col = Column(data=fitted_data_altaz.alt, name=alt_fitted_col_)
az_fitted_col = Column(data=fitted_data_altaz.az, name=az_fitted_col_)
delta_alt_cata_col = Column(data=fitted_data_altaz.alt-cata_data_altaz.alt, name=delta_alt_cata_col_)
delta_az_cata_col = Column(data=fitted_data_altaz.az-cata_data_altaz.az, name=delta_az_cata_col_)
new_cols = [alt_cata_col,
az_cata_col,
delta_az_cata_col,
delta_alt_cata_col,
alt_fitted_col,
az_fitted_col]
input_table.add_columns(new_cols)
return input_table
def _to_altaz(self, c1, c2, times, csys):
"""
"""
# Make sure to have corresponding dimensions
elements = [times.mjd, c1, c2]
if all(map(np.isscalar, elements)):
time = [times]
c1 = [c1]
c2 = [c2]
elif all(hasattr(i, '__len__') for i in elements):
if len(set(len(i) for i in elements)) == 1:
pass
else:
raise ValueError('Different lengths found')
else:
raise ValueError(
'times, c1 and c2 are mixed with scalars and lists')
# Convert coordinates
if csys.lower() == 'radec':
radec = ICRS(ra=c1 * u.deg, dec=c2 * u.deg)
altaz_frame = AltAz(obstime=times, location=nenufar_loc)
altaz = radec.transform_to(altaz_frame)
az = altaz.az.deg
el = altaz.alt.deg
elif csys.lower() == 'altaz':
az = c1
el = c2
else:
raise ValueError('{} not understood'.format(csys))
return az, el
def to_altaz(ra, dec, time, location=None):
""" Transform altaz coordinates to ICRS equatorial system
:param radec:
Equatorial coordinates
:type altaz: :class:`astropy.coordinates.ICRS`
:param time:
Time at which the local coordinates should be
computed. It can either be provided as an
:class:`astropy.time.Time` object or a string in ISO
or ISOT format.
:type time: str, :class:`astropy.time.Time`
:returns: :class:`astropy.coordinates.AltAz` object
:rtype: :class:`astropy.coordinates.AltAz`
:Example:
>>> from nenupysim.astro import eq_coord
>>> radec = eq_coord(
ra=51,
dec=39,
)
"""
if location is None:
location = nenufar_loc()
if not isinstance(location, EarthLocation):
raise TypeError('time is not an astropy EarthLocation.')
altaz_frame = AltAz(obstime=time, location=location)
eq = ICRS(ra=ra * u.deg, dec=dec * u.deg)
altaz = eq.transform_to(altaz_frame)
return altaz
def convert_radec_file_to_altaz(input_file,
obs_cfg_file,
output_file,
alt_key='altitude', az_key='azimuth',
ra_key='ra', dec_key='dec'):
'''
Convert RA DEC file to Alt-Az
input_file: File containing equatorial coordinates
obs_cfg_file: Oberver config file
output_file: file to save
keys: column header keywords
'''
if ra_key.lower() == 'ha':
ra_unit = u.hour
else:
ra_unit = u.deg
input_table = Table.read(input_file, format='ascii.csv', guess=False, delimiter=',')
station, obstime = parse_observer_cfg_file(obs_cfg_file)
equatorial_data = ICRS(ra=input_table[ra_key]*ra_unit, dec=input_table[dec_key]*u.deg)
horizontal_data = equatorial_data.transform_to(AltAz(obstime=obstime,location=station))
alt_col = Column(data=horizontal_data.alt, name=alt_key)
az_col = Column(data=horizontal_data.az, name=az_key)
output_table = Table([az_col, alt_col])
output_table.write(output_file, format='ascii.csv', delimiter=',', overwrite=True)
def test_coord_get():
# Test default (instance=None)
obs = Helioprojective.observer
assert obs is "earth"
# Test get
obstime = "2013-04-01"
obs = Helioprojective(observer="earth", obstime=obstime).observer
earth = get_earth(obstime)
assert isinstance(obs, HeliographicStonyhurst)
assert_quantity_allclose(obs.lon, earth.lon)
assert_quantity_allclose(obs.lat, earth.lat)
assert_quantity_allclose(obs.radius, earth.radius)
# Test get
obstime = "2013-04-01"
obs = Helioprojective(obstime=obstime).observer
earth = get_earth(obstime)
assert isinstance(obs, HeliographicStonyhurst)
assert_quantity_allclose(obs.lon, earth.lon)
assert_quantity_allclose(obs.lat, earth.lat)
assert_quantity_allclose(obs.radius, earth.radius)
# Test get mars
obstime = Time(parse_time("2013-04-01"))
obs = Helioprojective(observer="mars", obstime=obstime).observer
out_icrs = ICRS(get_body_barycentric("mars", obstime))
mars = out_icrs.transform_to(HeliographicStonyhurst(obstime=obstime))
assert isinstance(obs, HeliographicStonyhurst)
assert_quantity_allclose(obs.lon, mars.lon)
assert_quantity_allclose(obs.lat, mars.lat)
assert_quantity_allclose(obs.radius, mars.radius)
def test_icrs_gcrscirs_sunish(testframe):
"""
check that the ICRS barycenter goes to about the right distance from various
~geocentric frames (other than testframe)
"""
# slight offset to avoid divide-by-zero errors
icrs = ICRS(0*u.deg, 0*u.deg, distance=10*u.km)
gcrs = icrs.transform_to(GCRS(obstime=testframe.obstime))
assert (EARTHECC - 1)*u.au < gcrs.distance.to(u.au) < (EARTHECC + 1)*u.au
cirs = icrs.transform_to(CIRS(obstime=testframe.obstime))
assert (EARTHECC - 1)*u.au < cirs.distance.to(u.au) < (EARTHECC + 1)*u.au
itrs = icrs.transform_to(ITRS(obstime=testframe.obstime))
assert (EARTHECC - 1)*u.au < itrs.spherical.distance.to(u.au) < (EARTHECC + 1)*u.au
def test_icrs_gcrscirs_sunish(testframe):
"""
check that the ICRS barycenter goes to about the right distance from various
