def airmassSpherical(zangle, obsAltitude, rearth=6371.0, yatm=10.0):
"""
Calculate the airmass for a given zenith angle and observer altitude.
This routine uses a geometric formula for a homogeneous, spherical
atmosphere with an elevated observer.
.. note:: In this model, the airmass is *not* necessarily one
toward the zenith.
Parameters
----------
zangle : float
Zenith angle of an object in deg.
obsAltitude : float
Elevation of the observer in meter.
rearth : float, optional
Earth's radius in km.
yatm : float, optional
Height of the atmosphere in km.
Returns
-------
Airmass : float
The airmass.
"""
# Convert observer's altitude to km to have
# consistent units
obsAltitude = obsAltitude/1000.0
r = (rearth/yatm)
y = (obsAltitude/yatm)
# Find maximal zenith angle
zmax = 180.0 - PC.radtodeg(np.arcsin(rearth/(rearth + obsAltitude)))
if zangle > zmax:
raise(PE.PyAValError("Zenith angle is too large. The maximum allowed angle is " + str(zmax) + " deg.", \
solution="Use an angle within the limit. Check observer's altitude."))
# Convert into deg
zangle = PC.degtorad(zangle)
return np.sqrt( ( r + y )**2 * np.cos(zangle)**2 + 2.*r*(1.-y) - y**2 + 1.0 ) - \
(r+y)*np.cos(zangle)
def airmassSpherical(zangle, obsAltitude, rearth=6371.0, yatm=10.0):
"""
Calculate the airmass for a given zenith angle and observer altitude.
This routine uses a geometric formula for a homogeneous, spherical
atmosphere with an elevated observer.
.. note:: In this model, the airmass is *not* necessarily one
toward the zenith.
Parameters
----------
zangle : float
Zenith angle of an object in deg.
obsAltitude : float
Elevation of the observer in meter.
rearth : float, optional
Earth's radius in km.
yatm : float, optional
Height of the atmosphere in km.
Returns
-------
Airmass : float
The airmass.
"""
# Convert observer's altitude to km to have
# consistent units
obsAltitude = obsAltitude / 1000.0
r = (rearth / yatm)
y = (obsAltitude / yatm)
# Find maximal zenith angle
zmax = 180.0 - PC.radtodeg(np.arcsin(rearth / (rearth + obsAltitude)))
if zangle > zmax:
raise(PE.PyAValError("Zenith angle is too large. The maximum allowed angle is " + str(zmax) + " deg.", \
solution="Use an angle within the limit. Check observer's altitude."))
# Convert into deg
zangle = PC.degtorad(zangle)
return np.sqrt( ( r + y )**2 * np.cos(zangle)**2 + 2.*r*(1.-y) - y**2 + 1.0 ) - \
(r+y)*np.cos(zangle)
def positionAngle(ra1, dec1, ra2, dec2, positive=True):
"""
Compute the position angle.
The position angle is measured from the first position
from North through East. If the `positive` flag is set
True (default) the result will be given as an angle from
0 to 360 degrees. If the flag is set False, the scale is
-180 to 180 degrees with negative number increasing from
North through West; note that this is the behavior of
the posAng IDL routine.
Parameters
----------
ra1 : float
Right ascension of first object [deg].
dec1 : float
Declination of first object [deg].
ra2 : float
Right ascension of second object [deg].
dec2 : float
Declination of second object [deg].
positive : boolean, optional
If True (default), the output will be
given as an angle between 0 and 360
degrees. Otherwise, the angle ranges
from -180 to +180 degrees.
Returns
-------
Position angle : float
The position angle in degrees.
Notes
-----
.. note:: This function was ported from the IDL Astronomy User's Library.
:IDL - Documentation:
NAME:
POSANG
PURPOSE:
Computes rigorous position angle of source 2 relative to source 1
EXPLANATION:
Computes the rigorous position angle of source 2 (with given RA, Dec)
using source 1 (with given RA, Dec) as the center.
CALLING SEQUENCE:
POSANG, U, RA1, DC1, RA2, DC2, ANGLE
INPUTS:
U -- Describes units of inputs and output:
0: everything radians
1: RAx in decimal hours, DCx in decimal
degrees, ANGLE in degrees
RA1 -- Right ascension of point 1
DC1 -- Declination of point 1
RA2 -- Right ascension of point 2
DC2 -- Declination of point 2
OUTPUTS:
ANGLE-- Angle of the great circle containing [ra2, dc2] from
the meridian containing [ra1, dc1], in the sense north
through east rotating about [ra1, dc1]. See U above
for units.
PROCEDURE:
The "four-parts formula" from spherical trig (p. 12 of Smart's
Spherical Astronomy or p. 12 of Green' Spherical Astronomy).
EXAMPLE:
For the star 56 Per, the Hipparcos catalog gives a position of
RA = 66.15593384, Dec = 33.94988843 for component A, and
RA = 66.15646079, Dec = 33.96100069 for component B. What is the
position angle of B relative to A?
