def angsep(ra1, dec1, ra2, dec2, input="sexigesimal", output="deg"):
"""
return angular separation in units of 'output'.
ra1, dec1, ra2, dec2 are all given in unites of 'input'.
If 'input' is not a string, it is assumed to be a 2-tuple, defining
the input format for ra1/dec1, and ra2/dec2 respectively.
Possible values for input and output are "sexigesimal", "deg" and "rad".
"""
if type(input)==types.StringType:
# input type is same for both sets of coords
input1 = input
input2 = input
else:
# Assume input argument is a tuple contaning 2 strings
input1 = input[0]
input2 = input[1]
if input1=="sexigesimal":
ra1_rad = protractor.convert(ra1, "hmsstr", "rad")
dec1_rad = protractor.convert(dec1, "dmsstr", "rad")
else:
ra1_rad = protractor.convert(ra1, input1, "rad")
dec1_rad = protractor.convert(dec1, input1, "rad")
if input2=="sexigesimal":
ra2_rad = protractor.convert(ra2, "hmsstr", "rad")
dec2_rad = protractor.convert(dec2, "dmsstr", "rad")
else:
ra2_rad = protractor.convert(ra2, input2, "rad")
dec2_rad = protractor.convert(dec2, input2, "rad")
angsep_rad = np.arccos(np.sin(dec1_rad)*np.sin(dec2_rad)+\
np.cos(dec1_rad)*np.cos(dec2_rad)*np.cos(ra1_rad-ra2_rad))
angsep = protractor.convert(angsep_rad, "rad", output)
return angsep
def altaz_to_hadec(alt, az, obslat, input="deg", output="sexigesimal"):
"""Given altitude, azimuth angle (provided in units of 'input')
and observer latitude (in degrees) return hour angle and
declination (in units of 'output').
Possible values for input and output are "sexigesimal", "deg" and "rad".
"""
# Convert input args to radians
if input == "sexigesimal":
input = "dmsstr"
alt = protractor.convert(alt, input, "rad")
az = protractor.convert(az, input, "rad")
# Do the conversion
ha = np.arctan2(np.sin(az), np.cos(az)*np.sin(obslat) + \
np.tan(alt)*np.cos(obslat))
decl = np.arcsin(np.sin(obslat)*np.sin(alt) - \
np.cos(obslat)*np.cos(alt)*np.cos(az))
# Ensure radian values are between 0 and 2pi
ha = np.mod(ha, np.pi * 2)
decl = np.mod(decl, np.pi * 2)
# Convert output values to desired units
if output == "sexigesimal":
ha = protractor.convert(ha, "rad", "hmsstr")
decl = protractor.convert(decl, "rad", "dmsstr")
else:
ha = protractor.convert(ha, "rad", output)
decl = protractor.convert(decl, "rad", output)
return (ha, decl)
def hadec_to_altaz(ha, decl, obslat, input="sexigesimal", output="deg"):
"""Given hour angle, declination (provided in units of 'input')
and observer latitude (in degrees) return local horizontal coordinates
(altitude and azimuth, in units of 'output').
Possible values for input and output are "sexigesimal", "deg" and "rad".
"""
# Convert equatorial coords to radians
if input == "sexigesimal":
ha = protractor.convert(ha, "hmsstr", "rad")
decl = protractor.convert(decl, "dmsstr", "rad")
else:
ha = protractor.convert(ha, input, "rad")
decl = protractor.convert(decl, input, "rad")
# Do the conversion
az = np.arctan2(np.sin(ha), np.cos(ha)*np.sin(obslat) - \
np.tan(decl)*np.cos(obslat))
alt = np.arcsin(np.sin(obslat)*np.sin(decl) + \
np.cos(obslat)*np.cos(decl)*np.cos(ha))
# Ensure radian values are between 0 and 2pi
az = np.mod(az, np.pi * 2)
alt = np.mod(alt, np.pi * 2)
# Convert output values to desired units
if output == "sexigesimal":
output = "dmsstr"
az = protractor.convert(az, "rad", output)
alt = protractor.convert(alt, "rad", output)
return (alt, az)
def altaz_to_hadec(alt, az, obslat, input="deg", output="sexigesimal"):
"""Given altitude, azimuth angle (provided in units of 'input')
and observer latitude (in degrees) return hour angle and
declination (in units of 'output').
Possible values for input and output are "sexigesimal", "deg" and "rad".