~geocentric frames (other than testframe)
"""
# slight offset to avoid divide-by-zero errors
icrs = ICRS(0*u.deg, 0*u.deg, distance=10*u.km)
gcrs = icrs.transform_to(GCRS(obstime=testframe.obstime))
assert (EARTHECC - 1)*u.au < gcrs.distance.to(u.au) < (EARTHECC + 1)*u.au
cirs = icrs.transform_to(CIRS(obstime=testframe.obstime))
assert (EARTHECC - 1)*u.au < cirs.distance.to(u.au) < (EARTHECC + 1)*u.au
itrs = icrs.transform_to(ITRS(obstime=testframe.obstime))
assert (EARTHECC - 1)*u.au < itrs.spherical.distance.to(u.au) < (EARTHECC + 1)*u.au
def test_coord_get():
# Test default (instance=None)
obs = Helioprojective.observer
assert obs is "earth"
# Test get
obstime = "2013-04-01"
obs = Helioprojective(observer="earth", obstime=obstime).observer
earth = get_earth(obstime)
assert isinstance(obs, HeliographicStonyhurst)
assert_quantity_allclose(obs.lon, earth.lon)
assert_quantity_allclose(obs.lat, earth.lat)
assert_quantity_allclose(obs.radius, earth.radius)
# Test get
obstime = "2013-04-01"
obs = Helioprojective(obstime=obstime).observer
earth = get_earth(obstime)
assert isinstance(obs, HeliographicStonyhurst)
assert_quantity_allclose(obs.lon, earth.lon)
assert_quantity_allclose(obs.lat, earth.lat)
assert_quantity_allclose(obs.radius, earth.radius)
# Test get mars
obstime = Time(parse_time("2013-04-01"))
obs = Helioprojective(observer="mars", obstime=obstime).observer
out_icrs = ICRS(get_body_barycentric("mars", obstime))
mars = out_icrs.transform_to(HeliographicStonyhurst(obstime=obstime))
assert isinstance(obs, HeliographicStonyhurst)
assert_quantity_allclose(obs.lon, mars.lon)
assert_quantity_allclose(obs.lat, mars.lat)
assert_quantity_allclose(obs.radius, mars.radius)
def from_body_ephem(cls, body, epoch=None):
"""Return osculating `Orbit` of a body at a given time.
"""
if not epoch:
epoch = time.Time.now().tdb
elif epoch.scale != 'tdb':
epoch = epoch.tdb
warn(
"Input time was converted to scale='tdb' with value "
"{}. Use Time(..., scale='tdb') instead.".format(
epoch.tdb.value), TimeScaleWarning)
r, v = get_body_barycentric_posvel(body.name, epoch)
if body == Moon:
moon_icrs = ICRS(x=r.x,
y=r.y,
z=r.z,
v_x=v.x,
v_y=v.y,
v_z=v.z,
representation=CartesianRepresentation,
differential_type=CartesianDifferential)
moon_gcrs = moon_icrs.transform_to(GCRS(obstime=epoch))
moon_gcrs.representation = CartesianRepresentation
r = CartesianRepresentation(
[moon_gcrs.x, moon_gcrs.y, moon_gcrs.z])
v = CartesianRepresentation(
[moon_gcrs.v_x, moon_gcrs.v_y, moon_gcrs.v_z])
return cls.from_vectors(body.parent, r.xyz.to(u.km),
v.xyz.to(u.km / u.day), epoch)
def test_array_coordinates_transformations(arrshape, distance):
"""
Test transformation on coordinates with array content (first length-2 1D, then a 3D array)
"""
# M31 coordinates from test_transformations
raarr = np.ones(arrshape) * 10.6847929
decarr = np.ones(arrshape) * 41.2690650
if distance is not None:
distance = np.ones(arrshape) * distance
print(raarr, decarr, distance)
c = ICRS(ra=raarr * u.deg, dec=decarr * u.deg, distance=distance)
g = c.transform_to(Galactic())
assert g.l.shape == arrshape
npt.assert_array_almost_equal(g.l.degree, 121.17440967)
npt.assert_array_almost_equal(g.b.degree, -21.57299631)
if distance is not None:
assert g.distance.unit == c.distance.unit
# now make sure round-tripping works through FK5
c2 = c.transform_to(FK5()).transform_to(ICRS())
npt.assert_array_almost_equal(c.ra.radian, c2.ra.radian)
npt.assert_array_almost_equal(c.dec.radian, c2.dec.radian)
assert c2.ra.shape == arrshape
if distance is not None:
assert c2.distance.unit == c.distance.unit
# also make sure it's possible to get to FK4, which uses a direct transform function.
fk4 = c.transform_to(FK4())
npt.assert_array_almost_equal(fk4.ra.degree, 10.0004, decimal=4)
npt.assert_array_almost_equal(fk4.dec.degree, 40.9953, decimal=4)
assert fk4.ra.shape == arrshape
if distance is not None:
assert fk4.distance.unit == c.distance.unit
# now check the reverse transforms run
cfk4 = fk4.transform_to(ICRS())
assert cfk4.ra.shape == arrshape
def test_array_coordinates_transformations(arrshape, distance):
"""
Test transformation on coordinates with array content (first length-2 1D, then a 3D array)
"""
# M31 coordinates from test_transformations
raarr = np.ones(arrshape) * 10.6847929
decarr = np.ones(arrshape) * 41.2690650
if distance is not None:
distance = np.ones(arrshape) * distance
print(raarr, decarr, distance)
c = ICRS(ra=raarr*u.deg, dec=decarr*u.deg, distance=distance)
g = c.transform_to(Galactic)
assert g.l.shape == arrshape
npt.assert_array_almost_equal(g.l.degree, 121.17440967)
npt.assert_array_almost_equal(g.b.degree, -21.57299631)
if distance is not None:
assert g.distance.unit == c.distance.unit
# now make sure round-tripping works through FK5
c2 = c.transform_to(FK5).transform_to(ICRS)
npt.assert_array_almost_equal(c.ra.radian, c2.ra.radian)
npt.assert_array_almost_equal(c.dec.radian, c2.dec.radian)
assert c2.ra.shape == arrshape
if distance is not None:
assert c2.distance.unit == c.distance.unit
# also make sure it's possible to get to FK4, which uses a direct transform function.
fk4 = c.transform_to(FK4)
npt.assert_array_almost_equal(fk4.ra.degree, 10.0004, decimal=4)
npt.assert_array_almost_equal(fk4.dec.degree, 40.9953, decimal=4)
assert fk4.ra.shape == arrshape
if distance is not None:
assert fk4.distance.unit == c.distance.unit
# now check the reverse transforms run
cfk4 = fk4.transform_to(ICRS)
assert cfk4.ra.shape == arrshape
def test_radec_to_munu():
from astropy import units as u
from astropy.coordinates import ICRS
from .. import SDSSMuNu
radec = ICRS(ra=0.0*u.deg,dec=0.0*u.deg)
munu = radec.transform_to(SDSSMuNu(stripe=10))
assert munu.mu.value == 0.0
assert munu.nu.value == 0.0
assert munu.incl.value == 0.0
def eq2gal(self,ra,dec):
try:
ra = Angle(ra)
dec = Angle(dec)
c = ICRS(ra=ra, dec=dec)
return c.transform_to(Galactic)
except Exception as e:
print(e)
return 0
def test_icrs_cirs():
"""
Check a few cases of ICRS<->CIRS for consistency.
Also includes the CIRS<->CIRS transforms at different times, as those go
through ICRS
"""
usph = golden_spiral_grid(200)
dist = np.linspace(0., 1, len(usph)) * u.pc
inod = ICRS(usph)
iwd = ICRS(ra=usph.lon, dec=usph.lat, distance=dist)
cframe1 = CIRS()
cirsnod = inod.transform_to(cframe1) # uses the default time
# first do a round-tripping test
inod2 = cirsnod.transform_to(ICRS())
assert_allclose(inod.ra, inod2.ra)
assert_allclose(inod.dec, inod2.dec)
# now check that a different time yields different answers
cframe2 = CIRS(obstime=Time('J2005'))
cirsnod2 = inod.transform_to(cframe2)
assert not allclose(cirsnod.ra, cirsnod2.ra, rtol=1e-8)
assert not allclose(cirsnod.dec, cirsnod2.dec, rtol=1e-8)
# parallax effects should be included, so with and w/o distance should be different
cirswd = iwd.transform_to(cframe1)
assert not allclose(cirswd.ra, cirsnod.ra, rtol=1e-8)
assert not allclose(cirswd.dec, cirsnod.dec, rtol=1e-8)
# and the distance should transform at least somehow
assert not allclose(cirswd.distance, iwd.distance, rtol=1e-8)
# now check that the cirs self-transform works as expected
cirsnod3 = cirsnod.transform_to(cframe1) # should be a no-op
assert_allclose(cirsnod.ra, cirsnod3.ra)
assert_allclose(cirsnod.dec, cirsnod3.dec)
cirsnod4 = cirsnod.transform_to(cframe2) # should be different
assert not allclose(cirsnod4.ra, cirsnod.ra, rtol=1e-8)
assert not allclose(cirsnod4.dec, cirsnod.dec, rtol=1e-8)
cirsnod5 = cirsnod4.transform_to(cframe1) # should be back to the same
assert_allclose(cirsnod.ra, cirsnod5.ra)
assert_allclose(cirsnod.dec, cirsnod5.dec)
def test_icrs_cirs():
"""
Check a few cases of ICRS<->CIRS for consistency.
Also includes the CIRS<->CIRS transforms at different times, as those go
through ICRS
"""
ra, dec, dist = randomly_sample_sphere(200)
inod = ICRS(ra=ra, dec=dec)
iwd = ICRS(ra=ra, dec=dec, distance=dist*u.pc)
cframe1 = CIRS()
cirsnod = inod.transform_to(cframe1) # uses the default time
# first do a round-tripping test
inod2 = cirsnod.transform_to(ICRS)
assert_allclose(inod.ra, inod2.ra)
assert_allclose(inod.dec, inod2.dec)
# now check that a different time yields different answers
cframe2 = CIRS(obstime=Time('J2005', scale='utc'))
cirsnod2 = inod.transform_to(cframe2)
assert not allclose(cirsnod.ra, cirsnod2.ra, rtol=1e-8)
assert not allclose(cirsnod.dec, cirsnod2.dec, rtol=1e-8)
# parallax effects should be included, so with and w/o distance should be different
cirswd = iwd.transform_to(cframe1)
assert not allclose(cirswd.ra, cirsnod.ra, rtol=1e-8)
assert not allclose(cirswd.dec, cirsnod.dec, rtol=1e-8)
# and the distance should transform at least somehow
assert not allclose(cirswd.distance, iwd.distance, rtol=1e-8)
# now check that the cirs self-transform works as expected
cirsnod3 = cirsnod.transform_to(cframe1) # should be a no-op
assert_allclose(cirsnod.ra, cirsnod3.ra)
assert_allclose(cirsnod.dec, cirsnod3.dec)
cirsnod4 = cirsnod.transform_to(cframe2) # should be different
assert not allclose(cirsnod4.ra, cirsnod.ra, rtol=1e-8)
assert not allclose(cirsnod4.dec, cirsnod.dec, rtol=1e-8)
cirsnod5 = cirsnod4.transform_to(cframe1) # should be back to the same
assert_allclose(cirsnod.ra, cirsnod5.ra)
assert_allclose(cirsnod.dec, cirsnod5.dec)
def test_icrs_cirs():
"""
Check a few cases of ICRS<->CIRS for consistency.