IDL> RA1 = 66.15593384/15.d & DC1 = 33.95988843
IDL> RA2 = 66.15646079/15.d & DC2 = 33.96100069
IDL> posang,1,ra1,dc1,ra2,dc2, ang
will give the answer of ang = 21.4 degrees
NOTES:
(1) If RA1,DC1 are scalars, and RA2,DC2 are vectors, then ANGLE is a
vector giving the position angle between each element of RA2,DC2 and
RA1,DC1. Similarly, if RA1,DC1 are vectors, and RA2, DC2 are scalars,
then DIS is a vector giving the position angle of each element of RA1,
DC1 and RA2, DC2. If both RA1,DC1 and RA2,DC2 are vectors then ANGLE
is a vector giving the position angle between each element of RA1,DC1
and the corresponding element of RA2,DC2. If then vectors are not the
same length, then excess elements of the longer one will be ignored.
(2) Note that POSANG is not commutative -- the position angle between
A and B is theta, then the position angle between B and A is 180+theta
PROCEDURE CALLS:
ISARRAY()
HISTORY:
Modified from GCIRC, R. S. Hill, RSTX, 1 Apr. 1998
Use V6.0 notation W.L. Mar 2011
"""
# Convert into rad
rarad1 = pyaC.degtorad(ra1)
rarad2 = pyaC.degtorad(ra2)
dcrad1 = pyaC.degtorad(dec1)
dcrad2 = pyaC.degtorad(dec2)
radif = rarad2 - rarad1
angle = arctan2(sin(radif),
cos(dcrad1) * tan(dcrad2) - sin(dcrad1) * cos(radif))
result = pyaC.radtodeg(angle)
if positive and (result < 0.0):
result += 360.0
return result
def positionAngle(ra1, dec1, ra2, dec2, positive=True):
"""
Compute the position angle.
The position angle is measured from the first position
from North through East. If the `positive` flag is set
True (default) the result will be given as an angle from
0 to 360 degrees. If the flag is set False, the scale is
-180 to 180 degrees with negative number increasing from
North through West; note that this is the behavior of
the posAng IDL routine.
Parameters
----------
ra1 : float
Right ascension of first object [deg].
dec1 : float
Declination of first object [deg].
ra2 : float
Right ascension of second object [deg].
dec2 : float
Declination of second object [deg].
positive : boolean, optional
If True (default), the output will be
given as an angle between 0 and 360
degrees. Otherwise, the angle ranges
from -180 to +180 degrees.
Returns
-------
Position angle : float
The position angle in degrees.
Notes
-----
.. note:: This function was ported from the IDL Astronomy User's Library.
:IDL - Documentation:
NAME:
POSANG
PURPOSE:
Computes rigorous position angle of source 2 relative to source 1
EXPLANATION:
Computes the rigorous position angle of source 2 (with given RA, Dec)
using source 1 (with given RA, Dec) as the center.
CALLING SEQUENCE:
POSANG, U, RA1, DC1, RA2, DC2, ANGLE
INPUTS:
U -- Describes units of inputs and output:
0: everything radians
1: RAx in decimal hours, DCx in decimal
degrees, ANGLE in degrees
RA1 -- Right ascension of point 1
DC1 -- Declination of point 1
RA2 -- Right ascension of point 2
DC2 -- Declination of point 2
OUTPUTS:
ANGLE-- Angle of the great circle containing [ra2, dc2] from
the meridian containing [ra1, dc1], in the sense north
through east rotating about [ra1, dc1]. See U above
for units.
PROCEDURE:
The "four-parts formula" from spherical trig (p. 12 of Smart's
Spherical Astronomy or p. 12 of Green' Spherical Astronomy).
EXAMPLE:
For the star 56 Per, the Hipparcos catalog gives a position of
RA = 66.15593384, Dec = 33.94988843 for component A, and
RA = 66.15646079, Dec = 33.96100069 for component B. What is the
position angle of B relative to A?
IDL> RA1 = 66.15593384/15.d & DC1 = 33.95988843
IDL> RA2 = 66.15646079/15.d & DC2 = 33.96100069
IDL> posang,1,ra1,dc1,ra2,dc2, ang
will give the answer of ang = 21.4 degrees
NOTES:
(1) If RA1,DC1 are scalars, and RA2,DC2 are vectors, then ANGLE is a
vector giving the position angle between each element of RA2,DC2 and
RA1,DC1. Similarly, if RA1,DC1 are vectors, and RA2, DC2 are scalars,
then DIS is a vector giving the position angle of each element of RA1,
DC1 and RA2, DC2. If both RA1,DC1 and RA2,DC2 are vectors then ANGLE
is a vector giving the position angle between each element of RA1,DC1
and the corresponding element of RA2,DC2. If then vectors are not the
same length, then excess elements of the longer one will be ignored.
(2) Note that POSANG is not commutative -- the position angle between
A and B is theta, then the position angle between B and A is 180+theta
PROCEDURE CALLS:
ISARRAY()
HISTORY:
Modified from GCIRC, R. S. Hill, RSTX, 1 Apr. 1998
Use V6.0 notation W.L. Mar 2011
"""
# Convert into rad
rarad1 = pyaC.degtorad(ra1)
rarad2 = pyaC.degtorad(ra2)
dcrad1 = pyaC.degtorad(dec1)
dcrad2 = pyaC.degtorad(dec2)
radif = rarad2 - rarad1
angle = arctan2(sin(radif), cos(dcrad1)*tan(dcrad2)-sin(dcrad1)*cos(radif))
result = pyaC.radtodeg(angle)
if positive and (result < 0.0):
result+= 360.0
return result