"""
# Convert input args to radians
if input == "sexigesimal":
input = "dmsstr"
alt = protractor.convert(alt, input, "rad")
az = protractor.convert(az, input, "rad")
# Do the conversion
ha = np.arctan2(np.sin(az), np.cos(az)*np.sin(obslat) + \
np.tan(alt)*np.cos(obslat))
decl = np.arcsin(np.sin(obslat)*np.sin(alt) - \
np.cos(obslat)*np.cos(alt)*np.cos(az))
# Ensure radian values are between 0 and 2pi
ha = np.mod(ha, np.pi*2)
decl = np.mod(decl, np.pi*2)
# Convert output values to desired units
if output == "sexigesimal":
ha = protractor.convert(ha, "rad", "hmsstr")
decl = protractor.convert(decl, "rad", "dmsstr")
else:
ha = protractor.convert(ha, "rad", output)
decl = protractor.convert(decl, "rad", output)
return (ha, decl)
def hadec_to_altaz(ha, decl, obslat, input="sexigesimal", output="deg"):
"""Given hour angle, declination (provided in units of 'input')
and observer latitude (in degrees) return local horizontal coordinates
(altitude and azimuth, in units of 'output').
Possible values for input and output are "sexigesimal", "deg" and "rad".
"""
# Convert equatorial coords to radians
if input == "sexigesimal":
ha = protractor.convert(ha, "hmsstr", "rad")
decl = protractor.convert(decl, "dmsstr", "rad")
else:
ha = protractor.convert(ha, input, "rad")
decl = protractor.convert(decl, input, "rad")
# Do the conversion
az = np.arctan2(np.sin(ha), np.cos(ha)*np.sin(obslat) - \
np.tan(decl)*np.cos(obslat))
alt = np.arcsin(np.sin(obslat)*np.sin(decl) + \
np.cos(obslat)*np.cos(decl)*np.cos(ha))
# Ensure radian values are between 0 and 2pi
az = np.mod(az, np.pi*2)
alt = np.mod(alt, np.pi*2)
# Convert output values to desired units
if output == "sexigesimal":
output = "dmsstr"
az = protractor.convert(az, "rad", output)
alt = protractor.convert(alt, "rad", output)
return (alt, az)
def precess_B1950_to_J2000(ra,
decl,
input="sexigesimal",
output="sexigesimal"):
"""Given right ascension and declination (in units of 'input') in B1950
equinox, precess to J2000 equinox (returned in units of 'output').
Possible values for input and output are "sexigesimal", "deg" and "rad".
NOTE: Followed http://www.stargazing.net/kepler/b1950.html
"""
# Convert equatorial coords to radians
if input == "sexigesimal":
ra = protractor.convert(ra, "hmsstr", "rad")
decl = protractor.convert(decl, "dmsstr", "rad")
else:
ra = protractor.convert(ra, input, "rad")
decl = protractor.convert(decl, input, "rad")
# Convert to rectangular coords
x = np.cos(ra) * np.cos(decl)
y = np.sin(ra) * np.cos(decl)
z = np.sin(decl)
# Rotate vector
x2 = 0.9999257080 * x - 0.0111789372 * y - 0.0048590035 * z
y2 = 0.0111789372 * x + 0.9999375134 * y - 0.0000271626 * z
z2 = 0.0048590036 * x - 0.0000271579 * y + 0.9999881946 * z
# Convert to equatorial
ra2000 = np.arctan2(y2, x2)
decl2000 = np.arcsin(z2)
# Ensure radian values are between 0 and 2pi
ra2000 = np.mod(ra2000, np.pi * 2)
decl2000 = np.mod(decl2000, np.pi * 2)
# Convert to desired units
if output == "sexigesimal":
ra2000 = protractor.convert(ra2000, "rad", "hmsstr")
decl2000 = protractor.convert(decl2000, "rad", "dmsstr")
else:
ra2000 = protractor.convert(ra2000, "rad", output)
decl2000 = protractor.convert(decl2000, "rad", output)
return (ra2000, decl2000)
def precess_B1950_to_J2000(ra, decl, input="sexigesimal", output="sexigesimal"):
"""Given right ascension and declination (in units of 'input') in B1950
equinox, precess to J2000 equinox (returned in units of 'output').
Possible values for input and output are "sexigesimal", "deg" and "rad".