Also includes the CIRS<->CIRS transforms at different times, as those go
through ICRS
"""
ra, dec, dist = randomly_sample_sphere(200)
inod = ICRS(ra=ra, dec=dec)
iwd = ICRS(ra=ra, dec=dec, distance=dist * u.pc)
cframe1 = CIRS()
cirsnod = inod.transform_to(cframe1) # uses the default time
# first do a round-tripping test
inod2 = cirsnod.transform_to(ICRS)
assert_allclose(inod.ra, inod2.ra)
assert_allclose(inod.dec, inod2.dec)
# now check that a different time yields different answers
cframe2 = CIRS(obstime=Time('J2005', scale='utc'))
cirsnod2 = inod.transform_to(cframe2)
assert not allclose(cirsnod.ra, cirsnod2.ra, rtol=1e-8)
assert not allclose(cirsnod.dec, cirsnod2.dec, rtol=1e-8)
# parallax effects should be included, so with and w/o distance should be different
cirswd = iwd.transform_to(cframe1)
assert not allclose(cirswd.ra, cirsnod.ra, rtol=1e-8)
assert not allclose(cirswd.dec, cirsnod.dec, rtol=1e-8)
# and the distance should transform at least somehow
assert not allclose(cirswd.distance, iwd.distance, rtol=1e-8)
# now check that the cirs self-transform works as expected
cirsnod3 = cirsnod.transform_to(cframe1) # should be a no-op
assert_allclose(cirsnod.ra, cirsnod3.ra)
assert_allclose(cirsnod.dec, cirsnod3.dec)
cirsnod4 = cirsnod.transform_to(cframe2) # should be different
assert not allclose(cirsnod4.ra, cirsnod.ra, rtol=1e-8)
assert not allclose(cirsnod4.dec, cirsnod.dec, rtol=1e-8)
cirsnod5 = cirsnod4.transform_to(cframe1) # should be back to the same
assert_allclose(cirsnod.ra, cirsnod5.ra)
assert_allclose(cirsnod.dec, cirsnod5.dec)
def test_regression_3920():
"""
Issue: https://github.com/astropy/astropy/issues/3920
"""
loc = EarthLocation.from_geodetic(0*u.deg, 0*u.deg, 0)
time = Time('2010-1-1')
aa = AltAz(location=loc, obstime=time)
sc = SkyCoord(10*u.deg, 3*u.deg)
assert sc.transform_to(aa).shape == tuple()
# That part makes sense: the input is a scalar so the output is too
sc2 = SkyCoord(10*u.deg, 3*u.deg, 1*u.AU)
assert sc2.transform_to(aa).shape == tuple()
# in 3920 that assert fails, because the shape is (1,)
# check that the same behavior occurs even if transform is from low-level classes
icoo = ICRS(sc.data)
icoo2 = ICRS(sc2.data)
assert icoo.transform_to(aa).shape == tuple()
assert icoo2.transform_to(aa).shape == tuple()
def test_regression_3920():
"""
Issue: https://github.com/astropy/astropy/issues/3920
"""
loc = EarthLocation.from_geodetic(0*u.deg, 0*u.deg, 0)
time = Time('2010-1-1')
aa = AltAz(location=loc, obstime=time)
sc = SkyCoord(10*u.deg, 3*u.deg)
assert sc.transform_to(aa).shape == tuple()
# That part makes sense: the input is a scalar so the output is too
sc2 = SkyCoord(10*u.deg, 3*u.deg, 1*u.AU)
assert sc2.transform_to(aa).shape == tuple()
# in 3920 that assert fails, because the shape is (1,)
# check that the same behavior occurs even if transform is from low-level classes
icoo = ICRS(sc.data)
icoo2 = ICRS(sc2.data)
assert icoo.transform_to(aa).shape == tuple()
assert icoo2.transform_to(aa).shape == tuple()
async def mtptg_telemetry(self) -> None:
while self.run_telemetry_loop:
if (self.controllers.mtptg.evt_summaryState.data.summaryState ==
salobj.State.ENABLED):
now = Time.now()
await self.controllers.mtptg.tel_timeAndDate.set_write(
timestamp=now.unix_tai,
utc=now.utc.mjd,
lst=now.sidereal_time("mean", self.location.lon).value,
)
if self.tracking:
radec_icrs = ICRS(
Angle(
self.controllers.mtptg.evt_currentTarget.data.ra,
unit=u.radian,
),
Angle(
self.controllers.mtptg.evt_currentTarget.data.
declination,
unit=u.radian,
),
)
coord_frame_altaz = AltAz(location=self.location,
obstime=now)
alt_az = radec_icrs.transform_to(coord_frame_altaz)
await self.controllers.mtptg.evt_currentTarget.set_write(
timestamp=now.tai.mjd,
azDegs=alt_az.az.deg,
elDegs=alt_az.alt.deg,
)
self.controllers.mtmount.tel_azimuth.set(
**{self.mtmount_demand_position_name: alt_az.az.deg})
self.controllers.mtmount.tel_elevation.set(
**{self.mtmount_demand_position_name: alt_az.alt.deg})
self.controllers.mtrotator.tel_rotation.set(
demandPosition=self.controllers.mtptg.
evt_currentTarget.data.rotPA)
self.controllers.mtmount.evt_target.set(
elevation=alt_az.alt.deg,
azimuth=alt_az.az.deg,
)
await asyncio.sleep(HEARTBEAT_INTERVAL)
def vec2pix(l, b):
if galactic:
f = ICRS(l * u.rad, b * u.rad)
g = f.transform_to(Galactic)
l, b = g.l.rad, g.b.rad
theta = np.pi / 2 - b
phi = l
if interp:
return get_interp_val(data, theta, phi, nest=nest)
return data[ang2pix(nside, theta, phi, nest=nest)]
def test_icrs_altaz_moonish(testframe):
"""
Check that something expressed in *ICRS* as being moon-like goes to the
right AltAz distance
"""
# we use epv00 instead of get_sun because get_sun includes aberration
earth_pv_helio, earth_pv_bary = erfa.epv00(*get_jd12(testframe.obstime, 'tdb'))
earth_icrs_xyz = earth_pv_bary[0]*u.au
moonoffset = [0, 0, MOONDIST.value]*MOONDIST.unit
moonish_icrs = ICRS(CartesianRepresentation(earth_icrs_xyz + moonoffset))
moonaa = moonish_icrs.transform_to(testframe)
# now check that the distance change is similar to earth radius
assert 1000*u.km < np.abs(moonaa.distance - MOONDIST).to(u.au) < 7000*u.km
def test_icrs_altaz_moonish(testframe):
"""
Check that something expressed in *ICRS* as being moon-like goes to the
right AltAz distance
"""
# we use epv00 instead of get_sun because get_sun includes aberration
earth_pv_helio, earth_pv_bary = epv00(*get_jd12(testframe.obstime, 'tdb'))
earth_icrs_xyz = earth_pv_bary[0]*u.au
moonoffset = [0, 0, MOONDIST.value]*MOONDIST.unit
moonish_icrs = ICRS(CartesianRepresentation(earth_icrs_xyz + moonoffset))
moonaa = moonish_icrs.transform_to(testframe)
# now check that the distance change is similar to earth radius
assert 1000*u.km < np.abs(moonaa.distance - MOONDIST).to(u.au) < 7000*u.km
def ProperMotionTransform(ra_coord, dec_coord, pmra_coord, pmdec_coord):
