def fk4_e_terms(equinox):
"""
Return the e-terms of aberation 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)
k = np.radians(k)
# Eccentricity of the Earth's orbit
e = earth.eccentricity(equinox.jd)
# Mean longitude of perigee of the solar orbit
g = earth.mean_lon_of_perigee(equinox.jd)
g = np.radians(g)
# Obliquity of the ecliptic
o = earth.obliquity(equinox.jd, algorithm=1980)
o = np.radians(o)
return e * k * np.sin(g), \
-e * k * np.cos(g) * np.cos(o), \
-e * k * np.cos(g) * np.sin(o)
def fk4_e_terms(equinox):
"""
Return the e-terms of aberation 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)
k = np.radians(k)
# Eccentricity of the Earth's orbit
e = earth.eccentricity(equinox.jd)
# Mean longitude of perigee of the solar orbit
g = earth.mean_lon_of_perigee(equinox.jd)
g = np.radians(g)
# Obliquity of the ecliptic
o = earth.obliquity(equinox.jd, algorithm=1980)
o = np.radians(o)
return e * k * np.sin(g), \
-e * k * np.cos(g) * np.cos(o), \
-e * k * np.cos(g) * np.sin(o)
def ecliptic2equitorial(ecliptic_skycoord,
err_lambda,
err_beta,
epoch,
equitorial_coord_frame='fk5'):
eps = earth_orientation.obliquity(
epoch.jd, algorithm=2006) * u.deg # Use IAU 2006 model.
equitorial_skycoord = ecliptic_skycoord.transform_to(
equitorial_coord_frame)
ecl_lambda = ecliptic_skycoord.lon.rad
beta = ecliptic_skycoord.lat.rad
ra = equitorial_skycoord.ra.rad
dec = equitorial_skycoord.dec.rad
# Error on dec
term1 = ((np.cos(beta) * np.cos(eps.to('radian')) -
np.sin(beta) * np.sin(eps.to('radian')) * np.sin(ecl_lambda)) *
err_beta)**2
term2 = (np.cos(beta) * np.sin(eps.to('radian')) * np.cos(ecl_lambda) *
err_lambda)**2
err_dec = np.sqrt(term1 + term2) / np.abs(np.cos(dec))
# Error on ra
term1 = (np.sin(ecl_lambda) * np.cos(beta) * err_lambda / np.cos(dec))**2
term2 = (np.cos(ecl_lambda) * np.sin(beta) * err_beta / np.cos(dec))**2
term3 = (np.cos(ecl_lambda) * np.cos(beta) * np.tan(dec) * err_dec /
np.cos(dec))**2
err_ra = np.sqrt(term1 + term2 + term3) / np.abs(np.sin(ra))
return equitorial_skycoord, err_ra, err_dec
def ra_sun(start):
# days since 1 Jan 2010 Epoch
t = Time(start, scale='utc')
d = (start - datetime(2010, 1, 1)).days
eg = 279.557208 # ecliptic longitude at epoch 2010
wg = 283.112438 # ecliptic longitude of perigee at epoch 2010
e = 0.016705 # eccentricity at 2010 epoch
N = (360. / 365.242191) * d % 360
m_sun = N + eg + wg
if m_sun < 0:
m_sun += 360.
Ec = (360. / pi) * e * sin(radians(m_sun))
l_sun = N + Ec + eg
obliquity = earth.obliquity(t.jd, algorithm=1980)
y = sin(radians(l_sun)) * cos(radians(obliquity))
x = cos(radians(l_sun))
ra = degrees(arctan2(y, x)) / 15
return ra
def ra_sun(start):
# days since 1 Jan 2010 Epoch
t = Time(start, scale='utc')
d = (start - datetime(2010, 1, 1)).days
eg = 279.557208 # ecliptic longitude at epoch 2010
wg = 283.112438 # ecliptic longitude of perigee at epoch 2010
e = 0.016705 # eccentricity at 2010 epoch
N = (360. / 365.242191) * d % 360
m_sun = N + eg + wg
if m_sun < 0:
m_sun += 360.
Ec = (360. / pi) * e * sin(radians(m_sun))
l_sun = N + Ec + eg
obliquity = earth.obliquity(t.jd, algorithm=1980)
y = sin(radians(l_sun)) * cos(radians(obliquity))
x = cos(radians(l_sun))
ra = degrees(arctan2(y, x)) / 15
return ra
def equitorial2ecliptic(equitorial_skycoord, err_ra, err_dec, epoch):
eps = earth_orientation.obliquity(
epoch.jd, algorithm=2006) * u.deg # Use IAU 2006 model.
ecliptic_skycoord = equitorial_skycoord.transform_to(
'geocentrictrueecliptic')
ra = equitorial_skycoord.ra.rad
dec = equitorial_skycoord.dec.rad
ecl_lambda = ecliptic_skycoord.lon.rad
beta = ecliptic_skycoord.lat.rad
# Error on beta
term1 = ((np.cos(dec) * np.cos(eps.to('radian')) +
np.sin(dec) * np.sin(eps.to('radian')) * np.sin(ra)) *
err_dec)**2
term2 = (np.cos(dec) * np.sin(eps.to('radian')) * np.cos(ra) * err_ra)**2
err_beta = np.sqrt(term1 + term2) / np.abs(np.cos(beta))
# Error on lambda
term1 = (np.sin(ra) * np.cos(dec) * err_ra / np.cos(beta))**2
term2 = (np.cos(ra) * np.sin(dec) * err_dec / np.cos(beta))**2
term3 = (np.cos(ra) * np.cos(dec) * np.tan(beta) * err_beta /
np.cos(beta))**2
err_lambda = np.sqrt(term1 + term2 + term3) / np.abs(np.sin(ecl_lambda))
return ecliptic_skycoord, err_lambda, err_beta
from . import SphericalBody, OrbitingSphericalBody
from astropy import time
from astropy import units as u
from astropy import constants as cnst
from astropy.coordinates import earth_orientation
sun = SphericalBody(cnst.R_sun, 1, cnst.M_sun)
# sneaky trick to use L_sun to compute radiance
sun.radiance = cnst.L_sun / sun.luminosity / u.sr
_J2017 = time.Time('J2017')
ec = earth_orientation.eccentricity(_J2017.jd)
obliq = earth_orientation.obliquity(_J2017.jd) * u.deg
sidday = 23.9344699 * u.hr
earth = OrbitingSphericalBody(cnst.R_earth, 0, cnst.M_earth, obliq, sidday,
1 * u.AU, ec, 0 * u.deg, sun)