NOTE: Followed http://www.stargazing.net/kepler/b1950.html
"""
# Convert equatorial coords to radians
if input == "sexigesimal":
ra = protractor.convert(ra, "hmsstr", "rad")
decl = protractor.convert(decl, "dmsstr", "rad")
else:
ra = protractor.convert(ra, input, "rad")
decl = protractor.convert(decl, input, "rad")
# Convert to rectangular coords
x = np.cos(ra) * np.cos(decl)
y = np.sin(ra) * np.cos(decl)
z = np.sin(decl)
# Rotate vector
x2 = 0.9999257080*x - 0.0111789372*y - 0.0048590035*z
y2 = 0.0111789372*x + 0.9999375134*y - 0.0000271626*z
z2 = 0.0048590036*x - 0.0000271579*y + 0.9999881946*z
# Convert to equatorial
ra2000 = np.arctan2(y2,x2)
decl2000 = np.arcsin(z2)
# Ensure radian values are between 0 and 2pi
ra2000 = np.mod(ra2000, np.pi*2)
decl2000 = np.mod(decl2000, np.pi*2)
# Convert to desired units
if output == "sexigesimal":
ra2000 = protractor.convert(ra2000, "rad", "hmsstr")
decl2000 = protractor.convert(decl2000, "rad", "dmsstr")
else:
ra2000 = protractor.convert(ra2000, "rad", output)
decl2000 = protractor.convert(decl2000, "rad", output)
return (ra2000, decl2000)
def equatorial_to_galactic(ra, decl, input="sexigesimal", output="deg", \
J2000=True):
"""Given right ascension and declination (in units of 'input') convert
to galactic longitude and latitude (returned in units of 'output').
Possible values for input and output are "sexigesimal", "deg" and "rad".
If "J2000" is True then input equinox is J2000, otherwise input equinox is
B1950.
"""
# Convert equatorial coords to radians
if input == "sexigesimal":
ra = protractor.convert(ra, "hmsstr", "rad")
decl = protractor.convert(decl, "dmsstr", "rad")
else:
ra = protractor.convert(ra, input, "rad")
decl = protractor.convert(decl, input, "rad")
# Conversion formula expects equatorial coords in B1950 equinox
if J2000:
ra, decl = precess_J2000_to_B1950(ra, decl, input='rad', output='rad')
# Define galactic north pole
ra_north = 3.35539549 # radians
decl_north = 0.478220215 # radians
# Do the conversion
x = np.arctan2(np.sin(ra_north-ra), np.cos(ra_north-ra)*np.sin(decl_north) - \
np.tan(decl)*np.cos(decl_north))
l = 5.28834763 - x # 303 deg = 5.28834763 rad (origin of galactic coords)
b = np.arcsin(np.sin(decl)*np.sin(decl_north) + \
np.cos(decl)*np.cos(decl_north)*np.cos(ra_north-ra))
# Ensure radian values are between 0 and 2pi
l = np.mod(l, np.pi * 2)
b = np.mod(b, np.pi * 2)
if type(b) == np.float64:
if b > np.pi:
b -= np.pi * 2
else: #assume its an array
for i in range(len(b)):
if b[i] > np.pi:
b[i] -= np.pi * 2
# Convert output values to desired units
if output == "sexigesimal":
output = "dmsstr"
l = protractor.convert(l, "rad", output)
b = protractor.convert(b, "rad", output)
return (l, b)
def equatorial_to_galactic(ra, decl, input="sexigesimal", output="deg", \
J2000=True):
"""Given right ascension and declination (in units of 'input') convert
to galactic longitude and latitude (returned in units of 'output').
Possible values for input and output are "sexigesimal", "deg" and "rad".
If "J2000" is True then input equinox is J2000, otherwise input equinox is
B1950.