# pmra_coord_cosdec = pmra_coord*np.cos(dec_coord*np.pi/180.)
pmra_coord_cosdec = pmra_coord
icrs = ICRS(ra=ra_coord * units.degree,
dec=dec_coord * units.degree,
pm_ra_cosdec=pmra_coord_cosdec * units.mas / units.yr,
pm_dec=pmdec_coord * units.mas / units.yr)
galactic = icrs.transform_to(Galactic)
pml = (galactic.pm_l_cosb) / np.cos(
galactic.b.radian) / (units.mas / units.yr)
pmb = galactic.pm_b / (units.mas / units.yr)
return (pml, pmb)
def astropy_icrstogal_rotation_matrix():
"""
Figure the ICRS to Galatic coordinates rotation matrix.
Returns
-------
The 3x3 matrix representing the rotation from ICRS Cartesian to Galactic Cartesian coordinates.
"""
# ICRS basis vectors
basis_icrs = ICRS(ra = [0,np.pi/2,0]*u.rad, dec = [0,0,np.pi/2]*u.rad)
# Rotate to Galactic
basis_gal = basis_icrs.transform_to(Galactic())
# Calculate and return matrix components
return np.array([np.cos(basis_gal.l.to(u.rad))*np.cos(basis_gal.b.to(u.rad)),
np.sin(basis_gal.l.to(u.rad))*np.cos(basis_gal.b.to(u.rad)), np.sin(basis_gal.b.to(u.rad))])
def get_elev(ra_source, dec_source, xyz_antenna, time):
#this one is by Michael Janssen
"""
given right ascension and declination of a sky source [ICRS: ra->(deg,arcmin,arcsec) and dec->(hour,min,sec)]
and given the position of the telescope from the vex file [Geocentric coordinates (m)]
and the time of the observation (e.g. '2012-7-13 23:00:00') [UTC:yr-m-d],
returns the elevation of the telescope.
Note that every parameter can be an array (e.g. the time)
"""
from astropy import units as u
from astropy.coordinates import EarthLocation, AltAz, ICRS, Angle
#angle conversions:
ra_src = Angle(ra_source, unit=u.rad)
dec_src = Angle(dec_source, unit=u.rad)
source_position = ICRS(ra=ra_src, dec=dec_src)
antenna_position = EarthLocation(x=xyz_antenna[0]*u.m, y=xyz_antenna[1]*u.m, z=xyz_antenna[2]*u.m)
altaz_system = AltAz(location=antenna_position, obstime=time)
trans_to_altaz = source_position.transform_to(altaz_system)
elevation = trans_to_altaz.alt
return elevation.rad
def get_body_heliographic_stonyhurst(body, time='now'):
"""
Return a `~sunpy.coordinates.frames.HeliographicStonyhurst` frame for the location of a
solar-system body at a specified time.
Parameters
----------
body : `str`
The solar-system body for which to calculate positions
time : various
Time to use as `~astropy.time.Time` or in a parse_time-compatible format
Returns
-------
out : `~sunpy.coordinates.frames.HeliographicStonyhurst`
Location of the solar-system body in the `~sunpy.coordinates.HeliographicStonyhurst` frame
"""
obstime = _astropy_time(time)
body_icrs = ICRS(get_body_barycentric(body, obstime))
body_hgs = body_icrs.transform_to(HGS(obstime=obstime))
return body_hgs
def get_body_heliographic_stonyhurst(body, time='now'):
"""
Return a `~sunpy.coordinates.frames.HeliographicStonyhurst` frame for the location of a
solar-system body at a specified time.
Parameters
----------
body : `str`
The solar-system body for which to calculate positions
time : various
Time to use as `~astropy.time.Time` or in a parse_time-compatible format
Returns
-------
out : `~sunpy.coordinates.frames.HeliographicStonyhurst`
Location of the solar-system body in the `~sunpy.coordinates.HeliographicStonyhurst` frame
"""
obstime = parse_time(time)
body_icrs = ICRS(get_body_barycentric(body, obstime))
body_hgs = body_icrs.transform_to(HGS(obstime=obstime))
return body_hgs
def stars(in_file, plots_flag):
# Create structured datatype correspond to given format
# and load data file
in_type = np.dtype([('ra' , 'f'),
('dec' , 'f'),
('d' , 'f'),
('vlos' , 'f'),
('pmra' , 'f'),
('pmdec', 'f')])
data = np.loadtxt(in_file,dtype=in_type,skiprows=1)
# astropy.SkyCoords doesn't support automatically converting the velocity components
# so we need to transform the data manually
icrs = ICRS(ra=data['ra'] * u.degree,
dec=data['dec'] * u.degree,
distance=data['d'] * u.kpc,
pm_ra_cosdec=(data['pmra'] * u.mas / u.yr),
#* np.cos(data['dec'] * u.degree)),
pm_dec=data['pmdec'] * u.mas / u.yr,
radial_velocity=data['vlos'] * u.km / u.s)
# Cartesian galactocentric coordinates
v_sun = CartesianDifferential(11.1, 12.248 + 238, 7.25, unit=u.km / u.s)
gal_cen = icrs.transform_to(Galactocentric(galcen_v_sun=v_sun,
galcen_distance=8.0 * u.kpc,
z_sun=0 * u.kpc))
# Output the 6D Cartesian coordinates
out_file = '6d.txt'
out_data = np.column_stack((gal_cen.x,
gal_cen.y,
gal_cen.z,
gal_cen.v_x,
gal_cen.v_y,
gal_cen.v_z))
cols = ('x[kpc]', 'y[kpc]', 'z[kpc]', 'v_x[km/s]', 'v_y[km/s]', 'v_z[km/s]')
np.savetxt(out_file, out_data, fmt='%9.4f', header=' '.join(cols))
print('6D coordinates written to {}'.format(out_file))
