def scFromCCPVOff(p, v, offP):
"""
Converts cartesian position, velocity and offset to spherical coordinates
(see also SCFromCC and SCFromCCPV).
Inputs:
- p(3) position (au)
- v(3) velocity (au per year)
- offP(3) offset position (au)
Returns:
- pos(2) spherical position (degrees)
ranges: axis 1: [0, 360), axis 2: [-90,90]
- pm(2) proper motion (arcsec per century)
- parlax parallax (arcsec)
- radVel radial velocity (km/s)
- offDir offset direction (degrees):
dir. of increasing pos[0] = 0
dir. of increasing pos[1] = 90
- offMag magnitude of offset (degrees on the sky)
- atPole true if at a pole; see "Error Cond." for implications
Error Conditions:
- Raises ValueError if |p| is too small to safely compute.
- If p is very near a pole, atPole is set true,
pos[1], pm[0], pm[1] and offDir are set to zero;
pos[0], parlax, radVel and offMag are still computed correctly
(pos[0] is +/-90.0, as appropriate).
- If inputs are too large, overflows are possible--roughly if p^2 or v^2 overflows.
History
2002-08-22 ROwen Converted to Python from the TCC's sph_CCPVOff2SC 6-1.
"""
# convert p and v from cartesian to spherical
pos, pm, parlax, radVel, atPole = scFromCCPV(p, v)
# convert offP from cartesian to spherical
offPos, magOffP, offAtPole = scFromCC(offP)
# compute offset direction and magnitude
ang_A, side_bb, ang_C, offAtPole2 = angSideAng(
90.0 - pos[1], offPos[0] - pos[0], 90.0 - offPos[1],
)
offMag = side_bb
if atPole:
offDir = 0.0
else:
offDir = 90.0 - ang_C
return (pos, pm, parlax, radVel, offDir, offMag, atPole)
def scFromDC(p):
"""Convert direction cosines or any cartesian vector to spherical coordinates.
Similar to scFromCC but magnitude is not returned.
Inputs:
- p(3) direction cosines or any cartesian vector
Returns a tuple containing:
- pos(2) spherical position (deg) as equatorial, polar angle,
e.g. (RA, Dec), (-HA, Dec) or (Az, Alt);
ranges are: pos[0]: [0, 360), pos[1]: [-90,90]
- atPole true if very near the pole, in which case pos[1] = 0,
and pos[0] = +/- 90 as appropriate.
Error Conditions:
- If |p| is too small, raises ValueError.
- If |p| is too large, overflows are possible--roughly if p^2 overflows.
Of course neither of these can occur if p is a direction cosine (unit vector).
History:
2002-07-23 R Owen.
"""
pos, mag, atPole = scFromCC(p)
return (pos, atPole)
def scFromCCPV(p, v):
"""
Converts cartesian position and velocity to spherical coordinates
(if you just want to convert position, use sph_CC2SC).
Inputs:
p(3) cartesian position (au)
v(3) cartesian velocity (au per year)
Returns a tuple containing:
pos(2) spherical position (degrees)
ranges: pos[0]: [0, 360), pos[1]: [-90,90]
pm(2) proper motion (arcsec per century)
dpos/dt, not velocity on the sky (i.e. large near the poles)
parallax parallax (arcsec)
radVel radial velocity (km/s, positive receding)
atPole true if at a pole; see "Error Cond." for implications
Error Conditions:
Raises valueError if |p| is too small
If p is very near a pole, atPole is set true and pos[1], pm[0] and pm[1]
are set to zero; pos[0], parallax and radVel are computed correctly
(pos[0] is +/-90.0, as appropriate).
If inputs are too large, overflows are possible--roughly if
p^2 or v^2 overflows.
History
2002-07-08 ROwen Converted from TCC's sph_SCPV2CC 1-1.
"""
x, y, z = p
vX, vY, vZ = v
pos, magP, atPole = scFromCC(p)
# warning: test atPole after computing radial velocity and parallax
# since they can be correctly computed even at the pole
# compute parallax; note that arcsec = 1 / parsec;
# the division is safe because magP must have some reasonable
# minimum value, else scFromCC would have raised an exception
parallax = RO.PhysConst.AUPerParsec / magP
# compute radial velocity in (au/year) and convert to (km/s)
radVel = float ((x * vX) + (y * vY) + (z * vZ)) / magP
radVel *= _KMPerSec_Per_AUPerYear
# now that parallax and radial velocity have been computed
# handle the "at pole" case
if atPole:
# pos, parallax and radVel are already set
pm = [0.0, 0.0]
else:
# useful quantities
magPxySq = float((x * x) + (y * y))
magPxy = math.sqrt (magPxySq)
magPSq = magPxySq + z * z
# compute proper motion in rad per year,
# then convert to arcsec per century;
# the divisions are save because:
# - magPxySq must have some reasonable minimum value,
# else sph_CC2SC would have set atPole true,
# and that case has already been handled above
# - magPSq must have some reasonable minimum value,
# else sph_CC2SC would have set isOK false
pm = [
((x * vY) - (y * vX)) / magPxySq,
((vZ * magPxy) - ((z / magPxy) * ((x * vX) + (y * vY)))) / magPSq,
]
pm[0] = pm[0] * _ASPerCy_Per_RadPerYear
pm[1] = pm[1] * _ASPerCy_Per_RadPerYear
return (pos, pm, parallax, radVel, atPole)