"""
# Convert equatorial coords to radians
if input == "sexigesimal":
ra = protractor.convert(ra, "hmsstr", "rad")
decl = protractor.convert(decl, "dmsstr", "rad")
else:
ra = protractor.convert(ra, input, "rad")
decl = protractor.convert(decl, input, "rad")
# Conversion formula expects equatorial coords in B1950 equinox
if J2000:
ra, decl = precess_J2000_to_B1950(ra, decl, input='rad', output='rad')
# Define galactic north pole
ra_north = 3.35539549 # radians
decl_north = 0.478220215 # radians
# Do the conversion
x = np.arctan2(np.sin(ra_north-ra), np.cos(ra_north-ra)*np.sin(decl_north) - \
np.tan(decl)*np.cos(decl_north))
l = 5.28834763 - x # 303 deg = 5.28834763 rad (origin of galactic coords)
b = np.arcsin(np.sin(decl)*np.sin(decl_north) + \
np.cos(decl)*np.cos(decl_north)*np.cos(ra_north-ra))
# Ensure radian values are between 0 and 2pi
l = np.mod(l, np.pi*2)
b = np.mod(b, np.pi*2)
if type(b) == np.float64:
if b > np.pi:
b -= np.pi*2
else: #assume its an array
for i in range(len(b)):
if b[i] > np.pi:
b[i] -= np.pi*2
# Convert output values to desired units
if output == "sexigesimal":
output = "dmsstr"
l = protractor.convert(l, "rad", output)
b = protractor.convert(b, "rad", output)
return (l, b)
def ecliptic_to_equatorial(lon, lat, input="deg", output="sexigesimal", \
J2000=True):
"""Given ecliptic longitude and latitude (provided in units of 'input')
return equatorial coordinates (right ascension, declination)
in units of 'output'.
If J2000 is true, assume input coords are in J2000 equinox,
otherwise assume input coords are in B1950 equinox.
Possible values for input and output are "sexigesimal", "deg" and "rad".
"""
if J2000:
obliquity = 0.409092804 # radians
else:
obliquity = 0.409206212 # radians
# Convert ecliptic coords to radians
if input == "sexigesimal":
input = "dmsstr"
lon = protractor.convert(lon, input, "rad")
lat = protractor.convert(lat, input, "rad")
# Do the conversion
ra = np.arctan2(np.sin(lon)*np.cos(obliquity) - \
np.tan(lat)*np.sin(obliquity), \
np.cos(lon))
decl = np.arcsin(np.sin(lat)*np.cos(obliquity) + \
np.cos(lat)*np.sin(obliquity)*np.sin(lon))
# Ensure radian values are between 0 and 2pi
ra = np.mod(ra, np.pi * 2)
decl = np.mod(decl, np.pi * 2)
if output == "sexigesimal":
ra = protractor.convert(ra, "rad", "hmsstr")
decl = protractor.convert(decl, "rad", "dmsstr")
else:
ra = protractor.convert(ra, "rad", output)
decl = protractor.convert(decl, "rad", output)
return (ra, decl)
def ecliptic_to_equatorial(lon, lat, input="deg", output="sexigesimal", \
J2000=True):
"""Given ecliptic longitude and latitude (provided in units of 'input')
return equatorial coordinates (right ascension, declination)
in units of 'output'.
If J2000 is true, assume input coords are in J2000 equinox,
otherwise assume input coords are in B1950 equinox.
Possible values for input and output are "sexigesimal", "deg" and "rad".
"""
if J2000:
obliquity = 0.409092804 # radians
else:
obliquity = 0.409206212 # radians
# Convert ecliptic coords to radians
if input == "sexigesimal":
input = "dmsstr"
lon = protractor.convert(lon, input, "rad")
lat = protractor.convert(lat, input, "rad")
# Do the conversion
ra = np.arctan2(np.sin(lon)*np.cos(obliquity) - \
np.tan(lat)*np.sin(obliquity), \
np.cos(lon))
decl = np.arcsin(np.sin(lat)*np.cos(obliquity) + \
np.cos(lat)*np.sin(obliquity)*np.sin(lon))
# Ensure radian values are between 0 and 2pi
ra = np.mod(ra, np.pi*2)
decl = np.mod(decl, np.pi*2)
if output == "sexigesimal":
ra = protractor.convert(ra, "rad", "hmsstr")
decl = protractor.convert(decl, "rad", "dmsstr")
else:
ra = protractor.convert(ra, "rad", output)
decl = protractor.convert(decl, "rad", output)
return (ra, decl)
def precess(ra, decl, inequinox, outequinox, \
input="sexigesimal", output="sexigesimal"):
"""Given right ascension and declination (in unitls of 'input') in 'inequinox'
equinox, precess to 'outequinox' equinox (returned in units of 'output').
Possible values for input and output are "sexigesimal", "deg" and "rad".
(Follow Jean Meeus' Astronomical Formulae For Calculators, 4th Ed., Ch 14
Rigorous Method.)
"""
warnings.warn("Results not exactly correct...")