# r = distance
# theta = latitude
# phi = azimuth/longitude
# NB This is opposite to how spherical coordinates are normally defined!
# Spherical galactocentric coordinates
gal_cen_sph = gal_cen.copy()
gal_cen_sph.representation = 'spherical'
# Calculate spherical velocity components and make units sensible
vr = (gal_cen_sph.d_distance
.to(u.km/u.s))
vtheta = ((gal_cen_sph.d_lat * gal_cen_sph.distance)
.to(u.rad * u.km/u.s) / u.rad)
vphi = ((gal_cen_sph.d_lon * gal_cen_sph.distance * np.cos(gal_cen_sph.lat))
.to(u.rad * u.km/u.s) / u.rad)
# Calculate standard deviations (sigma) for three velocity components
vr_dev = np.std(vr)
vtheta_dev = np.std(vtheta)
vphi_dev = np.std(vphi)
# Calculate the velocity anisotropy parameter beta
v_anis = vel_anisotropy(vr, vtheta, vphi)
# Calculate the rotation velocity
# Assumed that this is the expectation value of vphi
v_rot = np.mean(vphi)
# Report the results
print('Velocity dispersion and anisotropy results:')
print(""" sigma_r = {}
sigma_theta = {}
sigma_phi = {}
v_rot = {}
beta = {}""".format(vr_dev, vtheta_dev, vphi_dev, v_rot, v_anis))
# Spit out some plots if the command line flag was given
if plots_flag:
#from matplotlib import rc
#rc('text', usetex=True)
# plot positions
fig = plt.figure()
ax = plt.gca()
ax.set_title('XY positions scatterplot')
ax.set_aspect('equal')
ax.set_xlabel('x [kpc]')
ax.set_ylabel('y [kpc]')
plt.scatter(gal_cen.x, gal_cen.y, s=2)
# radius histogram
hist_fig = plt.figure()
ax = plt.gca()
ax.set_title('Histogram of radial distances')
ax.set_xlabel('Radial distance [kpc]')
ax.set_ylabel('Count')
plt.hist(gal_cen_sph.distance, bins='auto')
# xyz histogram
xyz_hist_fig = plt.figure()
ax = plt.gca()
ax.set_title('Histogram of Cartesian position components')
ax.set_xlabel('Position [kpc]')
ax.set_ylabel('Count')
plt.hist(np.array(gal_cen.x), bins=50, alpha=0.4, label='x')
plt.hist(np.array(gal_cen.y), bins=50, alpha=0.4, label='y')
plt.hist(np.array(gal_cen.z), bins=50, alpha=0.4, label='z')
plt.legend()
# velocities
vel_fig = plt.figure()
ax = plt.gca()
ax.set_title('Histogram of spherical velocity components')
ax.set_xlabel('Velocity [km/s]')
ax.set_ylabel('Count')
plt.hist(np.array(vr), bins=50, range=(-500, 500),alpha=0.4,label='vr')
plt.hist(np.array(vtheta), bins=50, range=(-500, 500), alpha=0.4,label='vtheta')
plt.hist(np.array(vphi), bins=50, range=(-500, 500),alpha=0.4,label='vphi')
#plt.hist(np.array(vtheta), bins=50, alpha=0.4,label='vtheta')
#plt.hist(np.array(vphi), bins=50, alpha=0.4,label='vphi')
plt.legend()
cart_vel_fig = plt.figure()
ax = plt.gca()
ax.set_title('Histogram of Cartesian velocity components')
ax.set_xlabel('Velocity [km/s]')
ax.set_ylabel('Count')
plt.hist(np.array(gal_cen.v_x), bins=50, range=(-500, 500),alpha=0.4,label='vx')
plt.hist(np.array(gal_cen.v_y), bins=50, range=(-500, 500), alpha=0.4,label='vy')
plt.hist(np.array(gal_cen.v_z), bins=50, range=(-500, 500),alpha=0.4,label='vz')
#plt.hist(np.array(vtheta), bins=50, alpha=0.4,label='vtheta')
#plt.hist(np.array(vphi), bins=50, alpha=0.4,label='vphi')
plt.legend()
print("Plots have been opened. Close them all to terminate the program.")
plt.show()
Array of shape (icrs_coords.ra.size, 5, 5) containing the Jacobians.
"""
ra = icrs_coords.ra.to(u.rad)
dec = icrs_coords.dec.to(u.rad)
l = gal_coords.l.to(u.rad)
b = gal_coords.b.to(u.rad)
A = astropy_icrstogal_rotation_matrix()
picrs = np.array([-np.sin(ra), np.cos(ra), np.zeros_like(ra)])
qicrs = np.array([-np.cos(ra)*np.sin(dec), -np.sin(ra)*np.sin(dec), np.cos(dec)])
pgal = np.array([-np.sin(l), np.cos(l), np.zeros_like(l)])
qgal = np.array([-np.cos(l)*np.sin(b), -np.sin(ra)*np.sin(b), np.cos(b)])
J = np.zeros((ra.size, 5, 5))
J[:,2,2] = 1.0
for i in range(ra.size):
G = np.matmul(A, np.stack([picrs[:,i], qicrs[:,i]]).T)
G = np.matmul(np.stack([pgal[:,i], qgal[:,i]]), G)
J[i,0:2,0:2] = G
J[i,3:5,3:5] = G
return J
if __name__ in ('__main__'):
print(astropy_icrstogal_rotation_matrix())
icrscoo = ICRS(ra = [0,np.pi/2,0,np.pi/3]*u.rad, dec = [0,0,np.pi/2,-np.pi/4]*u.rad)
galcoo = icrscoo.transform_to(Galactic())
astropy_icrstogal_jacobian(icrscoo, galcoo)
dcrad2 = np.array([comp_dec*np.pi/180.0])
radif = rarad2-rarad1
angle = np.arctan(np.sin(radif),np.cos(dcrad1)*np.tan(dcrad2)-np.sin(dcrad1)*np.cos(radif))
sep = 60*(np.arccos(np.sin(targ_dec*np.pi/180.0)*np.sin(comp_dec*np.pi/180) + np.cos(comp_dec*np.pi/180)*np.cos(targ_dec*np.pi/180)*np.cos(comp_ra*np.pi/180 - targ_ra*np.pi/180)))*180.0/np.pi
c1 = SkyCoord(targ_ra*u.deg,targ_dec*u.deg)
c2 = SkyCoord(comp_ra*u.deg,comp_dec*u.deg)
pa = c1.position_angle(c2).degree
if args.precess and not args.apass:
targ_coords_ICRS = ICRS(ra=targ_ra*u.degree,dec=targ_dec*u.degree,pm_ra_cosdec=table[0]['pmRA']*u.mas/u.yr,pm_dec=table[0]['pmDE']*u.mas/u.yr)
comp_coords_ICRS = ICRS(ra=comp_ra*u.degree,dec=comp_dec*u.degree,pm_ra_cosdec=table[which_comp]['pmRA']*u.mas/u.yr,pm_dec=table[which_comp]['pmRA']*u.mas/u.yr)
targ_coors_precessed = targ_coords_ICRS.transform_to(FK5(equinox=args.precess))
comp_coors_precessed = comp_coords_ICRS.transform_to(FK5(equinox=args.precess))
corrected_targ = SkyCoord(targ_coors_precessed.ra,targ_coors_precessed.dec)
corrected_comp = SkyCoord(comp_coors_precessed.ra,comp_coors_precessed.dec)
corrected_pa = corrected_targ.position_angle(corrected_comp).degree
corrected_mid_ra = (corrected_targ.ra + corrected_comp.ra)/2.
corrected_mid_dec = (corrected_targ.dec + corrected_comp.dec)/2.
corrected_mid = SkyCoord(ra=corrected_mid_ra,dec=corrected_mid_dec)
corrected_sep = 60*(np.arccos(np.sin(corrected_targ.dec*np.pi/180.0)*np.sin(corrected_comp.dec*np.pi/180) + np.cos(corrected_comp.dec*np.pi/180)*np.cos(corrected_targ.dec*np.pi/180)*np.cos(corrected_comp.ra*np.pi/180 - corrected_targ.ra*np.pi/180)))*180.0/np.pi
def obs2xyz(cooFil='cowleyLine.txt', Verbose=True, outFil='test.fits'):
"""Uses astropy to convert observed ICRS coordinates to Galactic coordinates (with proper motions) and (Galactocentric) Cartesian coordinates. Arguments:
cooFil = text file giving input coordinates. Column names are read from this file.
Verbose=True -- set this to print to the terminal a selection of the converted data
outFil -- filename for the output. (I like .fits format because it preserves metadata and units)
"""
# First read in the data
try:
tCoo = Table.read(cooFil, format='ascii')
except:
print("cooDemo.obs2xyz WARN - problem reading file %s" % (cooFil))
return
# we attach our guess for units in-place to the table (moved to a
# separate method for clarity here).
guessUnits(tCoo)
# ... convert parallax to distance
tCoo['distance'] = tCoo['parallax'].to(u.parsec,
equivalencies=u.parallax())
# set up a proper motion (RA) scaled by cos(delta)
tCoo['mu_RAcosDec'] = tCoo['mu_RA'] * np.cos(tCoo['DEC'].to(u.radian))
# print the table, including units
#if Verbose:
# print(tCoo)
# ... and now we are in business. Set up our frame object...
icrs = ICRS(ra=tCoo['RA'], dec=tCoo['DEC'], \
distance=tCoo['distance'], \
pm_ra_cosdec=tCoo['mu_RAcosDec'], pm_dec=tCoo['mu_dec'], \
radial_velocity=tCoo['RV=rho'])
# Now, to find the coordinates and velocities in different formats
# (Cartesian, say), we just look up the relevant attributes for
# the ICRS object we've created. Here we shunt the cartesian
# coordinates and velocities into our output table:
tCoo['X'] = icrs.cartesian.x
tCoo['Y'] = icrs.cartesian.y
tCoo['Z'] = icrs.cartesian.z
# ... then the velocities
tCoo['vX'] = icrs.velocity.d_x
tCoo['vY'] = icrs.velocity.d_y
tCoo['vZ'] = icrs.velocity.d_z
# We can also transform these to different frames. Here are two
lsr = icrs.transform_to(LSR)
galactic = icrs.transform_to(Galactic)
galcen = icrs.transform_to(Galactocentric)
# Now, we populate the output table with our chosen coords and
# velocities in these frames. Here are the outputs in Galactic
# coordinates...
tCoo['l'] = galactic.l
tCoo['b'] = galactic.b
tCoo['pm_l_cosb'] = galactic.pm_l_cosb
tCoo['pm_b'] = galactic.pm_b
#print(icrs.velocity)
# ... and here are the cartesian coords and velocities in galactocentric
# coordinates
tCoo['X'] = galcen.cartesian.x
tCoo['Y'] = galcen.cartesian.y
tCoo['Z'] = galcen.cartesian.z
tCoo['U'] = galcen.velocity.d_x
tCoo['V'] = galcen.velocity.d_y
tCoo['W'] = galcen.velocity.d_z
tCoo.write('test.fits', format='fits', overwrite=True)
# if verbose, we write some columns of interest
if Verbose:
# make the formats for certain columns a bit more reasonable
for sCoo in ['l','b','distance', 'X','Y','Z','U','V','W', \
'pm_l_cosb', 'pm_b']:
tCoo[sCoo].format = '%7.4f'
for sCoo in ['l', 'b']:
tCoo[sCoo].format = '%.6f'
print(tCoo['RV=rho','parallax','RA','DEC','mu_RA','mu_dec', \
'l','b','pm_l_cosb','pm_b','distance',\
'X','Y','Z','U','V','W'])
print("####")
print("INFO - Quantities used:")
print("Input assumed ICRS, so J2000.0 equinox")
print(
"Galactic coords use the IAU 1958 definition (see https://docs.astropy.org/en/stable/api/astropy.coordinates.Galactic.html)"
)
print("Galactic center distance:", galcen.galcen_distance, \
"Solar motion:", galcen.galcen_v_sun, \
", z_sun:", galcen.z_sun)
print("(Column units for input data guessed.)")
def test_radec_to_munu(self):
radec = ICRS(ra=0.0 * u.deg, dec=0.0 * u.deg)
munu = radec.transform_to(SDSSMuNu(stripe=10))
assert munu.mu.value == 0.0
assert munu.nu.value == 0.0
assert munu.incl.value == 0.0
def make_plot(args):
"""
Take the steps to make the plot.