# Convert equatorial coords to radians
if input == "sexigesimal":
ra = protractor.convert(ra, "hmsstr", "rad")
decl = protractor.convert(decl, "dmsstr", "rad")
else:
ra = protractor.convert(ra, input, "rad")
decl = protractor.convert(decl, input, "rad")
inJD = calendar.date_to_JD(inequinox, 0, 0, gregorian=True)
outJD = calendar.date_to_JD(outequinox, 0, 0, gregorian=True)
print inJD, outJD
intau = (inJD - 2415020.313) / 36524.2199
outtau = (outJD - inJD) / 36524.2199
print intau, outtau
# The following 3 variables are in arcseconds
zeta = (2304.250 +
1.396 * intau) * outtau + 0.302 * outtau**2 + 0.018 * outtau**3
z = zeta + 0.791 * outtau**2 + 0.001 * outtau**3
theta = (2004.682 -
0.853 * intau) * outtau - 0.426 * outtau**2 - 0.042 * outtau**3
print zeta, z, theta
# Convert to radians
zeta = zeta / 3600 * protractor.DEGTORAD
z = z / 3600 * protractor.DEGTORAD
theta = theta / 3600 * protractor.DEGTORAD
A = np.cos(decl) * np.sin(ra + zeta)
B = np.cos(theta) * np.cos(decl) * np.cos(ra + zeta) - np.sin(
theta) * np.sin(decl)
C = np.sin(theta) * np.cos(decl) * np.cos(ra + zeta) + np.cos(
theta) * np.sin(decl)
print A, B, C
outra = np.arctan2(A, B) + z
outdecl = np.arcsin(C)
# Ensure radian values are between 0 and 2pi
outra = np.mod(outra, np.pi * 2)
outdecl = np.mod(outdecl, np.pi * 2)
# Convert to desired units
if output == "sexigesimal":
outra = protractor.convert(outra, "rad", "hmsstr")
outdecl = protractor.convert(outdecl, "rad", "dmsstr")
else:
outra = protractor.convert(outra, "rad", output)
outdecl = protractor.convert(outdecl, "rad", output)
return (outra, outdecl)
def precess(ra, decl, inequinox, outequinox, \
input="sexigesimal", output="sexigesimal"):
"""Given right ascension and declination (in unitls of 'input') in 'inequinox'
equinox, precess to 'outequinox' equinox (returned in units of 'output').
Possible values for input and output are "sexigesimal", "deg" and "rad".
(Follow Jean Meeus' Astronomical Formulae For Calculators, 4th Ed., Ch 14
Rigorous Method.)
"""
warnings.warn("Results not exactly correct...")
# Convert equatorial coords to radians
if input == "sexigesimal":
ra = protractor.convert(ra, "hmsstr", "rad")
decl = protractor.convert(decl, "dmsstr", "rad")
else:
ra = protractor.convert(ra, input, "rad")
decl = protractor.convert(decl, input, "rad")
inJD = calendar.date_to_JD(inequinox, 0, 0, gregorian=True)
outJD = calendar.date_to_JD(outequinox, 0, 0, gregorian=True)
print inJD, outJD
intau = (inJD - 2415020.313)/36524.2199
outtau = (outJD - inJD)/36524.2199
print intau, outtau
# The following 3 variables are in arcseconds
zeta = (2304.250 + 1.396*intau)*outtau + 0.302*outtau**2 + 0.018*outtau**3
z = zeta + 0.791*outtau**2 + 0.001*outtau**3
theta = (2004.682 - 0.853*intau)*outtau - 0.426*outtau**2 - 0.042*outtau**3
print zeta, z, theta
# Convert to radians
zeta = zeta/3600*protractor.DEGTORAD
z = z/3600*protractor.DEGTORAD
theta = theta/3600*protractor.DEGTORAD
A = np.cos(decl)*np.sin(ra+zeta)
B = np.cos(theta)*np.cos(decl)*np.cos(ra+zeta)-np.sin(theta)*np.sin(decl)
C = np.sin(theta)*np.cos(decl)*np.cos(ra+zeta)+np.cos(theta)*np.sin(decl)
print A, B, C
outra = np.arctan2(A, B)+z
outdecl = np.arcsin(C)
# Ensure radian values are between 0 and 2pi
outra = np.mod(outra, np.pi*2)
outdecl = np.mod(outdecl, np.pi*2)
# Convert to desired units
if output == "sexigesimal":
outra = protractor.convert(outra, "rad", "hmsstr")
outdecl = protractor.convert(outdecl, "rad", "dmsstr")
else:
outra = protractor.convert(outra, "rad", output)
outdecl = protractor.convert(outdecl, "rad", output)
return (outra, outdecl)