Parameters
----------
args: dict
Command line arguments
Returns
-------
Nothing
"""
infile = './data/' + args['inputFile']
basename = 'PMmap-' + args['inputFile'].split('.')[0]
default_proj = ccrs.PlateCarree()
sky_proj = ccrs.Mollweide()
backgr = plt.imread(
'../star-trail-animation/sky-images/GaiaSky-colour-2k.png')
nside = hp.order2nside(args['hplevel'])
hpcol = 'healpix_{0}'.format(args['hplevel'])
edr3data = Table.read(infile)
alpha, delta = hp.pix2ang(nside, edr3data[hpcol], lonlat=True, nest=True)
pmra = edr3data['avg_pmra']
pmdec = edr3data['avg_pmdec']
icrs = ICRS(ra=alpha * u.degree,
dec=delta * u.degree,
pm_ra_cosdec=pmra * u.mas / u.yr,
pm_dec=pmdec * u.mas / u.yr)
galactic = icrs.transform_to(Galactic)
pmtot = np.sqrt(galactic.pm_l_cosb.value**2 + galactic.pm_b.value**2)
fig = plt.figure(figsize=(16, 9),
dpi=120,
frameon=False,
tight_layout={'pad': 0.01})
gs = GridSpec(1, 1, figure=fig)
ax = fig.add_subplot(gs[0, 0], projection=sky_proj)
ax.imshow(np.fliplr(backgr),
transform=default_proj,
zorder=-1,
origin='upper')
pmcmap = cm.viridis
veccolor = plt.cm.get_cmap('tab10').colors[9]
linecolor = plt.cm.get_cmap('tab10').colors[9]
if args['quiver']:
vscale = np.median(pmtot) / 10
ax.quiver(galactic.l.value,
galactic.b.value,
galactic.pm_l_cosb.value,
galactic.pm_b.value,
transform=default_proj,
angles='xy',
scale=vscale,
scale_units='dots',
color=veccolor,
headwidth=1,
headlength=3,
headaxislength=2.5)
else:
if args['colourstreams']:
ax.streamplot(galactic.l.value,
galactic.b.value,
galactic.pm_l_cosb.value,
galactic.pm_b.value,
transform=default_proj,
linewidth=2.0,
density=2,
color=pmtot,
cmap=pmcmap,
maxlength=0.5,
arrowsize=1,
arrowstyle=ArrowStyle.Fancy(head_length=1.0,
head_width=.4,
tail_width=.4))
elif args['lwcode'] > 0:
ax.streamplot(galactic.l.value,
galactic.b.value,
galactic.pm_l_cosb.value,
galactic.pm_b.value,
transform=default_proj,
linewidth=args['lwcode'] * pmtot / np.median(pmtot),
density=2,
color=linecolor,
maxlength=0.5,
arrowsize=1,
arrowstyle=ArrowStyle.Fancy(head_length=1.0,
head_width=.4,
tail_width=.4))
else:
ax.streamplot(galactic.l.value,
galactic.b.value,
galactic.pm_l_cosb.value,
galactic.pm_b.value,
transform=default_proj,
linewidth=1.5,
density=2,
color=linecolor,
maxlength=0.5,
arrowsize=1,
arrowstyle=ArrowStyle.Fancy(head_length=1.0,
head_width=.4,
tail_width=.4))
ax.invert_xaxis()
if args['pdfOutput']:
plt.savefig(basename + '.pdf')
elif args['pngOutput']:
plt.savefig(basename + '.png')
else:
plt.show()
def test_radec_to_munu(self):
radec = ICRS(ra=0.0*u.deg, dec=0.0*u.deg)
munu = radec.transform_to(SDSSMuNu(stripe=10))
assert munu.mu.value == 0.0
assert munu.nu.value == 0.0
assert munu.incl.value == 0.0
vb_errp = np.percentile(vb_samples, 84, axis=1) - vb
vb_errm = vb - np.percentile(vb_samples, 16, axis=1)
gaia_mc["vb"] = vb
gaia_mc["vb_err"] = vb_err
# print("Calculating vl")
# vl_samples = calc_vl(gaia_mc)
# vl, vl_err = np.median(vl_samples, axis=1), np.std(vl_samples, axis=1)
# vl_errp = np.percentile(vl_samples, 84, axis=1) - vl
# vl_errm = vl - np.percentile(vl_samples, 16, axis=1)
# gaia_mc["vl"] = vl
# gaia_mc["vl_err"] = vl_err
# Calculate b
icrs = ICRS(ra=gaia_mc.ra.values * u.degree, dec=gaia_mc.dec.values * u.degree)
lb = icrs.transform_to(Galactic)
b = lb.b * u.degree
l = lb.l * u.degree
gaia_mc["b"] = b.value
gaia_mc["l"] = l.value
print("Calculating VZ")
mrv = gaia_mc.radial_velocity.values != 0.00
vz, vz_err = calc_vz(gaia_mc)
vz[~mrv] = np.ones(len(vz[~mrv])) * np.nan
vz_err[~mrv] = np.ones(len(vz_err[~mrv])) * np.nan
gaia_mc["vz"] = vz
gaia_mc["vz_err"] = vz_err
# Calculate v_ra and v_dec
d = gaia_mc.r_est.values * u.pc
inc=32.521 * u.deg,
epoch=date_launch)
#Moon Orbit aqcuisition and conversion to GCRS
EPOCH = date_arrival
moon = Orbit.from_body_ephem(Moon, EPOCH)
moon_icrs = ICRS(x=moon.r[0],
y=moon.r[1],
z=moon.r[2],
v_x=moon.v[0],
v_y=moon.v[1],
v_z=moon.v[2],
representation=CartesianRepresentation,
differential_cls=CartesianDifferential)
moon_gcrs = moon_icrs.transform_to(GCRS(obstime=EPOCH))
moon_gcrs.representation = CartesianRepresentation
moon_gcrs
moon = Orbit.from_vectors(
Earth, [moon_gcrs.x, moon_gcrs.y, moon_gcrs.z] * u.km,
[moon_gcrs.v_x, moon_gcrs.v_y, moon_gcrs.v_z] * (u.km / u.s),
epoch=EPOCH)
ss0 = apollo
ssf = moon
#Solve for Lambert's Problem (Determining Translunar Trajectory)
(v0, v), = iod.lambert(Earth.k, ss0.r, ssf.r, tof)
ss0_trans = Orbit.from_vectors(Earth, ss0.r, v0, date_launch)
